A cost analysis framework for NEMO prefix delegation-based schemes

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					     A Cost Analysis Framework for NEMO
        Prefix Delegation based Schemes
      Abu Zafar M. Shahriar, Shohrab Hossain,
             Mohammed Atiquzzaman

                 TR-OU-TNRL-10-101
                       Jan 2010




Telecommunication & Network Research Lab

       School of Computer Science

         THE UNIVERSITY OF OKLAHOMA


       110 W. Boyd, Room 260, Norman, Oklahoma 73019-6151
          (405)-325-4042, atiq@ou.edu, www.cs.ou.edu/˜atiq
                                                                                                                                    1




       A Cost Analysis Framework for NEMO Prefix
               Delegation based Schemes
                      Abu Zafar M. Shahriar, Md. Shohrab Hossain and Mohammed Atiquzzaman
                                             School of Computer Science
                                     University of Oklahoma, OK 73019, USA
                                      Email: {shahriar, shohrab, atiq}@ou.edu



   Abstract— A number of prefix delegation-based schemes have         in the way prefix is delegated. These differences affect the
been proposed in the literature to solve the route optimization      performance of the schemes, and the overheads arising from
problem in NEMO, where a group of hosts move together as a           the performance gain.
mobile network.
   Approaches used by the schemes trade off delivery of packets         In NEMO, network parameters (such as, network size,
through partially optimized route with signaling and other           mobility rate, traffic rate, distances from mobility agents)
processing overheads. Cost of delivering packets through partially   influence signaling and routing overheads arising from prefix
optimized route, signaling and other processing needs to be          delegation-based schemes. These overheads include delivery
measured to find the gain from tradeoff. However, cost analysis       of packets through partially optimized route, updating home
performed so far on NEMO protocols consider only the cost of
signaling. In this paper, we have developed analytical framework     agents about the change of location, sending updates to
to measure the costs of the basic protocol for NEMO, and             hosts with ongoing communication, processing and lookup
four prefix delegation-based schemes. The framework will help         by mobility agents, and the delegation of prefix. Overheads
in visualizing the effects of future network expansion on the        consume the transmission and processing power at the network
cost of route optimization schemes of NEMO. Our results show         (i.e. routers in the network) between the end hosts and at the
that cost of packet delivery through partially optimized route
dominates over other costs. Therefore, performance improvement       mobility management entities such as home agents and mobile
of the route optimization schemes should focus/concentrate/give      routers. We use the term network mobility cost to refer to those
attention to on optimizing the route completely rather than          costs incurred for sending packets to the hosts inside a mobile
reducing signaling.                                                  network.
                                                                        With the rapid expansion and popularity of mobile and
                      I. I NTRODUCTION                               wireless networks, network mobility costs and consequent
                                                                     performance degradation of the schemes as well as the net-
   To efficiently manage the mobility of multiple IP-enabled
                                                                     work will increase. Hence, the network mobility costs of the
hosts moving together, such as hosts in a vehicle, Internet
                                                                     schemes, and the consequent impact on various important
Engineering Task Force proposed NEtwork MObility (NEMO)
                                                                     entities of the network needs to be analyzed quantitatively
[1]. Hosts, and mobile routers, managing the mobility of
                                                                     to prevent performance degradation due to the overloading
hosts, constitute the mobile network. Hosts can be fixed or
                                                                     of these mobility entities. Network mobility cost will give a
mobile with respect to the mobile network. The basic protocol
                                                                     measure of the cost incurred by the schemes to improve the
called NEMO Basic Support Protocol (NEMO BSP) enables
                                                                     performance in terms of route and handoff.
communication with mobile network through a bidirectional
                                                                        Cost analysis of NEMO protocols have been performed
tunnel between mobile routers and a router called home agent
                                                                     in [12], [13]. They present only signaing cost of NEMO by
in the home network [1]. Tunneling results in the problem of
                                                                     constructing analytical models that measure the transmission
inefficient route between end hosts. The problem worsen when
                                                                     and processing costs incurred by the signaing packets. How-
the mobile network is nested i.e. a mobile network attaches to
                                                                     ever, they do not consider the cost of packet delivery through
another one.
                                                                     unoptimized route, and parameters like nesting and the types
   A number of route optimization schemes have been pro-
                                                                     of nodes in NEMO that affect the network mobility cost.
posed to solve the inefficient routing problem. The schemes
                                                                     Moreover, the cost of prefix delegation is not included in the
trade off between the degree of route optimization and re-
                                                                     analysis. Therefore, the analysis presented in [12], [13] cannot
sulting overheads, such as signaling, processing, and memory
                                                                     be used for evaluating costs of the prefix delegation-based
consumption. The schemes have been classified and compared
                                                                     schemes. Our objective is to perform a cost evaluation of the
[2] based on the approaches used for route optimization; prefix
                                                                     prefix delegation-based schemes by developing a framework
delegation-based schemes have been found to perform better
                                                                     to include all costs associated with network mobility. We
than other schemes in terms of route efficacy and overheads
                                                                     believe this to be the first such work which will help in
[2]. Although prefix delegation-based schemes [3–11] follow a
                                                                     finding out the impact of network parameters on the network
common approach of delegating prefixes, they differ in degree
                                                                     and mobility management entities. Unlike any previous cost
of optimizing route depending on the type of nodes, and
                                                                     analysis of mobility protocols, we analyze the costs incurred at
  The work has been supported by NASA Grant NNX06AE44G.              the mobility entities that are hubs of mobile communications.
                                                                                                                                  2



   In this paper, we have selected four prefix delegation-based      nesting, they are not general enough in terms of nesting, and
schemes for evaluation: Simple Prefix Delegation (SPD) [3],          does not consider the types of nodes in a mobile network that
Mobile IPv6-based Route Optimization (MIRON) [7], Optimal           affect the network mobility cost of route optimization schemes.
Path Registration (OPR) [9] and Ad hoc protocol-based route         Moreover, none of the above mentioned analysis consider the
optimization (Ad hoc-based) [8]. The differences among the          cost associated with the packet delivery and the approach
schemes represents all possible ways the prefix delegation-          of route optimization. Route optimization schemes trade off
based schemes can differ. We have developed analytical cost         between the degree of unoptimized route and signaling or other
models to measure the network mobility costs on mobility            costs arising from the approach used for route optimization.
and network entities. Based on the cost models, we have             Therefore, associated costs should be an integrated part of
presented a comparative study of NEMO BSP and the four              network mobility cost.
prefix delegation schemes.                                              Performance evaluation of the prefix delegation-based
   The contributions of our work are : (i) developing analytical    schemes have been performed in terms of throughput, end-to-
framework to measure network mobility costs of the prefix            end delay, handoff latency, header overhead, and memory con-
delegation-based schemes, and (ii) comparative analysis of          sumption [3], [7–9], [17], [18]. To achieve the performance,
the schemes based on the network mobility costs. Analytical         the network mobility cost for the network and mobility entities
models developed in this paper will provide useful framework        may increase. Therefore, we present a comprehensive cost
to analyze other route optimization schemes. Our results            analysis of the prefix delegation-based schemes by developing
provide a new insight for trading off the degree of route           cost models that include nesting, and the types and number
optimization with required signaling by showing that the            of nodes in the mobile network. Unlike any previous cost
cost of packet delivery dominates over the cost of signaling.       analysis for NEMO, we present the costs for mobility entities
Results presented in this paper will complement the results         that are hubs of all communications. Our analysis can be used
of performance evaluation of the schemes in deciding the            to measure the cost of achieving the performance gain by the
approach to adopt for route optimization in NEMO.                   schemes, and provide a framework for analyzing costs of other
   The rest of the paper is organized as follows. A literature of   route optimization schemes.
cost analysis of NEMO is given in Sec. II. NEMO architecture,
NEMO BSP and prefix delegation-based route optimization                                       III. NEMO
schemes are summarized in Sec. III and IV. Analytical models
                                                                       In this section, we summarize NEMO architecture and BSP
for costs are presented in Sec. V. Sec. VI presents the results
                                                                    to help the reader in understanding the rest of the paper.
and comparison among the schemes. Finally, Sec. VII has the
concluding remarks.
                                                                    A. NEMO Architecture
                  II. L ITERATURE R EVIEW                              Fig. 1 shows the architecture of a mobile network [1].
                                                                    Mobile Routers (MRs) act as gateways for the nodes inside the
   A few cost analysis have been performed for the host             mobile network, each called a Mobile Network Node (MNN).
mobility protocols. Fu et al. [14] present a cost analysis of       Different types of MNNs are - a Local Fixed Node (LFN)
HMIPv6 and Seamless IP-diversity based Generalized Mobil-           that does not move with respect to the mobile network, a
ity Architecture (SIGMA). Xie et al. [15] perform cost analysis     Local Mobile Node (LMN) that usually resides in the mobile
of Mobile IP to minimize the signaling cost while introducing       network and can move to other networks, and a Visiting
a novel regional location management scheme. Makaya et              Mobile Node (VMN) that gets attached to the mobile network
al. [?] present an analytical model for the performance and         from another network. LMNs and VMNs are MIPv6 capable,
cost analysis of IPv6-based mobility protocols (i.e., MIPv6,        and we refer them as mobile nodes from this point onward. An
HMIPv6, FMIPv6 and F-HMIPv6). These cost analysis frame-            MR attaches to another MR to form a nested mobile network.
works on host mobility protocols are not adequate for NEMO          The MR, directly attached to the wired network through an
protocols since NEMO has more parameters and cost com-              Access Router (AR), is called the Top Level MR (TLMR)
ponents such as, number and types of nodes in the mobile            while MR1, MR2 etc. are nested under TLMR. Mobile nodes
network, nesting levels, cost of route optimization approaches      are also nested when they attaches under an MR.
(e.g. prefix delegation cost).                                          A mobile network is usually connected to a network called
   There have been a number of works on cost analysis of            the home network where an MR is registered with a router
NEMO protocols. Reaz et al. [12] present a cost analysis            called the Home Agent (HA). The HA is notified the location
of a transport layer-based network mobility protocol called         of the MR, and re-directs packets, sent by the Correspondent
SINEMO [16] and NEMO BSP [1]. Their objective was to                Node (CN) to MNNs. Although only one HA is shown in
compare the signaing cost of the protocols by developing            Fig. 1, MRs and mobile nodes in a mobile network may be
analytical models that considers transmission and processing        registered to different HAs.
costs incurred at the mobility and network entities. However,
the signaling cost presented in [12] does not consider nesting
in NEMO. Jalil et al. [13] also perform a signaling cost            B. NEMO BSP
analysis of NEMO using the similar models developed in                 An MR is assigned a prefix in its home network to advertise
[12]. Although the cost models presented in [13] considers          in its mobile network. MNNs obtain addresses, called Home
                                                                                                                                3



