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									                Performance Evaluation of Deadline Monotonic Policy
                               over 802.11 protocol

                                  Ines El Korbi and Leila Azouz Saidane
                                       National School of Computer Science
                                       University of Manouba, 2010 Tunisia
                             Emails: ines.korbi@gmail.com Leila.saidane@ensi.rnu.tn



                                                 ABSTRACT
               Real time applications are characterized by their delay bounds. To satisfy the
               Quality of Service (QoS) requirements of such flows over wireless
               communications, we enhance the 802.11 protocol to support the Deadline
               Monotonic (DM) scheduling policy. Then, we propose to evaluate the performance
               of DM in terms of throughput, average medium access delay and medium access
               delay distrbution. To evaluate the performance of the DM policy, we develop a
               Markov chain based analytical model and derive expressions of the throughput, the
               average MAC layer service time and the service time distribution. Therefore, we
               validate the mathematical model and extend analytial results to a multi-hop
               network by simulation using the ns-2 network simulator.

               Keywords: Deadline Monotonic, 802.11, Performance evaluation, Average
               medium access delay, Throughput, Probabilistic medium access delay bounds.



1   INTRODUCTION                                           use a distributed scheduling and introduce a new
                                                           medium access backoff policy. Therefore, we focus
    Supporting applications with QoS requirements          on performance evaluation of the DM policy in terms
has become an important challenge for all                  of achievable throughput, average MAC layer
communications networks. In wireless LANs, the             service time and MAC layer service time
IEEE 802.11 protocol [5] has been enhanced and the         distribution. Hence, we follow these steps:
IEEE 802.11e protocol [6] was proposed to support                First, we propose a Markov Chain
quality of service over wireless communications.                     framework modeling the backoff process of
    In the absence of a coordination point, the IEEE                  n contending stations within the same
802.11 defines the Distributed Coordination                          broadcast region [1].
Function (DCF) based on the Carrier Sense Multiple                   Due to the complexity of the mathematical
Access with Collision Avoidance (CSMA/CA)                            model, we restrict the analysis to n
protocol. The IEEE 802.11e proposes the Enhanced                     contending stations belonging to two traffic
Distributed Channel Access (EDCA) as an extension                    categories (each traffic category is
for DCF. With EDCA, each station maintains four                      characterized by its own delay bound).
priorities called Access Categories (ACs). The                       From the analytical model, we derive the
quality of service offered to each flow depends on                   throughput achieved by each traffic
the AC to which it belongs.                                          category.
    Nevertheless, the granularity of service offered             Then, we use the generalized Z-transforms
by 802.11e (4 priorities at most) can not satisfy the                [3] to derive expressions of the average
real time flows requirements (where each flow is                     MAC layer service time and the service
characterized by its own delay bound).                               time distribution.
                                                                 As the analytical model was restricted to
    Therefore, we propose in this paper a new                        two traffic categories, analytical results are
medium access mechanism based on the Deadline                        extended by simulation to different traffic
Monotonic (DM) policy [9] to schedule real time                      categories.
flows over 802.11. Indeed DM is a real time
                                                                 Finally, we consider a simple multi-hop
scheduling policy that assigns static priorities to flow
                                                                     scenario to deduce the behavior of the DM
packets according to their deadlines; the packet with
                                                                     policy in a multi hop environment.
the shortest deadline being assigned the highest
priority. To support the DM policy over 802.11, we


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     The rest of this paper is organized as follows. In   maximum achievable throughput. The native model
section 2, we review the state of the art of the IEEE     is also extended in [10] to a non saturated
802.11 DCF, QoS support over 802.11 mainly the            environment. In [12], the authors derive the average
IEEE 80.211e EDCA and real time scheduling over           packet service time at a 802.11 node. A new
802.11. In section 3, we present the distributed          generalized Z-transform based framework has been
scheduling and introduce the new medium access            proposed in [3] to derive probabilistic bounds on
backoff policy to support DM over 802.11. In section      MAC layer service time. Therefore, it would be
4, we present our mathematical model based on             possible to provide probabilistic end to end delay
Markov chain analysis. Section 5 and 6 present            bounds in a wireless network.
respectively throughput and the service time
analysis. Analytical results are validated by             2.2 Supporting QoS over 802.11
simulation using the ns-2 network simulator [16]. In         2.2.1 Differentiation mechanisms over 802.11
section 7, we extend our study by simulation, first to         Emerging applications like audio and video
take into consideration different traffic categories,     applications require quality of service guarantees in
second, to study the behavior of the DM algorithm in      terms of throughput delay, jitter, loss rate, etc.
a multi-hop environment where factors like                Transmitting      such     flows     over    wireless
interferences or routing protocols exist. Finally, we     communications       require    supporting    service
conclude the paper in section 8.                          differentiation mechanisms over such networks.

2   LITTERATURE REVIEWS                                        Many medium access schemes have been
                                                          proposed to provide some QoS enhancements over
2.1 The 802.11 protocol                                   the IEEE 802.11 WLAN. Indeed, [4] assigns
   2.1.1 Description of the IEEE 802.11 DCF               different priorities to the incoming flows. Priority
     Using DCF, a station shall ensure that the           classes are differentiated according to one of three
channel is idle when it attempts to transmit. Then it     802.11 parameters: the backoff increase function, the
selects a random backoff in the contention                Inter Frame Spacing (IFS) and the maximum frame
window 0 , CW  1 , where CW is the current             length. Experiments show that all the three
window size and varies between the minimum and            differentiation schemes offer better guarantees for
the maximum contention window sizes. If the               the highest priority flow. But the backoff increase
channel is sensed busy, the station suspends its          function mechanism doesn’t perform well with TCP
backoff until the channel becomes idle for a              flows because ACKs affect the differentiation
Distributed Inter Frame Space (DIFS) after a              mechanism.
successful transmission or an Extended Inter Frame
Space (EIFS) after a collision. The packet is                 In [7], an algorithm is proposed to provide
transmitted when the backoff reaches zero. A packet       service differentiation using two parameters of IEEE
is dropped if it collides after maximum                   802.11, the backoff interval and the IFS. With this
retransmission attempts.                                  scheme high priority stations are more likely to
     The above described two way handshaking              access the medium than low priority ones. The above
packet transmission procedure is called basic access      described researches led to the standardization of a
mechanism. DCF defines a four way handshaking             new protocol that supports QoS over 802.11, the
technique called Request To Send/Clear To Send            IEEE 802.11e protocol [6].
(RTS/CTS) to prevent the hidden station problem. A
station S j is said to be hidden from S i if S j is         2.2.2 The IEEE 802.11e EDCA
                                                              The IEEE 802.11e proposes a new medium
within the transmission range of the receiver of S i      access mechanism called the Enhanced Distributed
and out of the transmission range of S i .                Channel Access (EDCA), that enhances the IEEE
   2.1.2 Performance evaluation of the 802.11             802.11 DCF. With EDCA, each station maintains
         DCF                                              four priorities called Access Categories (ACs). Each
     Different works have been proposed to evaluate       access category is characterized by a minimum and a
the performance of the 802.11 protocol based on           maximum contention window sizes and an
Bianchi’s work [1]. Indeed, Bianchi proposed a            Arbitration Inter Frame Spacing (AIFS).
Markov chain based analytical model to evaluate the
saturation throughput of the 802.11 protocol. By               Different analytical models have been proposed
saturation conditions, it’s meant that contending         to evaluate the performance of 802.11e EDCA. In
stations have always packets to transmit.                 [17], Xiao extends Bianchi’s model to the prioritized
     Several works extended the Bianchi model either      schemes provided by 802.11e by introducing
to suit more realistic scenarios or to evaluate other     multiple ACs with distinct minimum and maximum
performance parameters. Indeed, the authors of [2]        contention window sizes. But the AIFS
incorporate the frame retry limits in the Bianchi’s       differentiation parameter is lacking in Xiao’s model.
model and show that Bianchi overestimates the                  Recently Osterbo and Al. have proposed



