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					 QoS Topology Control and
  Energy Efficient Routing
in Ad hoc Wireless Networks


         Prof. Xiaohua Jia
    Dept of Computer Science,
     City Univ of Hong Kong

                                1
  Mobile Ad Hoc (Wireless) Networks

What’s a mobile ad hoc network?
1) Mobility
2) No wired infrastructure




                 S


                                  2
   Energy-efficiency in ad hoc networks

Power function:
   p(u,v) = dα(u,v), 2 ≤ α ≤ 4

Two special features of radio transmission:
1) Broadcast in nature.
2) p(u,w) + p(w,v) < p(u,v),
   relaying messages by a third node may result in
   a smaller energy cost.
                                                     3
  Topology Control Problem

Given a set of wireless nodes V in a plane,
for each node u, adjust its transmission
power to p(u), such that the network is fully
connected and                is minimized.




                                                4
    R. Ramanathan, R. Rosales-Hain, “Topology control of
    multihop wireless networks using transmit power
    adjustment”, INFOCOM’00.


Greedy algorithm (based on Kruskal’s MST algorithm)



          4
                                           5
                        3
                  C                D
              1                        1
                  A                B
                        3
Side-effect edge problem
Distributed algorithms: LINT and LILT
                                                           5
     R. Wattenhofer, L. Li, P. Bahl and Y.M. Wang, “Distributed
     topology control for power efficient operation in multihop
     wireless ad hoc networks”, INFOCOM’01.

G: topology by max power; G’: topology by min power.
Algorithm:
1) Divide uniformly a node’s region into cones with angle α;
2) Increase a node-power until there is a neighbor in each
    cone, or it reaches max power of the node.

Theorem. Let α ≤ 2π/3. G’ is connected if G is connected.

          u        α


                                                               6
      N. Li, J. Hou and Lui Sha, “Design and Analysis of an MST-based
      Topology Control Algorithm”, IEEE INFOCOM’03.
      N. Li and J. Hou, “Topology control in heterogeneous wireless networks:
      problems and solutions”, IEEE INFOCOM’04.


Algorithm:
1)  Collect information about maximally reachable neighbors;
2)  Construct a local MST (in terms of transmission power) among
    neighbors by each node;
3)  Determine the actual power of each node (the neighbors of u in
    G’ are 1-hop nodes in u’s local MST).

Theorem 1. G’ is connected if G is connected.

Theorem 2. The degree of any node in G’ is bounded by 6.

                                                                         7
      QoS topology control

Given a set of nodes in a plane:
B, max bandwidth capacity at a node.
λs,d, end-end traffic demand between s, d.
Δs,d, maximal hop-count allowed between s, d.

Problem. Find transmission power p(i) for 0  i  n,
such that λs,d, for all pairs (s,d), can be routed within Δs,d,
and Pmax is minimized, where Pmax = max{p(i) | 0  i  n}.

                                                             8
    Traffic Non-splittable Formulations

Variables:
xi,j - boolean, xi,j = 1 if there is a link from node i to
node j; otherwise, xi,j = 0.
     - boolean, = 1 if the route from s to d goes
through the link (i,j); otherwise         = 0.
Pmax - the maximum transmitting power of nodes.




                                                             9
     Traffic non-splittable
Objective : Min Pmax
Topology constraints:
                                 i
                                 j’       j
Transmission power constraint:



Delay constraint:                     i



                                          10
    Traffic non-splittable

Bandwidth constraint:



Flow constraints:




Binary constraint:


                             11
Traffic non-splittable

Topology of six nodes and six requests




Non-splittable case              Splittable case
                                                   12
     Trarffic Splittable Formulation

Variables:
     and Pmax remain the same.

    - amount of (s, d)’s traffics going through link (i, j).

Objective : Min Pmax

Topology constraints:
                                                               i
                                                               j’   j
Transmission power constraint:


                                                                        13
   Formulation (cont’d)

Bandwidth constraint:



Flow constraints:




Variable constraints:


                          14
   Two steps of solution
    Step 1. QoS load-balanced routing


Lmax: maximal node-load

Problem. Given a network graph G and traffic
demands between node pairs, route these
traffics in this graph, such that Lmax minimized.