                                                                delegation. Thus, each MR incurs the overhead of performing
                                                                functionalities (e.g. authentication, accounting etc.) related to
                                                                prefix delegation. Since LFNs are not MIPv6 capable, they are
                                                                unable to optimize route. Therefore, packets for the LFNs go
                                                                through a tunnel between the LFNs’ MR and its HA.

                                                                B. MIPv6 based Route Optimization (MIRON)
                                                                   In MIRON [7], an MIPv6 capable MNN obtain a CoA from
                                                                the foreign network using PANA [20] and DHCPv6. When the
                                                                mobile network moves to a new network, the TLMR obtains
                                                                a CoA using DHCPv6, and starts PANA re-authentication
                                                                phase to inform the attached MNNs that a new CoA has to
                                                                be obtained. Attached MNNs send DHCPv6 request which
                                                                is conveyed up along the chain of intermediate MRs to the
                                                                foreign network. The DHCPv6 reply, containing the CoA,
                                                                follows the same path in the reverse direction to reach the
                                                                MNN. To optimize route for attached LFNs, an MR sends
Fig. 1.   Architecture of a mobile network.                     BUs to CNs on behalf of LFNs. To send BU to CNs, MR
Addresses (HoA), from the prefix. Packets, sent to the HoA,      needs to track the CN-LFN communications.
reach the HA that forwards the packets to the mobile network
in home.                                                        C. Optimal Path Registration (OPR)
   When a mobile network moves to a foreign network, the           Unlike the other prefix delegation-based schemes, OPR [9]
MR obtains a new address called Care-of-Address (CoA) from      does not use MIPv6 route optimization. Prefixes of the foreign
the prefix of the foreign network, and sends a Binding Update    network are delegated hierarchically to MRs only through
(BU) to the HA informing the CoA. The HA intercepts packets     multi-cast router advertisements. After handoff, MRs obtain
sent to MNN’s HoA, and tunnels them to MR. Since a mobile       CoAs from the prefix, and send BUs to their HAs. MNNs
network, nested under another mobile network, obtains the       other than MRs are transparent to the mobility of the network.
CoA from the prefix of the mobile network above, packets first       To optimize route for attached MNNs, MRs perform address
go to the HA of the nested mobile network and then to the       translation using the delegated prefix. For address translation,
HA of the mobile network above. Thus, packets are tunneled      MRs maintain a table where the information regarding the
through multiple HAs resulting in suboptimal route and header   translated addresses of MNNs are stored. When a packet
overhead. Moreover, the HA has the load of forwarding all       from an MNN is received, the MR searches the table for the
packets for mobile networks and nodes. Therefore, several       translated address. If the address is found, the source address
route optimization schemes, based on various approaches, have   is replaced with the translated address, and the source address
been proposed. An overview of the prefix delegation-based        is put in a header called OPR header [9] which also carries
schemes are presented in Sec. IV.                               information for the CN to register the translated address in
                                                                the BC. Thus, no BU is required to be sent to CNs for route
           IV. P REFIX DELEGATION - BASED SCHEMES               optimization. If the address is not found a translated address is
                                                                created using the delegated prefix. For incoming packets from
   In prefix delegation-based schemes, MNNs obtain CoAs          CNs, MRs do the reverse operations.
from the prefix of the foreign network, and uses MIPv6 [19]
like route optimization where MNNs send the CoA to CNs
                                                                D. Ad hoc protocol-based (Ad hoc-based)
through BUs. A BU is sent to the HA and the CN whenever a
new CoA is obtained, and periodically for refreshing. CNs          Su et al. [8] proposes a scheme where an Ad hoc protocol
use the CoAs to send packets directly (without using any        (e.g. AODV [21]) is used by the MRs to find the AR to use
tunnel) to the foreign network where the MNNs are in. Prefix     as the gateway to send packets to the wired network. In this
delegation-based schemes vary in prefix delegation or CoA        scheme, in addition to MR’s own router advertisement for its
obtention process, and route optimization for MNNs. Four        network, the router advertisement of the AR is broadcast by the
of the prefix delegation-based schemes are described in the      MRs to the attached MRs. After handoff, CoAs are obtained
following subsections.                                          by the MRs from the router advertisement, and the route to the
                                                                AR is discovered using AODV to send BUs. Other MNNs are
                                                                transparent to the movement of the mobile network, and obtain
A. Simple prefix delegation (SPD)                                addresses from the prefix of the mobile network. Therefore,
   In this scheme [3], the prefix of the foreign network is      mobile nodes do not need to send BUs due to the handoff of
hierarchically delegated inside the mobile network by the       the mobile network. But MNNs’ packets undergo one tunnel
MRs through router advertisement. A new neighbor discovery      between the MR above and its HA.
option, called Delegated Prefix Option is proposed in this          Prefix delegation-based schemes tradeoff overheads of route
scheme, and is used by the MR to advertise the prefix for        inefficiency with the overheads of signaling and processing at
                                                                                                                                4