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different works to evaluate the performance of the         backoff value is inferred from the deadline
IEEE 802.11e EDCA [13], [14], [15]. They proposed          information.
a model that takes into consideration all the
differentiation parameters of the EDCA especially          3   SUPPORTING DEADLINE MONOTONIC
the AIFS one. Moreover different parameters of QoS             (DM) POLICY OVER 802.11
have been evaluated such as throughput, average
service time, service time distribution and                    With DCF all the stations share the same
probabilistic response time bounds for both saturated      transmission medium. Then, the HOL (Head of Line)
and non saturated cases.                                   packets of all the stations (highest priority packets)
                                                           will contend for the channel with the same priority
     Although the IEEE 802.11e EDCA classifies the         even if they have different deadlines.
traffic into four prioritized ACs, there is still no           Introducing DM over 802.11 allows stations
guarantee of real time transmission service. This is       having packets with short deadlines to access the
due to the lack of a satisfactory scheduling method        channel with higher priority than those having
for various delay-sensitive flows. Hence, we need a        packets with long deadlines. Providing such a QoS
scheduling policy dedicated to such delay sensitive        requires distributed scheduling and a new medium
flows.                                                     access policy.

2.3 Real time scheduling over 802.11                       3.1 Distributed Scheduling over 802.11
                                                               To realize a distributed scheduling over 802.11,
    A distributed solution for the support of real-        we introduce a priority broadcast mechanism similar
time sources over IEEE 802.11, called Blackburst, is       to [18]. Indeed each station maintains a local
discussed in [8]. This scheme modifies the MAC             scheduling table with entries for HOL packets of all
protocol to send short transmissions in order to gain      other stations. Each entry in the scheduling table of
priority for real-time service. It is shown that this                                                  
                                                           node S i comprises two fields S j , D j where S j is
approach is able to support bounded delays. The
main drawback of this scheme is that it requires           the source node MAC address and D j is the
constant intervals for high priority traffic; otherwise    deadline of the HOL packet of node S j . To
the performance degrades very much.                        broadcast HOL packets deadlines, we propose to use
                                                           the two way handshake DATA/ACK access mode.
     In [18], the authors introduced a distributed
priority scheduling over 802.11 to support a class of
                                                                When a node S i transmits a DATA packet, it
dynamic priority schedulers such as Earliest
Deadline First (EDF) or Virtual Clock (VC). Indeed,        piggybacks the deadline of its HOL packet. Nodes
the EDF policy is used to schedule real time flows         hearing the DATA packet add an entry for S i in
according to their absolute deadlines, where the           their local scheduling tables by filling the
absolute deadline is the node arrival time plus the        corresponding fields. The receiver of the DATA
delay bound.                                               packet copies the priority of the HOL packet in ACK
     To realize a distributed scheduling over 802.11,      before sending the ACK frame. All the stations that
the authors of [18] used a priority broadcast              did not hear the DATA packet add an entry for S i
mechanism where each station maintains an entry for        using the information in the ACK packet.
the highest priority packet of all other stations. Thus,
stations can adjust their backoff according to other       3.2 DM medium access backoff policy
stations priorities.                                           Let’s consider two stations S 1               S2and
     The overhead introduced by the broadcast              transmitting two flows with the same deadline D1
priority mechanism is negligible. This is due to the       ( D1 is expressed as a number of 802.11 slots). The
fact that priorities are exchanged using native DATA       two stations having the same delay bound can access
and ACK packets. Nevertheless, authors of [18]             the channel with the same priority using the native
proposed a generic backoff policy that can be used         802.11 DCF.
by a class of dynamic priority schedulers no matter if          Now, we suppose that S 1 and S 2 transmit flows
this scheduler targets delay sensitive flows or rate
sensitive flows.                                           with different delay bounds D1 and D2 such as
                                                            D1  D2 , and generate two packets at time instants
    In this paper, we focus on delay sensitive flows        t 1 and t 2 . If S 2 had the same delay bound as S 1 ,
and propose to support the fixed priority Deadline
Monotonic (DM) policy over 802.11 to schedule              its packet would have been generated at time t '2 such
delay sensitive flows. For instance, we use a priority     as t '2  t 2  D 21 , where D 21  D 2  D1  .
broadcast mechanism similar to [18] and introduce a
                                                               At that time, S 1 and S 2 would have the same
new medium access backoff policy where the
                                                           priority and transmit their packets according to the


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802.11 protocol.                                           following assumptions:
    Thus, to support DM over 802.11, each station
uses a new backoff policy where the backoff is given       Assumption 1:
by:                                                        The system under study comprises n contending
   The random backoff selected in 0 , CW  1            stations hearing each other transmissions.
       according to 802.11 DCF, referred as BAsic
       Backoff (BAB).                                      Assumption 2:
   The DM Shifting Backoff (DMSB):                        Each station S i transmits a flow Fi with a delay
       corresponds to the additional backoff slots that    bound Di . The n stations are divided into two
       a station with low priority (the HOL packet
                                                           traffic categories C1 and C 2 such as:
       having a large deadline) adds to its BAB to
       have the same priority as the station with the            C1 represents n1 nodes transmitting flows
       highest priority (the HOL packet having the                     with delay bound D1 .
       shortest deadline).                                            C 2 represents n 2 nodes transmitting flows
     Whenever a station S i sends an ACK or hears                      with delay bound D2 , such as D1  D2 ,
an ACK on the channel its DMSB is revaluated as                        D 21  D 2  D1  and n1  n 2   n .
follows:
                                                           Assumption 3:
    DMSBS i   DeadlineHOLS i   DTmin S i  (1)    We operate in saturation conditions: each station has
                                                           immediately a packet available for transmission after
                                                           the service completion of the previous packet [1].
    Where DTmin S i  is the minimum of the HOL
packet deadlines present in S i scheduling table and       Assumption 4:
DeadlineHOLS i  is the HOL packet deadline of          A station selects a BAB in a constant contention
node S i .                                                 window 0 ,W  1 independently of the transmission
                                                           attempt. This is a simplifying assumption to limit the
    Hence, when S i has to transmit its HOL packet
                                                           complexity of the mathematical model.
with a delay bound Di , it selects a BAB in the
contention window 0 , CW min  1 and computes the        Assumption 5:
WHole Backoff (WHB) value as follows:                      We are in stationary conditions, i.e. the n stations
                                                           have already sent one packet at least.
             WHBS i   DMSBS i   BAB S i     (2)
                                                               Depending on the traffic category to which it
                                                           belongs, each station S i will be modeled by a
     The station S i  decrements its BAB when it
                                                           Markov Chain representing its whole backoff (WHB)
senses an idle slot. Now, we suppose that S i senses       process.
the channel busy. If a successful transmission is
heard, then S i  revaluates its DMSB when a correct       4.1 Markov chain modeling a station of category
ACK is heard. Then the station S i adds the new                     C1
                                                                 Figure 1 illustrates the Markov chain modeling a
DMSB value to its current BAB as in equation (2).
                                                           station S 1 of category C1 . The states of this Markov
Whereas, if a collision is heard, S i reinitializes its
DMSB and adds it to its current BAB to allow              chain are described by the following quadruplet
colliding stations contending with the same priority      R , i , i  j , D21  where:
as for their first transmission attempt. S i transmits
                                                                    R : takes two values denoted by C 2 and
when its WHB reaches 0. If the transmission fails, S i
doubles its contention window size and repeats the                  ~ C 2 . When R ~ C 2 , the n 2 stations of
above procedure until the packet is successfully                    category C 2 are decrementing their shifting
transmitted     or    dropped     after   maximum                    backoff (DMSB) during D21 slots and
retransmission attempts.
                                                                     wouldn’t contend for the channel. When
                                                                      R  C 2 , the D21 slots had already been
4    MATHEMATICAL MODEL OF THE DM                                    elapsed and stations of category C 2 will
     POLICY OVER 802.11                                              contend for the channel.
                                                                    i : the value of the BAB selected by S 1 in
    In this section, we propose a mathematical
model to evaluate the performance of the DM policy
                                                                     0 ,W  1 .
using Markov chain analysis [1]. We consider the