                                               15
Formulation of QoS routing problem

Objective : Min Lmax
Constraints:




                               16
   Step 2. QoS topology control

Algorithm:
1) sort all node-pairs (i,j) in ascending order
   according to their distance d(i,j).
2) pick up the node-pair with closest distance but
   not yet connected and increase the power to
   make them connected.
3) run the QoS routing algorithm on G to obtain
   Lmax. If Lmax ≤ B, then stop; otherwise repeat (b)
   and (c).

                                                        17
Experimental results




    (a) λ = 0.02B    (b) = 0.1B




   (c) λ = 0.2B     (d) λ = 0.32B   18
  Experimental results

                                                            max               avg            min

                            14
              node degree   12
                            10
                             8
                             6
                             4
                             2
                             0
                                 0.025B


                                           0.05B


                                                   0.075B


                                                              0.1B


                                                                     0.125B


                                                                                0.15B


                                                                                        0.175B


                                                                                                   0.2B


                                                                                                          0.225B
                                                                     λm


                                          Node-degrees versus λm


X. Jia, D. Li, and D. Du, “QoS topology control in ad
hoc wireless networks” , INFOCOM’04.
                                                                                                                   19
    Routing Protocols in Ad Hoc
    Networks
•   Proactive protocols (routing table based), such as
    DSDV (Destination Sequenced Distance Vector),
    OLSR (Optimized Link State Routing), etc.
•   On-demand protocols (reactive protocols), such
    as DSR (Dynamic Source Routing), AODV (Ad-
    hoc On-demand Distance Vector), etc.
•   Virtual backbone based protocols, such as
    Spine-based method, clustering method,
    hierarchical protocols, etc.
                                                     20
    D. B. Johnson, D. A. Maltz, Y.C. Hu, and J. G. Jetcheva, The
    Dynamic Source Routing Protocol for Mobile Ad Hoc Networks,
    http://www.ietf.org, draft-ietf-manet-dsr-05.txt, Mar 01.

Dynamic Source Routing (DSR):
1.  Source s finds a route to
    destination d by flooding a Rreq
    packet.
2.  d replies a Rrep packet to s by
    reversing the route appended to
    the Rreq.
3.  s includes the route to d in each
    data packet to d (called source
    routing).

                                                                21
       Route Caching in DSR

•   Each node learns routing
    information from both Rreq
    and Rrep packets and
    caches the routes.
•   When a node receives a
    Rreq to d and it has a valid
    route in its cache, it replies
    the route to s.
                                     22
        Charles E. Perkins, E. M. Royer and Samir R. Das, “Ad-hoc
        On-Demand Distance Vector (AODV) Routing”, draft-ietf-
        manet-aodv-08.txt, http://www.ietf.org, Mar 2001.

AODV (Ad-hoc On-demand Distance Vector)
•   It is similar to DSR in route
    discovery, but improves DSR by
    keeping routing tables (next-hop) at
    nodes (no route info in data packets).
•   When a node receives a Rreq, it sets
    up a reverse path to the source in its
    routing table.
•   Rrep travels along the reverse set-up
    path to s and the forward-path (i.e.,
    the route from s to d) is set up as the
    Rrep travels to s.
•   Entries in routing table are purged
    after a timeout.
                                                             23
   C. E. Perkins and Pravin Bhagwat, “Highly Dynamic
   Destination-Sequenced Distance-Vector Routing (DSDV) for
   Mobile Computers”, ACM SIGCOMM, Oct 1994, pp.234-244.


Destination Sequence Distance Vector Routing:
• It mimics the Distance Vector Routing.
• Each node keeps a routing table: next-hop and
  distance to each destination, and dest-sequnce-no.
• Each node periodically exchange the routing table
  with neighbors.
• Data packets are forwarded towards destinations
  by using the next-hop info in routing tables on the
  way.

                                                      24
    Power-Aware Routing

•   Define optimization goals on energy cost
    for routing, e.g., minimum energy cost per
    packet, maximum network lifetime,
    maximum minimum residual energy.
•   Assign a weight to each link according to
    optimization goal, e.g., energy cost over a
    link, residual energy at nodes.
•   Perform routing with minimum weight.