various mobility and routing entities. In Sec. V, we present        •   We consider the handoff of the mobile network as a
costs of these overheads associated with NEMO.                          whole. Intra mobile network movements of MRs, and the
                                                                        movements of the mobile nodes inside the network are
                    V. C OSTS A NALYSIS                                 not considered. This assumption comply with the type
                                                                        of movement of a nested mobile network in a vehicular
   This section presents costs to support NEMO for the se-
                                                                        scenario that actually motivated NEMO [?].
lected prefix delegation-based schemes using analytical mod-
                                                                    •   Number of nodes in the mobile network and the number
els. The costs measure the amount of additional resources
                                                                        of nodes registered with an HA are assumed to be equal.
being used by the schemes to support NEMO. Our cost
                                                                        This is because we assume uniform distribution of mobile
analysis resembles the analysis performed in [14], [15], [22].
                                                                        nodes and networks resulting from their mobility.
Unlike [14], [15], [22], we introduce costs of prefix delegation
                                                                    •   We assume the worst possible scenario for the analysis
or CoA obtention, and effects of nesting on costs that are
                                                                        such as, all MNNs are communicating simultaneously,
unique for NEMO. We have considered a general NEMO
                                                                        the CN for each session are different. These assumptions
architecture (as shown in Fig. 1) that includes LFNs, LMNs,
                                                                        were also made in [14], [22].
VMNs, multiple visiting mobile networks, and multiple levels
of nesting. We also consider the cost to send refreshing BUs,
and deliver a packet only through the additional route when       C. Notations
unoptimized route is used. In addition to finding costs incurred      In this section, we introduce the notations that are used to
over the Internet including the mobile network, we find costs      present the models developed in Sec. V-D. In the notations
incurred at the entities like the TLMR and the HA because         for costs, we have used the superscript X and the subscript Y
these entities are the hubs for all communication of the mobile   to indicate the scheme and the type of cost, respectively. X
network and nodes. For tractability reasons, models were          will be replaced by N ,S, M , O and A for NEMO BSP, SPD,
developed based on assumptions. Types of costs analyzed,          MIRON, OPR and Ad hoc-based schemes, respectively. Y will
assumptions, notations, and the models are presented in the       be replaced by T , LU , SC, P D, and CO for total, location
following subsections.                                            update, session continuity, packet delivery and prefix/CoA
                                                                  obtention costs, respectively.
A. Types of costs                                                    ΛX = Cost of type Y incurred at network for scheme X,
                                                                       Y
  We measure the following costs of the schemes:                     ΨX = Cost of type Y incurred at TLMR for scheme X,
                                                                       Y
                                                                     ΦX = Cost of type Y incurred at HA for scheme X,
                                                                       Y
  • Location update cost: To maintain reachability, a node
                                                                     Nr = Number of MRs in mobile network
    sends a BU to the HA to inform its current location                 (i)
                                                                     Nr =Number of MRs at level i
    whenever it obtains a CoA. Periodic BUs are sent for
                                                                     Nm = Number of LMNs and VMNs in mobile network
    refreshing the binding entries. Resources (e.g. transmis-
                                                                     Nf = Number of LFNs in mobile network
    sion and processing power etc.), consumed by these BUs,             (i)
    comprise the location update cost.                               Nm =Number of LMNs and VMNs at level i
                                                                        (i)
  • Session continuity cost: To continue session through an
                                                                     Nf =Number of LFNs at level i
    optimized route, BUs have to be sent to CNs whenever the         Nc = Number of CNs communicating with each node,
    mobile network changes the subnet. Resources consumed            l=     Nesting Level (hops to TLMR),
    by these BUs, comprise the this cost. OPR employs a              hah = Average number of hops from AR to HA
    technique (see IV-C) other than sending BUs to continue          hac = Average number of hops from AR to CN,
    sessions, and the cost incurred by the technique are also        hhc = Average number of hops from HA to CN,
    included in this type of cost.                                   hhh = Average number of hops from HA to HA,
  • Packet delivery cost: To send a packet to the mobile net-
                                                                     τl = Per hop transmission cost for location update
    work, the HA has to perform a look up to retrieve the CoA        τs = Per hop transmission cost for session continuity,
    for tunneling towards the mobile network. In addition,           τdt = Per hop transmission cost for packets without tunnel
    HA and MR tunnel/de-tunnel packets. A measure of the                    header,
    processing and transmission power used for look up and           τip = Per hop transmission cost for tunnel header,
    tunneling is given by the packet delivery cost. Moreover,        τd = Average transmission cost of DHCPv6 messages,
    transmission power required by original packets are also         τp = Average transmission cost of PANA messages,
    included in this cost.                                           τa = Average transmission cost of route request-reply
  • Prefix/CoA obtention cost: After handoff, prefixes/CoAs
                                                                            messages of AODV protocol,
    are obtained from the foreign network. Resources con-            τr = Transmission cost for the router advertisement,
    sumed by the control messages required to obtain pre-            σ = proportionality constant of transmission cost over
    fixes/CoAs comprise this cost.                                           wired and wireless network,
                                                                     ψ = linear coefficient for lookup costs,
                                                                     πt = Tunnel processing costs at HA and MR,
B. Assumptions                                                       λs = average session arrival rate for a node,
  For tractability reasons, our models are based on the as-          S = number of sessions,
sumptions mentioned below.                                           F = File size,
                                                                                                                                                                     5



  P =        maximum transmission unit,
  Tr =       subnet residence time,
                                                                                                                                     Tr              l
  Tlf =      Lifetime of BE,                                                                                                    1+   Tlf
  Tra =      interval of sending periodic router advertisement.                      ΛN
                                                                                      LU   = (2(hah + σ)τl + πh )                             +2               (i)
                                                                                                                                                              Nr
                                                                                                                                   Tr               i=1
  φ=         Fraction of MRs acting as TLMR
                                                                                                                           i
      (i)                                                                               (i)
 Nm denote number of mobile nodes in level i. Similar                                + Nm         (i + 1)στl + σ                jτip + 2iπt + (hah + ihhh )τl (3)
             (i)    (i)
meaning for Nf and Nr .                                                                                                   j=1
                                                                                                     i−1                                                         Tr
                                                                                                                                  1                              Tlf
                                                                                     + hah iτip +        jhhh τip + iψ(Nr + Nm ) + πh
D. Cost models for the schemes                                                                       j=0
                                                                                                                                  2                              Tr

  Analytical models for the costs are presented in the follow-                   •   Session continuity cost: Each mobile node sends BUs to
ing subsections:                                                                     (and receive a BAs from) its CNs for session continuity.
  1) NEMO BSP:                                                                       Since only TLMR’s CoA changes during handoff, mobile
  •   Location update cost: After handoff, TLMR sends a BU                           nodes send only refreshing BUs. Thus, the cost incurred
      to the HA to perform the location update, and receives                         at the TLMR is
      a BA. Location update happens every Tr seconds. In
      addition to the BU sent after handoff, MRs and mobile
                                    Tr                                                                       l                                        Tr
      nodes send refreshing BU Tlf times during the period                                                                                            Tlf
                                                                                        ΨN
                                                                                         SC      = 2Nc             (i)
                                                                                                                  Nm     (σ (τs + iτip ) + πt )                  (4)
      of Tr seconds. Moreover, BUs sent from MRs and mobile                                                                                              Tr
                                                                                                         i=1
      nodes at level i undergoes i number of tunneling resulting
      in additional transmission cost due to tunnel header. Since                    Since BUs are tunneled through the HA, the cost incurred
      all BU/BAs goes through the TLMR, the cost at the                              at the HA includes look up, tunneling and transmission
      TLMR is given by                                                               costs, and is given as follows:

                              Tr               i=l
                         1+   Tlf                                                                                   l
            ΨN = 2στl
             LU                         + 2σ           (i)  (i)
                                                      Nr + Nm
                            Tr                 i=1
                                                                                            ΦN
                                                                                             SC     = 2Nc                 (i)
                                                                                                                         Nm τs + iτip + πt
                                                                         (1)                                       i=1
                                  Tr                                                                                                                             (5)
                                  Tlf                                                                                                         Tr
            × (τl + iτip + πt )                                                                                                               Tlf
                                  Tr                                                                                +ψ(Nr + Nm )
                                                                                                                                              Tr
      To find the cost incurred at the HA due to the location
      update, we need to consider the updating of the binding                        The session continuity cost for the network also includes
      cache in addition to the cost mentioned above. Updating                        the costs at each hop upto CNs, and at other MRs, and
      the binding cache is required for each MR and mobile                           is given by Eqn. (6).
      node registered to an HA. In addition, tunneled BUs
      incurs the look up cost which is proportional to ψ(Nr +
                                                                                                         l                                     i
      Nmh ). Therefore, cost incurred at HA due to location
      update becomes                                                                  ΛN = 2Nc
                                                                                       SC
                                                                                                                  (i)
                                                                                                                 Nm (i + 1)στs + σ                  jτip
                                                                                                      i=1                                     j=1
                                                                                       + 2iπt + (hah + (i − 1)hhh + hhc )τs + hah iτip                           (6)
                                          Tr               l
                                    1+    Tlf
                                                                                           i−1                                          Tr
      ΦN = φNr (2τl + πh )
       LU                                            +2          (i)  (i)
                                                                Nr + Nm                +         jhhh τip + iψ(Nr + Nm )
                                                                                                                                        Tlf
                                         Tr               i=1                                                                           Tr
                                                                               (2)         j=0
                                                                   Tr
                                          1                        Tlf
       × (τl + iτip + πt ) + ψ(Nr + Nm ) + πh                                    •   Packet delivery cost: Data packets incurs transmission
                                          2                        Tr
                                                                                     and tunneling cost which is similar to that of BU packets.
      The cost of location update for the network includes                           For each MNN-CN pair, costs are incurred at a rate
      transmission costs at all hops upto the HA including the                       proportional to the packet arrival rate given by λs F/P .
      costs incurred at MRs and the HA. Transmission costs                           For the packets sent to mobile nodes, we assume that
      for MRs and mobile nodes at level i are incurred at                            only the first packet is sent through the HA before a BU is
      hah + ihhh wired hops and at i + 1 wireless hops. The                          received at the CN, and additional costs are incurred every
      transmission cost upto the TLMR increases by τip at each                       λs /S seconds. TLMR needs to de-tunnel and forward
      level due to tunneling, and at each HA it decreases by the                     packets to the MNNs at the next level. Additional cost
      same amount. Also, each BU sent from a node at level                           incurred at the TLMR for the first packets sent to mobile
      i undergoes 2i number of tunneling and de-tunneling.                           nodes is the increased transmission cost for one additional
      Therefore, location update cost is given by Eqn. (15).                         tunnel. Therefore, the cost at the TLMR is
                                                                                                                                                          6