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Figure 1: Markov chain modeling a category C1 Station


       i  j  :   corresponds to the current backoff               moves     to the state ~ C 2 , i  j , i  j , D 21 ,
       of the station S 1 .                                           i  1..W  1 , j  0.. minD21  1, i  1 .
       D21 : corresponds to D 2  D1  . We choose
       the negative notation  D21 for stations of                              Now, If      S1   is in    one of     the states
        C1 to express the fact that only stations of                  C 2 , i , i  D21 , D21  , i  D21  1..W  1 and at
       category C 2 have a positive DMSB equal to                     least one of the n  1 remaining stations (either a
        D21 .                                                         category C1 or a category C 2 station) transmits,
    Initially S 1 selects a random BAB and is in                      then        S1      moves    to     one   of    the    states
one of the states ~ C 2 , i , i , D 21  , i  0..W  1 .           ~ C 2 , i  D21 , i  D21 , D21  , i  D21  1..W  1 .
During D21  1 slots, S 1 decrements its backoff if
                                                                               Markov chain modeling a station of
none of the n1  1 remaining stations of category
                                                                      4.2
                                                                               category C2
C1 transmits. Indeed, during these slots, the n 2                            Figure 2 illustrates the Markov chain modeling
                                                                      a station S 2 of category C 2 . Each state of S 2
stations of category C 2 are decrementing their
                                                                      Markov chain is represented by the quadruplet
DMSB and wouldn’t contend for the channel.
                                                                      i , k , D21  j , D21  where:
      When       S1     is    in       one     of   the     states              i : refers to the BAB value selected by S 2 in
~ C 2 , i , i  D21  1, D21  ,     i  D 21 ..W  1     and                 0 ,W  1 .
senses the channel idle, it decrements its             th
                                                      D21     slot.              k : refers to the current BAB value of S 2 .
But S 1 knows that henceforth the n 2 stations of                                D 21  j : refers to the current DMSB of S 2 ,
category C 2 can contend for the channel (the D21                                 j  0 , D21  .
slots had been elapsed). Hence, S 1 moves to one of                              D21 : corresponds to D  D  .
                                                                                                         2   1
the states C 2 , i , i  D21 , D 21  , i  D21 ..W  1 .
                                                                       When S 2 selects a BAB, its DMSB equals
     However, when the station S 1 is in one of the                   D 21 and is in one of the states i , i , D 21 , D 21  ,
states ~ C 2 , i , i  j , D 21  , for i  1..W  1 ,              i  0..W  1 . During D 21 slots, only the n1
 j  0.. minD 21  1, i  1 and at least one of the                 stations of category C1 contend for the channel.
n1  1     remaining stations              of category
                                                C1
transmits, then the stations of category C 2 will                           If S 2 senses the channel idle during D21 slots, it
reinitialize their DMSB and wouldn’t contend for                      moves to one of the states i , i ,0 , D 21  , i  0..W  1 ,
channel during additional D21 slots. Therefore, S 1                   where it ends its shifting backoff.




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Figure 2: Markov chain modeling a category C 2 Station


  When S 2 is in one of the states i , i ,0 , D 21  ,                       2  i , i , D 21  j , D 21 , i  0..W  1,
i  0..W  1 , the n 2  1 other stations of category                       j  0..D 21  1
C 2 have also decremented their DMSB and can                                 2 : the set of states of S 2 , where stations
contend for the channel. Thus, S 2 decrements its                            of category C 2 contend for the channel
BAB and moves to the state                 i , i  1,0 , D 21  ,           (pink states in figure 2).
i  2..W  1 , only if none of the      n  1 remaining                     2  i , i ,0 , D21 , i  0..W  1
stations transmits.                                                            i , i  1,0 , D 21 , i  2..W  1

  If S 2 is in one of the states i , i  1,0 , D 21  ,                 Therefore, when stations of category C1 are in
i  2..W  1 , and at least one of the n  1                       one the states of  1 , stations of category C 2 are in
remaining stations transmits, the n 2 stations of                    one of the states of  2 . Similarly, when stations of
category C 2 will reinitialize their DMSB and S 2                    category C1 are is in one of the states of  1 ,
moves to the state              i  1, i  1, D21 , D21  ,         stations of category C 2 are in one of the states of
i  2..W  1 .
                                                                     2.
4.3 Blocking probabilities in the Markov chains                            Hence, we derive the expressions of                      S1
     According to the explanations given in                          blocking probabilities            p 11 and          p 12 shown in
paragraphs 4.1 and 4.2, the states of the Markov                     figure 1 as follows:
chains modeling stations S 1 and S 2 can be divided
into the following groups:                                                  p 11 : the probability that S 1 is blocked given
                                                                             that S 1 is in one of the states of  1 . p 11 is
       1 : the set of states of S 1 where none of the                                                                '
                                                                             the probability that at least a station S 1 of
       n 2 stations of category C 2 contends for the
                                                                             the other n1  1 stations of C1 transmits
       channel (blue states in figure 1).
        1  ~ C 2 , i , i  j , D 21 , i  0..W  1,
                                                                                          '
                                                                             given that S 1 is in one of the states of  1 .
        j  0.. minmax0 , i  1, D 21  1                                                   p 11  1  1   11 n1 1                  (3)
                                                                                                                            '
                                                                             where  11 is the probability that a station S 1
       1 : the set of states of S 1 where stations of                                                   '
                                                                             of C1 transmits given that S 1 is in one of
       category C 2 can contend for the channel
                                                                             the states of  1 :
       (pink states in figure 1).
        1  C 2 , i , i  D 21 , D 21 , i  D 21 ..W  1                          '
                                                                              11  Pr S 1 transmits  1            
                                                                                                       ~ C2 ,0 ,0 , D21 
                                                                                                    1
        2 : the set of states of S 2 where stations of                                                                                     (4)
                                                                                      W 1  min max 0 ,i 1,D21 1                  
       category C 2 do not contend for the channel                                        
                                                                                           