                                                  25
   Energy Efficient Broadcasting
Ts: broadcast tree rooted from source s;
NL(Ts): set of non-leaf nodes of Ts.
Problem. Given a set of nodes in a plane, for each node u,
adjust its transmission power p(u), to form a Ts, such that:




                        S

To determine, for each node u:
1) Transmission power of u, and
2) The children of u.
                                                               26
   J. Cartigny, D.Simplot, and I. Stojmenovic, “Localized minimum-energy
   broadcast in ad-hoc networks”, IEEE INFOCOM’03.




Algorithm:
1)  Construct a connected topology that has min total energy.
2)  Derive the broadcast tree from the min-energy topology
    using neighbor elimination scheme.




                        S

                                                                   27
    J.E. Wieselthier, G. D. Nguyen, and A. Ephremides, “On the
    Construction of Energy-Efficient Broadcast and Multicast
    Trees in Wireless Networks”, IEEE Infocom’00.



BIP (broadcast incremental power):
1) It is based on Prim’s MST algorithm.
2) Starting from s, each time a new node that can be
   connected by a tree-node with least incremental power is
   added to the tree, until all nodes are in the tree.




                              s


                                                                 28
  Energy Efficient Broadcast with
  Given Transmission Power

p(v): transmission power of node v;
Ts: broadcast tree rooted from source s;
NL(Ts): set of non-leaf nodes of Ts.
Problem. Given a set of nodes in a plane
and p(v) for each node v, find a Ts that:


                                        29
  Transforming the problem to the
  Steiner tree problem




The broadcast routing problem is transformed to: finding a
directed tree Ts’ in G’ that spans all nodes in V’ and the
total weights of Ts’ is minimized.
                                                             30
  A Greedy Heuristic

U: uncovered set; D: covered set;
Vi: set of outgoing neighbors of node i;
1) D ←Vs; U ← V – Vs;
2) Pick from D a node i that has the largest
  value of: | Vi∩U|/p(i);
  D ← D + Vi; U ← U - Vi;
3) Repeat step 2 until D = V.
                                               31
A Node-weighted Steiner Tree Based Heuristic


Theorem 1. Given G(V, E) and s, this heuristic
 can output a broadcast tree in time O(n4).

Theorem 2. The approximation ratio is at most
 2ln(n-1)+1.



                                            32
    Experimental Results

                     4000                                                    4000
                                 NST-h                                                   NST-h
                     3750        Greedy-h                                    3750        Greedy-h
                                 SPT-h                                                   SPT-h
                     3500
                                                                             3500
       energy cost




                                                               energy cost
                     3250
                                                                             3250
                     3000
                     2750                                                    3000

                     2500                                                    2750
                     2250                                                    2500
                     2000
                                                                             2250
                            0   20     40     60    80   100
                                                                                    0   20     40     60    80   100
                                 the num ber of nodes
                                                                                         the num ber of nodes



D. Li , Xiaohua Jia and H. Liu, "Energy efficient broadcast routing in ad
   hoc wireless networks", IEEE Trans on Mobile Computing, Vol. 3, No.
   2, Apr - Jun, 2004, pp.144-151.

                                                                                                                       33
   Energy-Balanced Multicast Routing

Given a wireless network G(V,E):
Ei – initial energy at node i.
wi,j – power cost per time-unit on link li,j, wi,j = dαi,j.
Problem. For a multicast request (s, D, t), find a routing tree,
such that the minimal remaining energy of nodes is
maximized after the multicast session.

S. Cheng, X. Jia, F. Hung, and Y. Wang, “Energy efficient broadcasting
and multicasting in static wireless ad hoc networks”, IEEE Trans on
Wireless Communications.



                                                                         34
 Maximizing broadcast/multicast
 duration routing

Given a wireless network G(V,E):
Ei – initial energy at node i;
wi,j – power cost per time-unit on link li,j.

Problem. Find a set of broadcast / multicast
trees, such that the duration of the broadcast /
multicast session is maximized.



                                                   35
The End


          36

				
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