                                                                               2) SPD:
                               l                                               • Location update cost: In SPD, location update after
                      F                      (i)                                 handoff is performed by each MR and mobile node by
    ΨND = Nc λs
     P
                                             (i)
                                       Nf + Nm          σ(τdt
                      P    i=1                                                   sending a BU to the HA, and receiving a BA. This
                                                                        (7)      location update happens every Tr seconds. In addition
                                                       λs                                                                            Tr
          + (i − 1)τip ) + πt                  + σNm Nc (τip + τdt )             to the BU sent after handoff, refreshing BU is sent Tlf
                                                       S
                                                                                 times during the period of Tr seconds. Since all BU/BAs
                                                                                 goes through the TLMR, the cost at the TLMR is given
    In addition to the transmission cost, costs incurred at the
                                                                                 by
    HA are due to look up, tunneling and the transmission
    cost for one additional tunnel. Therefore, the packet                                                                 1+      Tr
                                                                                                                                  Tlf
    delivery cost at the HA is as follows:                                                    ΨS = 2στl (Nr + Nm )
                                                                                               LU                                                      (13)
                                                                                                                                Tr
                                                                                   To find the cost incurred at the HA due to the location
                           l                                                       update, we need to consider the updating of the binding
                    F                  (i)
    ΦND
     P     = N c λs                    (i)
                                (Nf + Nm ) (τdt + iτip )                           cache in addition to the cost mentioned above. Therefore,
                    P     i=1                                                      cost incurred at HA due to location update becomes
                                                                       (8)
     + (ψ (Nr + Nm ) + πt )
                                                                                                                                      Tr
                                                                                                                           1+         Tlf
         λs                                                                             ΦS    = (2τl + πh ) (Nr + Nm )                                 (14)
     + Nc Nm ((τdt + 2τip ) + (ψ(Nr + Nm ) + πt ))                                       LU
                                                                                                                                 Tr
         S
                                                                                   The cost of location update for the network includes
    The packet delivery cost for the network can be obtained
                                                                                   transmission costs at all hops upto the HA including the
    like we obtain costs at each hop for the session continuity
                                                                                   costs incurred at the TLMR and the HA. Transmission
    cost. Additionally, for the first packet sent through the HA
                                                                                   costs for all MRs and mobile nodes are incurred at hah
    of mobile nodes, costs are incurred due to transmission
                                                                                   wired hops. For nodes at level i, transmission costs are
    through hhh hops, tunneling, look up and transmission
                                                                                   incurred at i+1 wireless hops. Therefore, location update
    of one additional tunnel header. Therefore, the packet
                                                                                   cost is given by Eqn. (15).
    delivery cost for the network is given by Eqn. (9).

                                                                                                                            l

                      F
                               l                                                    ΛS =
                                                                                     LU       2τl (Nr + Nm ) hah + σ             (i + 1)
                                             (i)
    ΛND = Nc λs
     P
                                             (i)
                                       Nf + Nm          iψ (Nr + Nm )                                                      i=0
                      P                                                                                                                     Tr
                                                                                                                                                       (15)
                           i=1                                                                                                    1+        Tlf
                                                                                       (i)  (i)
    + 2iπt + (hah + (i − 1)hhh + hhc ) τdt + ihah τip                               × Nr + Nm            + (Nr + Nm ) πh
                                                                                                                                        Tr
        i−1                        i
    +         jhhh τip + σ             jτip + στdt (i + 1)               (9)   •   Session continuity cost: In SPD, each mobile node
        j=0                    j=1                                                 sends BUs to (and receive BAs from) CNs for session
           λs
                 l                                                                 continuity. The cost incurred at the TLMR is thus
                       (i)
    + Nc              Nm hhh (τdt + τip ) + ψ (Nr + Nm )
           S    i=1                                                                                                    1+       Tr
                                                                                                                                Tlf
                                                                                                ΨS = 2στs Nm Nc
                                                                                                 SC                                                    (16)
    + πt + σiτip + hah τip + ihhh τip + hhh τdt                                                                            Tr
                                                                                   The session continuity cost for the network also includes
•   Prefix/CoA obtention cost: After every handoff, only                            costs at each hop upto CNs, and at other MRs, and is
    TLMR obtains a CoA from the foreign network. There-                            given by Eqn. (17).
    fore, costs incurred due to prefix or CoA obtention are
    zero.                                                                                                                                          Tr
                                                                                                                  l                         1+
•   Total cost: Combining the costs presented above, we find                                                                                        Tlf
                                                                                   ΛS = 2τs Nc
                                                                                    SC              Nm hac + σ                 (i)
                                                                                                                       (i + 1)Nm
    the costs incurred at the TLMR, the HA and the network                                                                                        Tr
                                                                                                                 i=0
    given by Eqns. (10), (11) and (12), respectively.                                                                                    (17)
                                                                               •   Packet delivery cost: For every packet, sent from a CN
                      ΨT = ΨN + ΨN + ΨND
                       N
                            LU   SC   P                            (10)            to an LFN, the HA of the LFN looks up the binding
                                                                                   cache to find the CoA to encapsulate the packet for
                                                                                   tunneling. Tunneling and look up costs are incurred at
                                                                                   a rate proportional to the packet arrival rate given by
                      ΦN = ΦN + ΦN + ΦND
                       T    LU   SC   P                            (11)
                                                                                   λs F/P . For the packets sent to mobile nodes, we assume
                                                                                   that only the first packet is sent through the HA before a
                                                                                   BU is received at the CN, and thus, the costs are incurred
                      ΛN = ΛN + ΛN + ΛND
                       T    LU   SC   P                            (12)            every λs /S seconds. TLMR needs to de-tunnel these
                                                                                                                                               7