                                                                                      i 0 
                                                                                                              1~ C2 ,i ,i  j , D21  
                                                                                                                 
                                                                                                                                         
       (blue states in figure 2).                                                                       j 0                             




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          
         1R ,i ,i  j , D21  is defined as the probability of
                                                                                                    p 22 : the probability that S 2 is blocked
        the state R , i , i  j , D21 , in the stationary
                                                                                                    given that S 2 is in one of the states of  2 .
        conditions and  1   1                  R ,i ,i  j , D21 
                                                                            is the                        p 22  1  1   12 n1 1   22 n2 1                (9)
        probability vector of a category C1 station.
                                                                                                The blocking probabilities described above
        p 12 : the probability that S 1 is blocked                                         allow deducing the transition state probabilities and
        given that S 1 is in one of the states of  1 .                                     having the transition probability matrix Pi , for a
         p 12 is the probability that at least a station                                    station of traffic category C i .
         '
        S1   of the other            n1  1            stations of C1                          Therefore, we can evaluate the state
                                         '
                                                                                            probabilities by solving the following system [11]:
        transmits given that            S1     is in one of the states
        of  1 or at least a station S '2 of the n 2                                                            i Pi   i
                                                                                                               
        stations of C 2 transmits given that                               S '2   is in                          
                                                                                                                 ij  1
                                                                                                                j
                                                                                                                                                               (10)
        one of the states of  2 .                                                                             
              p 12  1  1   12 n1 1 1   22 n2                            (5)      4.4 Transition probability matrices
                                                                                              4.4.1 Transition probability matrix of a
        where  12 is the probability that a station                                               category C1 station
          '                              '
        S 1 of C1 transmits given that S 1 is in one                                            Let P1 be the transition probability matrix of
                                                                                            the station S 1 of category C1 . P1 i , j is the
        of the states of  1 .
                               '
                                 
                    12  Pr S 1 transmits  1                                             probability to transit from state i to state j . We
                                                                                            have:
                                        C2 ,D21 ,0 , D21 
                                     1
                                W 1
                                                                                   (6)      P1 ~ C 2 , i , i  j , D 21 , ~ C 2 , i , i   j  1, D 21 
                                 
                              i  D21
                                        1C2 ,i ,i  D21 , D21 
                                                                                             1  p11 , i  2..W  1, j  0.. mini  2 , D 21  2 
                                                                                                                                                           (11)
                                                                                            P1 ~ C 2 , i ,1, D 21 , ~ C 2 ,0 ,0 , D 21   1  p11 ,
                                                  '
        and  22 the probability that a station S 2 of                                      i  1.. minW  1, D 21  1
                                   '
        C 2 transmits given that S 2 is in one of the                                                                                                        (12)
        states of  2 .                                                                     P1 ~ C 2 , i , i  D 21  1, D 21 , C 2 , i , i  D 21 , D 21 
                                                                                             1  p 11 , i  D 21 ..W  1
                     '
           12  Pr S 2 transmits  2                                                                                                                         (13)
                                     2   0 ,0 ,0 ,D21                                     P1~ C2 , i , i  j , D21 , ~ C2 , i  j , i  j , D21 
                                                                                                                                                               (14)
                   W 1                        W 1
                                                                                   (7)        p11 , i  2..W  1, j  1.. mini  1, D21  1
                           i ,i ,0 ,D21 
                             2                            i ,i 1,0 ,D21 
                                                             2
                    i 0                           i2                                      P1~ C2 , i , i , D21 , ~ C2 , i , i , D21   p11 ,
                                                                                                                                                               (15)
                                                                                            i  1..W  1
          
         2i ,k ,D21  j ,D21  is defined as the probability
        of the state             i , k , D21  j , D 21 ,                 in the          P1C2 ,i ,i  D21 , D21 ,~ C2 ,i  D21 ,i  D21 , D21 
                                                                                             p12 ,i  D21  1..W  1
        stationary condition.  2   2                        i ,k ,D21  j ,D21 
                                                                                                                                                              (16)
        is the probability vector of a category C 2
        station.                                                                            P1C2 ,i ,i  D21 , D21 ,C2 ,i  1,i  1  D21 , D21 
                                                                                             1  p12 ,i  D21  1..W  1
      In the same way, we evaluate p 21 and p 22 the
                                                                                                                                                               (17)
blocking probabilities of station S 2 shown in
figure 2:                                                                                                                                        1
                                                                                            P1~ C2 ,0 ,0 , D21 , ~ C2 , i , i , D21       ,
       p 21 : the probability that S 2 is blocked                                                                                               W             (18)
        given that S 2 is in one of the states of  2 .                                     i  0..W  1
                             p 21  1  1   11               n1
                                                                                   (8)
                                                                                              If D 21  W  then:



                             Ubiquitous Computing and Communication Journal                                                                                   -7 -
P1C2 , D21 ,0 , D21 , ~ C2 , i , i , D21  
                                                         1
                                                           ,                              11  f  11 , 12 , 22 
                                                         W                 (19)            f  , , 
                                                                                          12
                                                                                         
                                                                                                       11 12 22
i  0..W  1
                                                                                          22  f  11 , 12 , 22 
                                                                                         under the constraint
    By replacing p11 and p 12 by their values in                                         
equations (3) and (5) and by replacing P1 and  1                                         11  0 , 12  0 , 22  0 , 11  1, 12  1, 22  1
                                                                                         