    packets only for attached LFNs. Therefore, the cost at                •   Total cost: Combining the costs presented above, we find
    the TLMR is                                                               the costs incurred at the TLMR, the HA and the network
                                                                              given by Eqns. (23), (24) and (25), respectively.
                    F    (1)              (1)
       ΨS D = Nc λs
        P              Nf πt + στip Nf − Nf                                             ΨS = Ψ S + Ψ S + Ψ S D + Ψ S
                                                                                         T     LU    SC    P       CO                       (23)
                    P                                              (18)
                                       λs
        + στdt (Nf + Nm ) + στip Nc Nm
                                       S
                                                                                                   ΦS = Φ S + ΦS D
                                                                                                    T     LU   P                            (24)
    The HA needs to perform look up, tunneling and transmit
    the packet resulting in a cost as follows:
                                                                                        ΛS = Λ S + Λ S + Λ S D + Λ S
                                                                                         T     LU    SC    P       CO                       (25)
                           F
    ΦS D = Nf Nc λs
     P                        ψ (Nr + Nm ) + τdt + τip + πt               3) MIRON:
                           P                                (19)
                   λs                                                     • Location update cost: Location update for MIRON is
     + Nm Nc            ψ (Nr + Nm ) + τdt + τip + πt                       similar to that of SPD. Therefore, location update costs
                   S
                                                                            for the TLMR, the HA and the network is as follows:
    The packet delivery cost for the network includes other
    costs in addition to the cost incurred at the HA and
                                                                                                         ΨM = ΨS
                                                                                                          LU   LU                           (26)
    TLMR. Other costs include the transmission costs at
    nested MRs and routers upto the CN. For the case of
    mobile nodes, transmission costs are incurred at each hop
                                                                                                         ΦM = ΦS
                                                                                                          LU   LU                           (27)
    between the AR and the CN for all but the first packet.
    For the case of LFNs and session’s first packet of mobile
    nodes, transmission costs are incurred at each hop from                                              ΛM = ΛS                            (28)
                                                                                                          LU   LU
    the CN upto the HA, and from the HA upto the AR. For
    the latter case, additional costs are incurred due to tunnel          •   Session continuity cost: For session continuity, BUs are
    header at each hop between the HA and the MR for the                      sent to CNs by mobile nodes, and by MRs on behalf
    destination MNN along with the tunneling cost incurred                    of the attached LFNs. Thus, the costs for MIRON are
    at the MR because it de-tunnels packets. Therefore, the                   similar to the costs of SPD except the additional but
    packet delivery cost for the network is given by Eqn. (20)                identical costs for LFNs. Therefore, the costs incurred
                                                                              at the TLMR and at the network are give by Eqns. (29)
                        F                                                     and (30), respectively.
    ΛS D = Nc λs
     P                    Nf (ψ (Nr + Nm ) + 2πt + (hah + hhc )τdt
                        P                                                                                               1+        Tr
                                                l                                                                                 Tlf
                                                             (i)   (i)                ΨM
                                                                                       SC       = 2Nc (Nf + Nm ) στs                        (29)
     + hah τip ) + hac Nm τdt + στdt                 (i + 1)(Nf + Nm )                                                       Tr
                                               i=1
               l                                                          (20)
                         (i)          λs                                                                                     l
     + στip         iNf        + Nc      Nm (ψ(Nr + Nm ) + πt
                                      S                                          ΛM = 2τs Nc
                                                                                  SC                   (Nf + Nm ) hac + σ         (i + 1)
              i=1
                                                                                                                            i=0
                                        l
                                                                                                               Tr
                                                                                                                                            (30)
     + hah (τdt + τip )) + στip                      (i)
                                             (i + 1)Nm                                (i)
                                                                                                          1+   Tlf
                                                                                                 (i)
                                                                                 ×   Nf     +   Nm
                                       i=1                                                                   Tr
•   Prefix/CoA obtention cost: In SPD, prefix and CoAs
                                                                          •   Packet delivery cost: In MIRON, route optimization
    can be obtained from the MR above using DHCPv6
                                                                              is performed for all MNNs. Therefore, packet delivery
    procedures. This requires a request and a reply message,
                                                                              cost for all MNNs are like that for mobile nodes in
    and some processing at the MR for prefix delegation [23].
                                                                              SPD. Therefore, the costs for the TLMR, the HA and
    Since the TLMR delegates prefixes to attached MRs and
                                                                              the network are given by Eqns. (31), (32) and (33),
    provide CoAs to attached mobile nodes, the cost incurred
                                                                              respectively.
    at the TLMR is as follows:
                                             (1)       (1)
                                   2στd Nr          + Nm                               λs    (1)                (1)
                        ΨS     =                                   (21)       ΨMD = Nc
                                                                               P            Nf πt + στip (Nf − Nf + Nm )
                         CO
                                              Tr                                        S                                (31)
                                                                                      F
    The cost incurred for the entire mobile network is given                  + σNc λs τdt (Nf + Nm )
                                                                                      P
    by Eqn. (22).
                                                                                                           λs
                                    2στd (Nr + Nm )                           ΦMD = (Nf + Nm ) Nc             (ψ (Nr + Nm ) + τdt + τip + πt )
                         ΛS =
                          CO                                       (22)        P
                                                                                                           S
                                           Tr                                                                                         (32)
                                                                                                                                                                  8




                                                                                                                         l
                λs
    ΛMD = Nc
     P             (Nf + Nmh ) ψ (Nr + Nmh ) + πt                                          ΛO =
                                                                                            LU         2 Nr hah + σ                   (i)
                                                                                                                              (i + 1)Nr        τl + Nr πh
                S
                                                                                                                        i=0
                                                                                                    Tr                                 l
    + (hah + hhc )τdt + hah τip + Nf πt + στip                                                 1+   Tlf
                                                                                           ×               + 2 Nm hah + σ                          (i)
                                                                                                                                           (i + 1)Nm         τl   (41)
          l                 l                                                   (33)              Tr
                (i)                     (i)                         F                                                               i=0
    ×          iNf +            (i + 1)Nm                 + Nc λs                                         Tr
                                                                    P                                     Tl f
         i=1           i=1                                                                 + Nm πh
                                                  l                                                      Tr
                                                                (i)  (i)
    × τdt (Nf + Nm )hac + στdt                         (i + 1)(Nf + Nm )               •   Session continuity cost: Since mobile nodes in OPR do
                                                 i=1                                       not need MIPv6 route optimization, we assume that no
•   Prefix/CoA obtention cost:                                                              BU is sent to CNs. Therefore, the session continuity cost
    Two DHCPv6 messages for each MNN (except LFNs)                                         due to the sending of BUs to CNs is zero. But for every
    are forwarded by the TLMR along with the transmission                                  packet sent to the CN from each attached MNN, the
    of two PANA messages for attached MRs resulting in the                                 MR needs to look up the DPT table for the translated
    cost incurred at the TLMR as follows:                                                  address. Therefore, the TLMR has to look up a table
                                                                                           for the attached nodes (except MRs) giving the session
                       (1)           (1)                                                   continuity cost at the TLMR as follows:
                      Nr        + Nm         τp + (Nr + Nm ) τd
      ΨM
       CO     = 2σ                                     (34)
                                   Tr                                                                     (1)                   F             (1)
    For each MNN except the TLMR and LFNs, four PANA                                        ΨO = Nf
                                                                                             SC
                                                                                                                     (1)
                                                                                                                 + N m N c λs          ψ Nf            (1)
                                                                                                                                                    + Nm
                                                                                                                                P
    messages have to be transmitted, and equal number of                                                                                                      (42)
    replies follow. Moreover, two DHCPv6 messages for each                                 Considering the look up cost for all MRs while assuming
    MR and mobile node at level i are transmitted across i                                 equal number of MNNs attached under each MR, the
    number of wireless hops. Therefore, prefix/CoA obtention                                session continuity cost for the network becomes,
    cost for the network becomes,
                                                                                                                    l
                                                                                                             F      1    (i+1)
                                                                                                                                                         2
                 σ                                                                           ΛO = Nc λs
                                                                                              SC               ψ    (i)
                                                                                                                        Nf        (i+1)
                                                                                                                               + Nm                           (43)
        ΛM
         CO    =    8 (Nr − 1 + Nm ) τp                                                                      P i=0 Nr
                 Tr
                        l
                                                                         (35)                       (i)
                                                                                           where Nr = 0.
                                         (i)  (i)
                 +2             (i + 1) Nr + Nm τd                                     •   Packet delivery cost: Similar to MIRON, the first packet
                       i=0                                                                 go through the HA until the CN receives the translated
•   Total cost: Like SPD, the total costs for MIRON are                                    address from the packet sent to the CN in response to
    given by Eqns. (36), (37) and (38).                                                    the first packet received at an MNN. Therefore, costs for
                                                                                           OPR are as follows:
               ΨM = ΨM + ΨM + ΨMD + ΨM
                T    LU   SC   P     CO                                  (36)
                                                                                                                    ΨOD = ΨMD
                                                                                                                     P     P                                  (44)
                        ΦM = ΦM + ΦMD
                         T    LU   P                                     (37)
                                                                                                                     ΦOD = ΦMD
                                                                                                                      P     P                                 (45)
               ΛM = ΛM + ΛM + ΛMD + ΛM
                T    LU   SC   P     CO                                  (38)
                                                                                                                     ΛOD = ΛMD
                                                                                                                      P     P                                 (46)
4) OPR:
• Location update cost: In OPR, only MRs obtain CoAs                                   •   Prefix/CoA obtention cost: Prefix obtention procedure
  after handoff, and perform location update with the HA.                                  is similar to that of SPD except that only MRs obtain the
  Mobile nodes, being transparent to the mobility, send                                    prefix. Therefore, by excluding the cost for mobile nodes
  refreshing BUs only. Therefore, we can find the costs                                     from the expressions derived for SPD, we can find the
  like the previous schemes by considering all BUs sent by                                 prefix/CoA obtention cost for the TLMR and the network
  MRs, and refreshing BUs sent by mobile nodes.                                            given by Eqns. (47) and (48), respectively.
                                                                                                                                    (1)
                                     Tr                        Tr                                                            2στd Nr
                                1+   Tlf                       Tlf                                                ΨO =
                                                                                                                   CO                                         (47)
        ΨO = 2Nr στl
         LU                                      + 2Nm στl               (39)                                                   Tr
                                  Tr                            Tr
                                                                                                                        2στd Nr
                                                                                                                   ΛO =
                                                                                                                    CO                       (48)
                                 1+        Tr                            Tr                                               Tr
                                           Tlf                           Tlf
    ΦO = Nr (2τl + πh )
     LU                                               + Nm (2τl + πh )                 •   Total cost: The total costs for OPR are given by Eqns.
                                     Tr                                  Tr
                                                                         (40)              (49), (50) and (51).
                                                                                                                                                 9



                                                                             •   Packet delivery cost: Like the packets for LFNs in
                 ΨO = Ψ O + Ψ O + Ψ O D + Ψ O
                  T     LU    SC    P       CO                        (49)       SPD, packets for all MNNs are tunneled through the HA.
                                                                                 Therefore, cost for the TLMR can be found from the
                                                                                 similar cost for SPD by considering all MNNs instead of
                         ΦO = ΦO + ΦOD
                          T    LU   P                                 (50)
                                                                                 the LFN, and is as follows:

                 ΛO = ΛO + ΛO + ΛOD + ΛO
                  T    LU   SC   P     CO                             (51)
                                                                                                    F         (1)
                                                                                 ΨAD = Nc λs
                                                                                  P                       Nf           (1)
                                                                                                                    + Nm πt + σ Nf + Nm −
5) Ad hoc-based:                                                                                    P
• Location update cost: Like OPR, location update after                                                                                              (58)
  handoff is performed by MRs, and mobile nodes send re-                          (1)         (1)                                         λs
                                                                                 Nf     −    Nm     τip + στdt (Nf + Nm )         + σNm Nc τip
  freshing BUs. Unlike OPR, BUs sent by attached mobile                                                                                   S
  nodes are tunneled by each MR to its HA. Therefore, the                        Similarly, the cost for the HA can be found, and is as
  costs incurred at the TLMR and the HA are the costs of                         follows:
  refreshing location update of mobile nodes in addition to
  the similar costs of OPR .                                                                                F
                                                                                 ΦAD = (Nf + Nm ) Nc λs
                                                                                  P                             ψ (Nr + Nm ) + πt +
                                                                                                            P                           (59)
                                                                     Tr
                                                                     Tlf                              λs
    ΨA = ΨO + (2Nm − Nm )στip + 2πt Nm
     LU   LU
                      (1)            (1)                                          τdt + τip + Nm Nc (ψ(Nr + Nm ) + τdt + 2τip )
                                                                     Tr                                S
                                                                      (52)       The cost for the network can also be found from the
                                                                                 cost of SPD in a similar way mentioned above except an
                                                          Tr                     additional cost which is due to find the route towards the
                                                          Tlf
     ΦA = ΦO +Nm 2πt +τip +ψ(Nr +Nm )
      LU   LU                                            (53)                    AR using AODV [21]. We assume that the cost of route
                                                    Tr
                                                                                 finding occurs once every handoff because change of AR
    The location update cost for network is more than that of                    occurs at handoff. We also assume that the route finding
    OPR because BUs sent by the mobile nodes are tunneled                        messages only travel one hop because the MRs already
    through the HA. Thus, in addition to the costs considered                    know the route to the AR (either old or new). Thus, to find
    in OPR, we need to consider the costs incurred at each                       the route, each MR broadcasts a route request message,
    hop from HA of the MR to the HA of the mobile node,                          and will reply twice once for the MRs above and below
    and the costs of tunneling. Therefore, the cost becomes                      each. Therefore, packet delivery cost for Ad hoc-based is
                                                                                 given by Eqn. (60).
                                           l
     ΛA = Λ O + 2
      LU    LU               Nm hah + σ           (i)
                                                iNm       τip                                       F
                                          i=0                                    ΛAD = Nc λs
                                                                                  P                     (Nf + Nm ) ψ (Nr + Nm ) + 2πt +
                                                          Tr
                                                                      (54)                          P
                                                          Tlf                                                               l
     + Nm hhh τl + Nm (ψ(Nr + Nm ) + 2πt )                                                                                            (i)(i)
                                                          Tr                     (hah + hhc )τdt + hah τip + στip                i Nf + Nm
                                                                                                                          i=1
•   Session continuity cost: Mobile nodes send refreshing                                l
    BUs to CNs, and therefore, session continuity cost for                                              (i) (i)
                                                                                 στdt         (i + 1) Nf + Nm                                  (60)
    the TLMR in Ad hoc-based scheme is similar to that of                               i=1
    SPD except that only refreshing BUs are considered.                                λs
                                                                                  + Nc      Nm (ψ (Nr + Nm ) + πt + hhh (τdt + τip )
                                                                                       S
                                                            Tr                                               l
                                                            Tlf                                                   (i)          1
       ΨA
        SC     = 2 σNm Nc (τs + τip ) +       (1)
                                          πt Nm Nc                                + hah τip + στip ) + στip     iNm + 3Nr στa
                                                                Tr                                          i=1
                                                                                                                               Tr
                                                     (55)
    Since BUs are tunneled through the HA, the session                       •   Prefix/CoA obtention cost: In ad hoc-based scheme,
    continuity cost at the HA is given by Eqn. (56).                             MRs obtain CoAs from the router advertisement of the
                                                                                 AR, and periodically broadcast the advertisement to the
                                                    Tr
                                                    Tlf                          attached MRs. Thus, the cost of CoA obtention becomes
                ΦA = 2Nm Nc (τs + τip + πt )
                 SC                                      (56)                    the cost of broadcasting the RA. Since the TLMR only
                                               Tr
                                                                                 broadcast one router advertisement, we ignore the cost for
    Considering the costs at each hop, the session continuity
                                                                                 the TLMR. Therefore, the cost for the network becomes
    cost for the network is
                                                                                                                                Tr
                                                                                                                       1+       Tra
                                                                                                    ΛA = 2στr Nr
                                                                                                     CO                                 (61)
    ΛA = 2Nc Nm ((hah + hhc ) τs + hah τip + 2πt )
     SC
                                                                                                                      Tr
           l                              Tr                          (57)       where, τr is the transmission cost for the router advertise-
                                    (i)   Tlf                                    ment, and Tra is the interval of sending periodic router
     +σ         ((i + 1)τs + iτip )Nm
          i=0
                                          Tr                                     advertisement.
                                                                                                                                                                         10


                            TABLE I                                                                                 4
                                                                                                                 x 10
      VALUES OF PARAMETERS USED IN THE NUMERICAL ANALYSIS .                                                              NEMO BSP
                                                                                                             8




                                                                             Network Mobility Cost on TLMR
                                                                                                                         SPD
 Parameter          Value       Parameter      Value
 Nm                 600         Nf             400                                                           7           MIRON
 Nr                 21          Nc             5                                                                         OPR
 Tr                 120         Tlf            420                                                           6           Ad hoc
 hah                35          hac            35
 hhc                35          hhh            35                                                            5
 l                  2           φ              0.1
 σ                  10          ψ              0.3                                                           4
 τl                 0.6         τs             0.6
 τip                0.4         πt             10
                                                                                                             3
 λs                 0.01        S              10
 F                  10240       P              576
                                                                                                             2
 τdt                5.76        τd             1.4                                                                 100   200   300   400   500   600   700   800   900
 τp                 0.56        τa             1.56                                                                        Number of Mobile Hosts (Nm)
 τr                 0.72        πh             25
                                                                     Fig. 2. Network Mobility Cost on TLMR vs. number of MHs for NEMO
  •   Total cost: The total costs for ad hoc-based scheme are        BSP, SPD, MIRON, OPR, and Ad hoc-based scheme.
      given by Eqns. (62), (63) and (64).