in (10) and solving the resulting system, we can                                                                                              (28)
               R ,i ,i  j , D21 
express  1                            as a function of  11 ,  12 and                  Solving the above system (28), allows deducing
 22 given respectively by equations (4), (6) and                                    the expressions of  11 ,  12 and  22 , and deriving
(7).                                                                                 the state probabilities of Markov chains modeling
                                                                                     category C1 and category C 2 stations.
  4.4.2 Transition probability matrix of a
       category C2 station
    Let P2 be the transition probability matrix of                                   5    THROUGHPUT ANALYSIS
the station S 2 belonging to the traffic category C 2 .
The transition probabilities of S 2 are:                                                  In this section, we propose to evaluate Bi , the
                                                                                     normalized throughput achieved by a station of
P2 i , i , D21  j , D21 , i , i , D21   j  1, D21                         traffic category C i [1]. Hence, we define:
                                                                           (20)
 1  p21 , i  0..W  1, j  0..D21  1
                                                                                          Pi ,s : the probability that a station                      Si
P2 i , i , D21  j , D21 , i , i , D21 , D21   p21 ,                               belonging to traffic category C i transmits a
                                                                           (21)
i  0..W  1, j  0..D21  1                                                            packet successfully. Let S 1 and S 2 be two
                                                                                          stations belonging respectively to traffic
 P2 i , i ,0 , D21 , i , i  1,0 , D21   1  p22 ,                                 categories C1 and C 2 . We have:
                                                                           (22)
i  2..W  1
                                                                                     P1,s  Pr S1 transmits successfully 1              Pr1 
P2 1,1,0 , D21 , 0 ,0 ,0 , D21   1  p22                            (23)       Pr S1 transmits successfully  1            Pr 1 
                                                                                       11 1  p11  Pr 1    12 1  p12  Pr  1 
P2 i , i ,0 , D21 , i , i , D21 , D21   p22 ,
                                                                           (24)                                                                      (29)
i  1..W  1
                                                                                     P2 ,s  Pr S 2 transmits successfully  2           Pr  2 
P2 i , i  1,0 , D21 , i  1, i  1, D21 , D21   p22 ,
                                                                          (25)        Pr S 2 transmits successfully  2            Pr 2 
i  2..W  1
                                                                                       22 1  p 22  Pr  2 
 P2 i , i  1,0 , D21 , i  1, i  2 ,0 , D21   1  p22 ,                                                                           (30)
                                                                           (26)
i  3..W  1                                                                              Pidle : the probability that the channel is idle.
                                                 1
 P2 0 ,0 ,0 , D21 , i , i , D21 , D21       , i  0..W  1 (27)
                                                 W                                        The channel is idle if the n1 stations of
                                                                                     category C1 don’t transmit given that these stations
     By replacing p 21 and p 22 by their values in                                   are in one of the states of  1 or if the n stations
equations (8) and (9) and by replacing P2 and  2                                    (both category C1 and category C 2 stations) don’t
in (10) and solving the resulting system, we can
                                                                                     transmit given that stations of category C1 are in
               i ,k ,D21  j ,D21 
express  2                              as a function of  11 ,  12                one of the states of  1 . Thus:
and  22 given respectively by equations (4), (6)
                                                       R ,i ,i  j , D21 
and (7). Moreover, by replacing  1                                            and   Pidle  1   11 n1 Pr  1   1   12 n1 1   22 n2 Pr  1 
  
 2i ,k ,D21  j ,D21  by their values, in equations (4), (6)                                                                                     (31)

and (7), we obtain a system of non linear equations                                      Hence, the expression of the throughput of a
as follows:                                                                          category C i station is given by:




                                       Ubiquitous Computing and Communication Journal                                                                -8 -
                                 Pi ,s T p                                8 and we depict the throughput achieved by the
    Bi                                                                   different stations present in the network as a
                                                 2              
             PIdle Te  Ps T s   1  PIdle 
                                 
                                 
                                                 n P
                                                 i 1
                                                        i i ,s
                                                                 Tc
                                                                 
                                                                 
                                                                          function of the contention window size W ,
                                                                           D 21  1 . We notice that the throughput achieved
                                                                   (32)   by category C1 stations (stations numbered from
                                                                          S 11 to S 14 ) is greater than the one achieved by
    Where Te denotes the duration of an empty
                                                                          category C 2 stations (stations numbered from S 21
slot, Ts and Tc denote respectively the duration of
                                                                          to S 24 ).
a successful transmission and a collision.
               2           
 1  PIdle 


              
              i 1
                   ni Pi ,s 
                            
                            
                              corresponds to    the

probability of collision. Finally T p denotes the
average time required to transmit the packet data
payload. We have:

                                   
Ts  T PHY  TMAC  T p  T D  SIFS 
                                                                  (33)
TPHY      T ACK  T D   DIFS

      
Tc  TPHY  TMAC  T p  TD  EIFS                               (34)

     Where T PHY , TMAC and T ACK are the
durations of the PHY header, the MAC header and
the ACK packet [1], [13]. TD is the time required to                      Figure 3: Normalized throughput as a function of
transmit the two bytes deadline information.                              the contention window size D 21  1, n  8 
Stations hearing a collision wait during EIFS before
resuming their packets.                                                        Analytically, stations belonging to the same
                                                                          traffic category have the same throughput given by
     For numerical results stations transmit 512                          equation (32). Simulation results validate analytical
bytes data packets using 802.11.b MAC and PHY                             results and show that stations belonging to the same
layers parameters (given in table 1) with a data rate                     traffic category (either category C1 or category
equal to 11Mbps. For simulation scenarios, the                            C 2 ) have nearly the same throughput. Thus, we
propagation model is a two ray ground model. The
                                                                          conclude the fairness of DM between stations of the
transmission range of each node is 250m. The
                                                                          same category.
distance between two neighbors is 5m. The EIFS
parameter is set to ACKTimeout as in ns-2, where:
                                                                              For subsequent throughput scenarios, we focus
                                                                          on one representative station of each traffic
ACKTimeout  DIFS  T PHY  T ACK  T D   SIFS
                                                                          category. Figure 4, compares category C1 and
                                              (35)
                                                                          category C 2 stations throughputs to the one
Table 1: 802.11 b parameters.                                             obtained with 802.11.

                                    11 Mb/s                                   Curves are represented as a function of W and
             Data Rate
                 Slot                20 µs                                for different values of D 21 . Indeed as D 21
                SIFS                 10 µs                                increases, the category C1 station throughput
                DIFS                 50 µs                                increases, whereas the category C 2 station
            PHY Header               192 µs                               throughput decreases. Moreover as W increases,
            MAC Header               272 µs                               the difference between stations throughputs is
                ACK                 112 µs                                reduced. This is due to the fact that the shifting
          Short Retry Limit            7                                  backoff becomes negligible compared to the
                                                                          contention window size.
     For all the scenarios, we consider that we are in
                                           n                                  Finally, we notice that the category C1 station
presence of n contending stations with        stations                    obtains better throughput with DM than with
                                           2
for each traffic category. In figure 3, n is fixed to



                            Ubiquitous Computing and Communication Journal                                                -9 -
802.11, but the opposite scenario happens to the        expression of the average service time and the
category C 2 station.                                   service time distribution. The service time depends
                                                        on the duration of an idle slot Te , the duration of a
                                                        successful transmission Ts and the duration of a
                                                        collision Tc [1], [3],[14]. As Te is the smallest
                                                        duration event, the duration of all events will be
                                                                  T     
                                                        given by  event  .
                                                                    Te 

                                                        6.1 Z-Transform of the MAC layer service time

                                                          6.1.1 Service time Z-transform of a category
                                                               C1 station:
                                                            Let TS 1 Z  be the service time Z-transform of
                                                        a station S 1 belonging to traffic category C1 . We
Figure 4: Normalized throughput as a function of
                                                        define:
the contention window size (different D 21 values)
                                                              H 1R ,i ,i  j , D21  Z  : The Z-transform of the
     In figure 5, we generalize the results for
different numbers of contending stations and fix the    time already elapsed from the instant S 1 selects a
contention window size W to 32.                         basic backoff in 0 ,W  1 (i.e. being in one of the
                                                        states ~ C 2 , i , i , D21  ) to the time it is found in the
                                                        state R , i , i  j , D 21  .
                                                             Moreover, we define:

                                                                    11
                                                                 Psuc : the probability that S 1 observes a
                                                                 successful transmission on the channel,
                                                                 while S 1 is in one of the states of  1 .
                                                                              Psuc  n1  1 11 1   11 n1  2
                                                                                11
                                                                                                                                      (36)

                                                                    12
                                                                 Psuc : the probability that S 1 observes a
                                                                 successful transmission on the channel,
                                                                 while S 1 is in one of the states of  1 .
Figure 5: Normalized throughput as a function of
                                                                   Psuc  n1  1 12 1   12 n1  2 1   22 n2
                                                                     12
the number of contending stations                                                                                                     (37)
                                                                         n2 22 1   22 n2 1 1   12 n1 1
     All the curves show that DM performs service
differentiation over 802.11 and offers better               We evaluate H 1R ,i ,i  j , D21  Z  for each state
throughput for category C1 stations independently
                                                        of S 1 Markov chain as follows:
of the number of contending stations.