                    ΨA = ΨA + ΨA + ΨAD
                     T    LU   SC   P                         (62)   A. Top Level Mobile Router
                                                                        In this subsection, we present results to show network
                     ΦA = ΦA + ΦA + ΦAD
                      T    LU   SC   P                        (63)   mobility costs on TLMR of NEMO BSP, SPD, MIRON, OPR,
                                                                     and Ad hoc based schemes. We vary number of mobile hosts,
                                                                     number of mobile routers, number of LFNs, subnet residence
                 ΛA = ΛA + ΛA + ΛAD + ΛA
                  T    LU   SC   P     CO                     (64)   time, and number of correspondent nodes.
                                                                        The cost incurred at the TLMR is given by Figs. 2, 3, 4,
                            VI. R ESULTS                             5 and 6 as a function of the number of mobile nodes, the
                                                                     number of MRs, the number of LFNs, subnet residence time
   In this section, we use the expressions derived in the cost       and the number of CNs, respectively. The cost associated with
analysis section in a simplified format. The route optimization       delivery of every packet dominates the other costs to determine
schemes differ in the way the route is optimized for different       the characteristics of the total costs. The cost of NEMO BSP is
types MNNs resulting in variation in the amount of signaing          the highest due to the packet delivery cost that results from the
(for location update and session continuity), variation in the       transmission cost of multiply tunneled packets. The cost of Ad
route of packets for packet delivery, and differences in ob-         hoc-based scheme is higher than the SPD, MIRON and OPR
tention of COA and prefix. The number of data packets sent            because of the transmission cost required for one additional
to the mobile network is proportional to the number of CNs           tunneling for all packets. SPD’s cost is smaller than OPR
to determine the packet delivery cost. The subnet residence          because the transmission cost of tunneled packets is incurred
time has been shown to affect the cost in [?]. Moreover, the         only for LFNs.
number of hops between various mobility entities determines             The costs of MIRON and OPR are smaller then the other
the packet delivery cost. Therefore, we present the network          schemes. MIRON’s cost is little higher than OPR due to the
mobility cost as a function of the number of mobile nodes,           transmission cost incurred for signaling which is required for
the number of MRs, the number of LFNs, subnet residence              only MRs in OPR. Also, MIRONs prefix obtention cost is
time and the number of hops between entities.                        higher than OPR.
   For measurement, we assume a mobile network topology                 The costs as a function of the number of MRs (Fig. 3 and
which is simplified from the network shown in Fig. 1 to               the subnet residence time (Fig. 5) show negligible changes
compute costs on TLMR, HA, and complete network. Since               because of the dominance of the packet delivery cost that does
there exists no standard architecture for NEMO, we are using         not depend on these two parameters.
a generalized topology upon which different prefix delegation-
based schemes have been proposed. We are assuming the
mobile network to have a two-level hierarchy of Mobile               B. Home Agent
Routers. There is one MR at level 0 or top level (which is              The effects of the number of mobile nodes, the number
                        (0)
the TLMR), hence Nr = 1. No LFN, LMN and VMN is                      of MRs, the number of LFNs, subnet residence time and the
connected directly to the TLMR. The TLMR is connected                number of CNs on the cost incurred at the Home Agent are
      (1)                                   (1)
to Nr number of level-1 routers, so Nr = Nr − 1 as                   shown in Figs. 7, 8, 9, 10 and 11, respectively. Like the
                                                      (2)
there is no other mobile router at level 2. Hence, Nr = 0.           costs incurred at the TLMR, the cost associated with the
There is no hosts (mobile or fixed) at level 0, and level 1. So       packet delivery dominates over other costs. Therefore, the
  (0)       (0)             (1)    (1)
Nm = Nf = 0, and Nm = Nf = 0. All the mobile and                     characteristics of the costs for the HA are similar to that for
                                   (2)              (2)
fixed nodes are at level 2, i.e., Nm = Nm , and Nf = Nf .             the TLMR except some differences that are explained below.
                                                                                                                                                                                                                                                          11


                                                                                                                                                                                          4
                                                                                                                                                                                   x 10
                                                                                                                                                                             14
                                             x 10
                                                 4                                                                                                                                                NEMO BSP




                                                                                                                                             Network Mobility Cost on TLMR
                                       6.5
       Network Mobility Cost on TLMR                                                                                                                                         12                   SPD
                                                                                                                                                                                                  MIRON
                                                          NEMO BSP                                                                                                           10                   OPR
                                                          SPD                                                                                                                                     Ad hoc
                                        6                                                                                                                                     8
                                                          MIRON
                                                          OPR
                                                                                                                                                                              6
                                                          Ad hoc
                                                                                                                                                                              4
                                       5.5

                                                                                                                                                                              2


                                                                                                                                                                              0
                                                                                                                                                                                   1          2         3         4     5     6     7    8     9    10
                                        5                                                                                                                                                         Number of Correspondent Nodes(Nc)
                                             5                10                15          20          25               30
                                                              Number of Mobile Routers (Nr)
                                                                                                                                 Fig. 6. Network Mobility Cost on TLMR vs. number of CNs for NEMO
                                                                                                                                 BSP, SPD, MIRON, OPR, and Ad hoc-based scheme
Fig. 3. Network Mobility Cost on TLMR vs. number of MRs for NEMO
BSP, SPD, MIRON, OPR, and Ad hoc-based scheme

                                                                                                                                                                                        5
                                                                                                                                                                                   x 10
                                                                                                                                                                             3.5
                                                                                                                                                                                              NEMO BSP
                                                                                                                                                                                              SPD




                                                                                                                                        Network Mobility Cost on HA
                                                                                                                                                                              3
                                                    4
                                             x 10                                                                                                                                             MIRON
                                        8
                                                          NEMO BSP                                                                                                           2.5              OPR
       Network Mobility Cost on TLMR




                                       7.5
                                                          SPD                                                                                                                                 Ad hoc
                                        7                 MIRON                                                                                                               2

                                       6.5                OPR
                                                                                                                                                                             1.5
                                                          Ad hoc
                                        6

                                       5.5                                                                                                                                    1

                                        5
                                                                                                                                                                             0.5
                                       4.5
                                                                                                                                                                              0
                                        4                                                                                                                                              100        200       300       400   500   600   700   800   900
                                                                                                                                                                                                     Number of Mobile Hosts (Nm)
                                       3.5

                                        3
                                                    100             200              300         400         500          600    Fig. 7. Network Mobility Cost of HA vs. number of MHs for NEMO BSP,
                                                                      Number of LFNs (Nf)                                        SPD, MIRON, OPR, and Ad hoc-based scheme

Fig. 4. Network Mobility Cost on TLMR vs. number of LFNs for NEMO
BSP, SPD, MIRON, OPR, and Ad hoc-based scheme

                                                                                                                                   The costs of NEMO BSP and Ad hoc-based scheme are
                                                                                                                                 almost equal. Although the cost of packet delivery in NEMO
                                                                                                                                 BSP is little higher than that of Ad hoc-based scheme, the
                                       6.5
                                             x 10
                                                 4
                                                                                                                                 overall cost is equal because of the additional signaling cost
                                                                                                                                 of Ad hoc-based scheme.
       Network Mobility Cost on TLMR




                                                         NEMO BSP                                                                   For NEMO BSP and Ad hoc-based schemes, costs increase
                                                         SPD                                                                     at a quadratic rate (Fig. 7) which is due to the lookup
                                        6
                                                         MIRON                                                                   cost incurred at the HA for the tunneled packets. Lookup is
                                                         OPR                                                                     performed for each mobile node in the binding entry database
                                                         Ad hoc
                                                                                                                                 of size proportional to the number of mobile nodes, and hence
                                       5.5                                                                                       quadratic. For SPD, the such look up cost is incurred for LFNs
                                                                                                                                 only resulting in a increase rate lower than NEMO BSP and
                                                                                                                                 Ad hoc-based scheme.
                                                                                                                                    For MIRON and OPR, the cost is much lower (when
                                        5
                                        100             200    300        400        500   600    700   800        900    1000   compared to the cost incurred at the TLMR) than the costs
                                                                   Subnet Residence Time (T )
                                                                                                        r                        of other schemes due to the reason described next. Firstly, the
                                                                                                                                 dominant look up cost is incurred only for the first packet of a
Fig. 5. Network Mobility Cost on TLMR vs. subnet residence time for
NEMO BSP, SPD, MIRON, OPR, and Ad hoc-based scheme                                                                               session, thus have negligible effect on the overall increase rate
                                                                                                                                 of the cost. Secondly, the location updates sent to the CNs do
                                                                                                                                 not incur any cost at the TLMR.
                                                                                                                                                                                                                                    12


                                                                                                                                                                              5
                                                                                                                                                                          x 10

                                           x 10
                                                  5
                                                                                                                                                                    3.5
                                                                                                                                                                                      NEMO BSP
                                      2
                                                                                                                                                                                      SPD




                                                                                                                                      Network Mobility Cost on HA
                                     1.8                                                                                                                             3                MIRON
       Network Mobility Cost on HA


                                     1.6                NEMO BSP                                                                                                                      OPR
                                                                                                                                                                    2.5
                                                        SPD                                                                                                                           Ad hoc
                                     1.4
                                                        MIRON                                                                                                        2
                                     1.2
                                                        OPR
                                      1                 Ad hoc                                                                                                      1.5

                                     0.8
                                                                                                                                                                     1
                                     0.6
                                                                                                                                                                    0.5
                                     0.4

                                     0.2                                                                                                                             0
                                                                                                                                                                          1       2      3     4    5    6    7    8       9   10
                                      0                                                                                                                                               Number of Correspondent Nodes (Nc)
                                           5                10                15          20          25               30
                                                             Number of Mobile Routers (Nr)
                                                                                                                               Fig. 11. Network Mobility Cost on HA vs. number of CNs for NEMO BSP,
                                                                                                                               SPD, MIRON, OPR, and Ad hoc-based scheme
Fig. 8. Network Mobility Cost of HA vs. number of MRs for NEMO BSP,
SPD, MIRON, OPR, and Ad hoc-based scheme


                                                                                                                               C. Complete Network
                                                                                                                                  The cost incurred over the network is given by Figs. 12, 13,
                                           x 10
                                               5                                                                               14, 15, 16 and 17 as a function of the number of mobile nodes,
                                     2.2
                                                        NEMO BSP                                                               the number of MRs, the number of LFNs, subnet residence
                                      2
                                                        SPD                                                                    time, the number of hops and the number of CNs, respectively.
       Network Mobility Cost on HA




                                     1.8
                                                        MIRON                                                                  The cost of NEMO BSP is higher than the other schemes due
                                     1.6                OPR
                                                                                                                               to the higher packet delivery cost that results from multiple
                                     1.4                Ad hoc
                                                                                                                               tunneling of every packet through the unoptimized route. Ad
                                     1.2
                                                                                                                               hoc-based scheme incurs higher cost than SPD, MIRON and
                                      1
                                                                                                                               OPR due to the single tunneling of every packet. Since only
                                     0.8
                                                                                                                               the first packets of sessions (in contrast to every packet) are
                                     0.6
                                                                                                                               tunneled through the unoptimized route, MIRON incurs the
                                     0.4
                                                                                                                               lowest cost. The costs incurred by the SPD and OPR varies
                                     0.2
                                                                                                                               depending on the parameters, and are explained below.
                                      0
                                                  100             200              300         400         500          600       The rate of increase of OPR’s cost with the number of
                                                            Number of Local Fixed Nodes (Nf)
                                                                                                                               mobile nodes is higher than that of SPD (see Fig. 12) due
Fig. 9. Network Mobility Cost of HA vs. number of LFNs for NEMO BSP,
                                                                                                                               to the quadratic look up cost required per packet for session
SPD, MIRON, OPR, and Ad hoc-based scheme                                                                                       continuity. When the number of mobile nodes is small, the
                                                                                                                               linear cost (with respect to mobile nodes) of tunneling LFN’s
                                                                                                                               packets, and signaling for mobile nodes dominates resulting
                                                                                                                               in SPD’s cost to be higher than OPR.
                                                                                                                                  As a function of the number of LFNs (Fig. 14) and the
                                                  5

                                      2
                                           x 10
                                                                                                                               number of hops (Fig. 16), the rate of increase of SPD’s cost
                                     1.8                                                                                       is higher than OPR’s because SPD does not optimize LFNs’
       Network Mobility Cost on HA




                                     1.6                NEMO BSP                                                               route completely. The higher cost results from the per packet
                                     1.4
                                                        SPD                                                                    tunneling and delivery cost incurred in the additional route.
                                                        MIRON                                                                     The higher rate of OPR (when compared to that of SPD) as
                                     1.2
                                                        OPR                                                                    a function of the number of CNs attributes to the per packet
                                      1                 Ad hoc
                                                                                                                               session continuity cost incurred for LFNs and mobile nodes.
                                     0.8

                                     0.6
                                                                                                                                                                                             VII. C ONCLUSION
                                     0.4

                                     0.2
                                                                                                                                  In this paper, we have developed mathematical models to de-
                                                                                                                               termine the network mobility costs on various mobility entities
                                      0
                                      100             200    300        400        500   600    700   800        900    1000   of NEMO BSP, and four representative prefix delegation-based
                                                                 Subnet Residence Time (T )
                                                                                                      r                        route optimization schemes of NEMO (SPD, MIRON, OPR,
                                                                                                                               and Ad hoc based schemes) in terms of network size, mobility
Fig. 10. Network Mobility Cost on HA vs. subnet residence time for NEMO
BSP, SPD, MIRON, OPR, and Ad hoc-based scheme                                                                                  rate, distance between mobility agents, and traffic rate.
                                                                                                                                  Results show that the effect of packet delivery cost dom-
                                                                                                                               inates other cost components in the network mobility costs
                                                                                                                                                                                                                                                                  13




                                                   5                                                                                                                                 5
                                              x 10                                                                                                                               x 10
       Network Mobility Cost (Network)   16                                                                                                                                11




                                                                                                                                         Network Mobility Cost (Network)
                                                            NEMO BSP                                                                                                                            NEMO BSP
                                         14                 SPD                                                                                                            10                   SPD
                                                            MIRON                                                                                                           9
                                                                                                                                                                                                MIRON
                                         12
                                                            OPR                                                                                                                                 OPR
                                         10                 Ad hoc                                                                                                          8                   Ad hoc
                                                                                                                                                                            7
                                          8

                                                                                                                                                                            6
                                          6

                                                                                                                                                                            5
                                          4
                                                                                                                                                                            4
                                          2
                                                                                                                                                                            3
                                                  100      200    300    400       500        600   700         800    900                                                  100          200     300        400   500   600    700     800           900   1000
                                                             Number of Mobile Nodes (Nm)                                                                                                          Subnet Residence Time (Tr)

Fig. 12. Network Mobility Cost on complete network vs. number of MHs                                                         Fig. 15. Network Mobility Cost on complete network vs. subnet residence
for NEMO BSP, SPD, MIRON, OPR, and Ad hoc-based scheme                                                                       time for NEMO BSP, SPD, MIRON, OPR, and Ad hoc-based scheme




                                                   5                                                                                                                                 5
                                              x 10                                                                                                                               x 10
                                                                                                                                                                           16
                                         11
       Network Mobility Cost (Network)




                                                                                                                                         Network Mobility Cost (Network)
                                                            NEMO BSP                                                                                                                            NEMO BSP
                                                                                                                                                                           14
                                         10                 SPD                                                                                                                                 SPD
                                                            MIRON                                                                                                          12                   MIRON
                                          9
                                                            OPR                                                                                                                                 OPR
                                          8                 Ad hoc                                                                                                         10                   Ad hoc

                                          7                                                                                                                                 8

                                          6
                                                                                                                                                                            6

                                          5
                                                                                                                                                                            4
                                          4
                                                                                                                                                                            2
                                          3
                                              5             10          15               20         25                30                                                                 10            20          30         40            50              60
                                                             Number of Mobile Routers (Nr)                                                                                                                  Number of Hops (h)

Fig. 13. Network Mobility Cost on complete network vs. number of MRs                                                         Fig. 16. Network Mobility Cost on complete network vs. number of hops
for NEMO BSP, SPD, MIRON, OPR, and Ad hoc-based scheme                                                                       for NEMO BSP, SPD, MIRON, OPR, and Ad hoc-based scheme




                                                   5                                                                                                                                 6
                                              x 10                                                                                                                               x 10
                                         14
       Network Mobility Cost (Network)




                                                                                                                                    Network Mobility Cost (Network)




                                                            NEMO BSP                                                                                                                            NEMO BSP
                                                                                                                                                                            2
                                         12                 SPD                                                                                                                                 SPD
                                                            MIRON                                                                                                                               MIRON
                                         10                 OPR                                                                                                                                 OPR
                                                                                                                                                                           1.5
                                                            Ad hoc                                                                                                                              Ad hoc
                                          8
                                                                                                                                                                            1

                                          6


                                                                                                                                                                           0.5
                                          4



                                          2
                                                                                                                                                                            0
                                                     100         200         300              400         500          600                                                       1        2       3          4     5     6         7    8             9     10
                                                           Number of Local Fixed Nodes (N )                                                                                                   Number of Correspondent Nodes (N )
                                                                                                           f                                                                                                                                     c


Fig. 14. Network Mobility Cost on complete network vs. number of LFNs                                                        Fig. 17. Network Mobility Cost on complete network vs. number of CNs
for NEMO BSP, SPD, MIRON, OPR, and Ad hoc-based scheme                                                                       for NEMO BSP, SPD, MIRON, OPR, and Ad hoc-based scheme
                                                                                                                                                         14



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might be intuitive that schemes such as NEMO BSP, SPD and                            IP-diversity based approach for network mobility in space,” in Second
                                                                                     International Conference on Space Mission Challenges for Information
Ad hoc-based cost less due to lower number of signaling than                         Technology, Pasadena, CA, Jul. 17-21, 2006.
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                                                                                     14-18, 2009.
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contrasting the results shown in [?]                                                 RFC 3775, Jun. 2004.
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