                                                                                                       Ts 
                                                                                        1  11  Te 
6   SERVICE TIME ANALYSIS                                 H 1~ C2 ,i ,i , D21 Z        Psuc Z   
                                                                                        W 
                                                                                               
                                                                                               
     In this section, we evaluate the average MAC
                                                                               Tc  
layer service time of category C1 and category C 2                              min i  D21 1,W 1

stations using the DM policy. The service time is                   11
                                                                         
                                                          p11  Psuc Z  e  
                                                                                T 
                                                                                                H 1~ C 2 ,k ,i , D21  Z 
the time interval from the time instant that a packet                                
                                                                                     
                                                                                          k i 1

becomes at the head of the queue and starts to                                                       Ts                  Tc  
                                                                                             12  Te 
                                                                                                                                
                                                                                                                            
contend for transmission to the time instant that
                                                           H C 2 ,i  D21 ,i , D21  Z  Psuc Z
                                                            ˆ1                                                      12     T
                                                                                                             p11  Psuc Z  e  
either the packet is acknowledged for a successful                                                                               
transmission or dropped [3].                                                                                                     
                                                                                                                                      (38)
  We propose to evaluate the Z-Transform of the               Where:
MAC layer service time [3], [14], [15] to derive an


                       Ubiquitous Computing and Communication Journal                                                                - 10 -
 H 1C ,i  D ,i , D  Z   H 1C ,i  D ,i , D  Z 
  ˆ                                                                                                                  Ts 

                                                                                                                             1  p11 H 1~ C ,0 ,0 , D
                                                                                                                     
                                                                                                 TS1 Z   Z                                                     Z 
       2       21        21             2   21      21
                                                                                                                     Te 

if i  D 21   W  1                                     (39)                                                                                 2          21 

ˆ                                                                                                                                                   m   c
                                                                                                                                                          T 
 H 1C2 ,i  D21 ,i , D21  Z   0 Otherwise

                                                                                                   1  p12 H 1C2 ,D21 ,0 , D21  Z             Te 
                                                                                                                                                        Z            p11H 1~C ,0 ,0 , D          Z 
                                                                                                                                                                                 2           21 
                                                                                                                                                   
                                                                                                                                                 i 0
      We also have:                                                                                                                                     
                                                                                                   p12 H 1C 2 ,D21 ,0 , D21  Z     i

                                      1  p11 Z  j H 1~ C2 ,i ,i , D21  Z                                                                                                            m 1
 H 1~ C2 ,i ,i  j , D21  Z                                                                     Tc 
                                                                                                     T 
                                                                                                                                                                                  
                                                                                                                                                                                  
                                                   Ts                               Tc 
                                                                                                              
                                                                                                    Z  e  p11 H 1~ C2 ,0 ,0 , D21 Z   p12 H 1C 2 ,D21 ,0 , D21  Z        
                                                                                      
                                                                                    
                                             11  Te                           11     T
                                      1   Psuc Z                p11        Psuc Z  e                                                                                        
                                                                                                                                                                                 
i  2..W  1, j  1..mini  1, D21  1
                                                                                           (40)                                                                                  (44)

                                      1  p11 Z D21 H 1~ C2 ,i ,i , D21 Z                     6.1.2 Service time Z-transform of a category
H 1C2 ,i ,i  D21 , D21  Z                                                                            C2 station:
                                                        Ts                          Tc 

                                                                                                       In the same way, let TS 2 Z  be the service
                                                                                    
                                            11
                                      1  Psuc Z        Te     p11          11     T
                                                                              Psuc Z  e 
 1  p12 ZH 1C2 ,i 1,i 1 D21 , D21  Z ,i  D21 ..W  2                                 time Z-transform of a station S 2 of category C 2 .
                                                                                                  We define:
                                                                                           (41)
                                                                                                      H 2i ,k ,D21  j ,D21  Z  : The Z-transform of the
H 1C2 ,W 1,W 1 D21 , D21 Z                                                                time already elapsed from the instant S 2 selects a
    1  p11 Z     D21
                            H 1~ C 2 ,W 1,W 1, D21  Z                                      basic backoff in 0 ,W  1 (i.e. being in one of the
                                                                                          (42)
                        Ts                             Tc                                     states i , i , D 21 , D 21  ) to the time it is found in the
                                                  
                                                       
               11
         1  Psuc Z 
                         Te              11
                                 p11  Psuc Z 
                                                          Te 
                                                                                                  state i , k , D21  j , D21  .
                                                                                                       Moreover, we define:
                                      1  p11 ZH 1~ C2 ,1,1, D21  Z 
H 1~ C2 ,0 ,0 , D21  Z                                                                                   21
                                               Ts                                  Tc                   Psuc : the probability that S 2 observes a
                                                                                  
                                                                                   
                                         11  Te                             11      T
                                  1   Psuc Z             p11             Psuc   Z e                    successful transmission on the channel,
                  min W 1,D21 1                                                                         while S 2 is in one of the states of  2 .
                                                                        1
 1  p11 Z              H 1
                            i2
                                      ~ C 2 ,i ,1, D21    Z  
                                                                        W                                                         Psuc  n1 11 1   11 n1 1
                                                                                                                                    21
                                                                                                                                                                                  (45)
                                                                                           (43)
                                                                                                               22
                                                                                                            Psuc : the probability that S 2 observes a
    If S 1 transmission state is ~ C 2 ,0 ,0 , D 21  ,                                                   successful transmission on the channel,
the transmission will be successful only if none of                                                         while S 2 is in one of the states of  2 .
the n1  1 remaining stations of C1 transmits.                                                                  Psuc  n1 12 1   12 n1 1 1   22 n2 1
                                                                                                                    22

Whereas when the station S 1 transmission state is                                                                                                                               (46)
                                                                                                                   n2  1 22 1   22 n2  2 1   12 n1
C 2 , D21 ,0 , D 21  , the transmission occurs
successfully only if none of                                 n  1          remaining               We evaluate H 2i ,i ,D21  j ,D21  Z  for each state
stations (either a category C1 or a category C 2
                                                                                                  of S 2 Markov chain as follows:
station) transmits.
                                                                                                                               1
                                                                                                   H 2i ,i ,D21 ,D21  Z     , i  0 and i  W  1   (47)
    If the transmission fails, S 1 tries another                                                                               W
transmission. After m retransmissions, if the                                                                                             Ts 
                                                                                                                              1  22  Te 
packet is not acknowledged, it will be dropped.                                                   H 2i ,i ,D21 ,D21  Z      Psuc Z   
Thus, the Z-transform of station S 1 service time is:                                                                         W 
                                                                                                                                 
                                                                                                                          Tc    
                                                                                                                   Z            
                                                                                                                          
                                                                                                                          Te 
                                                                                                                                   H 2i 1,i ,0 ,D21  Z , i  1..W  2
                                                                                                               22
                                                                                                      p 22  Psuc
                                                                                                                                  
                                                                                                                                  
                                                                                                                                                                                 (48)




                                       Ubiquitous Computing and Communication Journal                                                                                          - 11 -
      To compute H 2i ,i ,D21  j ,D21  Z  , we                  define                        Tc                          
                                                                                                                                              m 1
                                                                                                                               
Tdec Z  , such as:
  j                                                                           TS 2 Z    p 22 Z  Te  H 2
                                                                                                              0 ,0 ,0 ,D21  Z                   
                                                                                                                                 
                                                                                                                                 
Tdec Z   1
  0
                                                                      (49)                    Ts                                               Tc                          
                                                                                                                                                                                    i
                                                                                                                                m
                                                                                                                                                                             
                                        1  p 21 Z
                                                                              1  p 22 Z    Te  H 2
                                                                                                                             
                                                                                                          0 ,0 ,0 ,D21  Z            p 22 Z
                                                                                                                                        
                                                                                                                                                  Te  H 2
                                                                                                                                                            0 ,0 ,0 ,D21  Z 
                                                                                                                                                                                
Tdec Z  
  j                                                                                                                              i 0
                                                                                                                                                                               
                        Ts                Tc  
                21  Te 
                                                       
                                                                                                                                                        (55)
           1   Psuc Z    p        21    Te  T j 1 Z 
                                21  Psuc Z         dec
                                                  
                                                  
                                                                              6.2 Average Service Time
for j  1..D 21
                                                                                  From equations (44) (respectively equation
                                                      (50)                    (55)), we derive the average service time of a
                                                                              category C1 station ( respectively a category C 2
      So:
                                                                              station). The average service time of a category C i
                                                                              station is given by:
H 2i ,i ,D21  j ,D21  Z   H 2i ,i ,D21  j 1,D21  Z  j
                                                              Tdec   Z ,
                                                                                                   X i  TS i1 1          (56)
i  0..W  1, j  1..D21 , i , j   0 , D 21 
                                                                       (51)
      And:
                                                                                  Where TS i1 Z  , is the derivate of the service
H 2i ,i 1,0 ,D21  Z   1  p 22 ZH 2i 1,i ,0 ,D21  Z              time Z-transform of a category C i station [11].
                 1  p 22 ZH 2i ,i ,0 ,D21  Z                                By considering the same configuration as in

               Ts                Tc                                     figure 3, we depict in figure 5, the average service
       22  Te 
                                           
                                    
  1   Psuc Z    p        22    Te  T D21 Z                           time of category C1 and category C 2 stations as a
                       22  Psuc Z         dec
                                                                            function of W . As for the throughput analysis,
                                         
                                                                              stations belonging to the same traffic category have
i  2..W  2                                                                  nearly the same average service value. Simulation
                                                                       (52)   service time values coincide with analytical values
                                                                              given by equation (56). These results confirm the
H 2W 1,W  2 ,0 ,D21  Z                                                  fairness of DM in serving stations of the same
             1  p 22 ZH 2W 1,W 1,0 ,D21  Z                           category.

                 Ts                Tc            (53)
         22  Te 
                                            
                                      
    1   Psuc Z    p        22    Te  T D21 Z 
                         22  Psuc Z         dec
                                           
                                           


    According to figure 2 and using equation (51),
we have:

H 20 ,0 ,0 ,D21  Z   H 20 ,1,0 ,D21  Z Tdec Z 
                                                  D21


                 1  p 22 ZH 21,1,0 ,D21  Z 

                 Ts                Tc            (54)
         22  Te 
                                           
                                      
    1   Psuc Z    p        22    Te  T D21 Z 
                         22  Psuc Z         dec
                                           
                                           
                                                                              Figure 6: Average service time as a function of the
                                                                              contention window size D 21  1, n  8 
    Therefore, we can derive an expression of S 2
Z-transform service time as follows:
                                                                                  In figure 7, we show that category C1 stations
                                                                              obtain better average service time than the one
                                                                              obtained with 802.11 protocol. Whereas, the
                                                                              opposite scenario happens for category C 2 stations



                                 Ubiquitous Computing and Communication Journal                                                                           - 12 -
independently of n , the number of contending           exceeds 0.01s equals 0.2%. Whereas, station S 2
stations in the network.                                service time exceeds 0.01s with the probability
                                                        57,6%. Thus, DM offers better service time
                                                        guarantees for the stations with the highest priority.

                                                            In figure 9, we double the size of the contention
                                                        window size and set it to 64. We notice that
                                                        category C1 and category C 2 stations service time
                                                        curves become closer. Indeed, when W becomes
                                                        large, the BAB values increase and the DMSB
                                                        becomes negligible compared to the basic backoff.
                                                        The whole backoff values of S 1 and S 2 become
                                                        closer and their service time accordingly.




Figure 7: Average service time as a function of the
number of contending stations

6.3 Service Time Distribution

    Service time distribution is obtained by
inverting the service time Z transforms given by
equations (44) and (55). But we are most interested
in probabilistic service time bounds derived by
inverting the complementary service time Z
transform given by [11]:
                                                        Figure 9: Complementary service time distribution
                ~          1  TS i Z                 for different values of D21 ( W  64 )
                X i Z                        (56)
                              1 Z
                                                            In figure 10, we depict the complementary
     In figure 8, we depict analytical and simulation   service time distribution for both category C1 and
values of the complementary service time
                                                        category C 2 stations and for different values of n ,
distribution of a category C1 and a category C 2
                                                        the number of contending nodes.
stations for different values of D21 and W  32  .




                                                        Figure 10: Complementary service time
Figure 8: Complementary service time distribution       distribution for different values of the contending
for different values of D21 , W  32                  stations

    All the curves drop gradually to 0 as the delay         Analytical and simulation results show that
increases. Category C1 stations curves drop to 0        complementary service time curves drop faster
                                                        when the number of contending stations is small for
faster than category C 2 curves. Indeed, when           both category C1 and category C 2 stations. This
D21  4 slots, the probability that S 1 service time    means that all stations service time increases as the


                        Ubiquitous Computing and Communication Journal                                 - 13 -
number of contending nodes increases.                               by different traffic categories stations as a function
                                                                    of the minimum contention window size CW min
                                                                    such as CW min is always smaller than CW max ,
7   EXTENTIONS OF THE ANAYTICAL
    RESULTS BY SIMULATION                                            CW max  1024 and K =1.
                                                                        Analytical and simulation results show that
     The mathematical analysis undertaken above                     throughput values increase with stations priorities.
showed that DM performs service differentiation                     Indeed, the station with the lowest delay bound has
over 802.11 protocol and offers better QoS                          the maximum throughput.
guarantees for highest priority stations
     Nevertheless, the analysis was restricted to two                     Moreover, figure 12 shows that stations
traffic categories. In this section, we first generalize            belonging to the same traffic category have the
the results by simulation for different traffic                     same throughput. For instance, when n is set to 15
categories. Then, we consider a simple multi-hop                    (i.e. m  3 ), the three stations each traffic category
and evaluate the performance of the DM policy                       have almost the same throughput.
when the stations belong to different broadcast
regions.

7.1 Extension of the analytical results
    In this section, we consider n stations
contending for the channel in the same broadcast
region. The n stations belong to 5 traffic categories
where n  5m and m is the number of stations of
the same traffic category. A traffic category C i is
characterized     by      a    delay     bound        Di ,   and
Dij  Di  D j     is the difference between the
deadline values of category C i and category C j
stations. We have:
                          Dij  i  j K                    (57)   Figure 12: Normalized throughput: different
    Where K is the deadline multiplicity factor                     stations belonging to the same traffic category
and is given by:
                 Di 1,i  Di 1  Di  K  (58)                           In figure 13, we depict the average service
                                                                    time of the different traffic categories stations as a
                                                                    function of K , the deadline multiplicity factor. We
    Indeed, when K varies, the Dij the difference                   notice that the highest priority station average
between deadline values of category C i                      and    service time decreases as the deadline multiplicity
category     Cj        stations   also      varies.     Stations    factor increases. Whereas, the lowest priority
                                                                    station average service time increases with K .
belonging to the traffic category C i are numbered
from S i 1 to S im .




                                                                    Figure 13: Average service time as a function of
Figure 11: Normalized throughput for different                      the deadline multiplicity factor K
traffic category stations
                                                                       In the same way, the probabilistic service time
    In figure 11, we depict the throughput achieved                 bounds offered to S 11 (the highest priority station)



                              Ubiquitous Computing and Communication Journal                                        - 14 -
are better than those offered to station S 51 (the          Flows packets are routed using the Ad-hoc On
lowest priority station). Indeed, the probability that   Demand (AODV) protocol. Flows F1 and F2 are
 S 11 service time exceeds 0.01s=0.3%. But, station      respectively transmitted by stations S 1 and S 2
S 51 service time exceeds 0.01s with the probability     with   delay    bounds      D1   and    D2    and
of 36%.                                                   D 21  D 2  D1 =5 slots. Flows F3 and F4 are
                                                         transmitted respectively by S 3 and S 4 and have
                                                         the same delay bound. Finally, F5 and F6 are
                                                         transmitted respectively by S 5 and S 6 with delay
                                                         bounds D5 and D6 and D65  D6  D5 = 4 slots.

                                                            Figure 16 shows that the throughput achieved
                                                         by F1 is smaller than the one achieved by F2 .
                                                         Indeed, both flows cross nodes 6 and 7, where F1
                                                         got a higher priority to access the medium than F2
                                                         when the DM policy is used. We obtain the same
                                                         results for flows F and F . Flows F3 and F4
                                                                             5        6
Figure 14: Complementary              service    time    have almost the same throughput since they have
distribution CWmin  32 , n  8                        equal deadlines.

    The above results generalize the analytical
model results and show once again that DM
performs service differentiation over 802.11 and
offer better guarantees in terms of throughput,
average service time and probabilistic service time
bounds for flows with short deadlines.

7.2 Simple Multi hop scenario
    In the above study, we considered that
contending stations belong to the same broadcast
region. In reality, stations may not be within one
hop from each other. Thus a packet can go through
several hops before reaching its destination. Hence,
factors like routing protocols or interferences may
preclude the DM policy from working correctly.           Figure 16: Normalized throughput using DM
                                                         policy
     In the following paragraph, we evaluate the
performance of the DM policy in a multi-hop                        Figure 17 show that the complementary
environment. Hence, we consider a 13 node simple         service time distribution curves drop to 0 faster for
mtlti-hop scenario described in figure 15. Six flows     flow F1 than for flow F2 .
are transmitted over the network.




                                                         Figure 17: End to end complementary service time
Figure 15: Simple multi hop scenario                     distribution



                       Ubiquitous Computing and Communication Journal                                  - 15 -
    The same behavior is obtained for flow F5 and           (PHY) specification, IEEE (1999).
F6 , where F5 has the shortest delay bound.            IEEE 802.11 WG: Draft Supplement to Part 11:
                                                            Wireless Medium Access Control (MAC) and
                                                            physical layer (PHY) specifications: Medium
     Hence, we conclude that even in a multi-hop            Access Control (MAC) Enhancements for
environment, the DM policy performs service                 Quality of Service (QoS), IEEE 802.11e/D13.0,
differentiation over 802.11 and provides better QoS         (January 2005).
guarantees for flows with short deadlines.             J. Deng, R. S. Chang: A priority Scheme for IEEE
                                                            802.11 DCF Access Method, IEICE
                                                            Transactions in Communications, vol. 82-B,
8   CONCLUSION                                              no. 1, (January 1999).
                                                       J.L. Sobrinho, A.S. Krishnakumar: Real-time traffic
     In this paper we proposed to support the DM            over the IEEE 802.11 medium access control
policy over 802.11 protocol. Therefore, we used a           layer, Bell Labs Technical Journal, pp. 172-
distributed backoff scheduling algorithm and                187, (1996).
introduced a new medium access backoff policy.         J. Y. T. Leung, J. Whitehead: On the Complexity of
Then we proposed a Markov Chain based                       Fixed-Priority Scheduling of Periodic, Real-
mathematical model to evaluate the performance of           Time      Tasks,     Performance     Evaluation
the DM policy in terms of throughput , average              (Netherlands), pp. 237-250, (1982).
medium access delay and medium access delay            K. Duffy, D. Malone, D. J. Leith: Modeling the
distribution. Analytical and simulation results             802.11 Distributed Coordination Function in
showed that DM performs service differentiation             Non-saturated       Conditions,     IEEE/ACM
over 802.11 and offers better guarantees in terms of        Transactions on Networking (TON),
throughput, average service time and probabilistic          Vol. 15 , pp. 159-172 (February 2007)
service time bounds for flows with small deadlines.    L. Kleinrock: Queuing Systems,Vol. 1: Theory,
Moreover, DM achieves fairness between stations             Wiley Interscience, 1976.
belonging to the same traffic category.                P. Chatzimisios, V. Vitsas, A. C. Boucouvalas:
                                                            Throughput and delay analysis of IEEE 802.11
     Then, we extended by simulation the analytical         protocol, in Proceedings of 2002 IEEE 5th
results obtained for two traffic categories to              International    Workshop      on Networked
different traffic categories. Simulation results            Appliances, (2002).
showed that even if contending stations belong to      P.E. Engelstad, O.N. Osterbo: Delay and
 K traffic categories, K  2 , the DM policy offers         Throughput Analysis of IEEE 802.11e EDCA
better QoS guarantees for highest priority stations.        with Starvation Prediction, In proceedings of
Finally, we considered a simple multi-hop scenario          the The IEEE Conference on Local Computer
and concluded that factors like routing messages or         Networks , LCN’05 (2005).
interferences don’t impact the behavior of the DM      P.E. Engelstad, O.N. Osterbo: Queueing Delay
policy and DM still provides better QoS guarantees          Analysis of 802.11e EDCA, Proceedings of
for stations with short deadlines.                          The Third Annual Conference on Wireless On
                                                            demand Network Systems and Services
                                                            (WONS 2006), France, (January 2006).
9   REFERENCES                                         P.E. Engelstad, O.N. Osterbo: The Delay
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G. Bianchi: Performance Analysis of the IEEE                802.11 DCF, in the proceeding of 25th IEEE
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    Access Control (MAC) and Physical Layer



                      Ubiquitous Computing and Communication Journal                                - 16 -

								
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