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: email@example.com Leila.firstname.lastname@example.org
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  has been enhanced and the distribution. Hence, we follow these steps:
IEEE 802.11e protocol  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 .
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  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  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  to a non saturated
802.11 DCF, QoS support over 802.11 mainly the environment. In , 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  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 . 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,  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 , 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 .
(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 . 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. , 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  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 , , . 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 . Indeed each station maintains a local
discussed in . 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 , 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  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  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  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 .
DMSBS i DeadlineHOLS 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 .
Where DTmin S i is the minimum of the HOL
packet deadlines present in S i scheduling table and Assumption 4:
DeadlineHOLS 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.
WHBS i DMSBS 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
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 . 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.. minD21 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
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 .
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.. minD 21 1, i 1 and at least one of the stations of category C1 contend for the channel.
n1 1 remaining stations of category
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 .
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.. minmax0 , 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
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
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 :
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
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
C2 ,D21 ,0 , D21
(6) P1 ~ C 2 , i , i j , D 21 , ~ C 2 , i , i j 1, D 21
1C2 ,i ,i D21 , D21
1 p11 , i 2..W 1, j 0.. mini 2 , D 21 2
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.. minW 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
W 1 W 1
(7) p11 , i 2..W 1, j 1.. mini 1, D21 1
i ,i ,0 ,D21
2 i ,i 1,0 ,D21
i 0 i2 P1~ C2 , i , i , D21 , ~ C2 , i , i , D21 p11 ,
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 P1C2 ,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
is the probability vector of a category C 2
station. P1C2 ,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
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
If D 21 W then:
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P1C2 , D21 ,0 , D21 , ~ C2 , i , i , D21
, 11 f 11 , 12 , 22
W (19) f , ,
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 . Hence, we define:
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
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:
i 2..W 1
P1,s Pr S1 transmits successfully 1 Pr1
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 ,
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)
i 3..W 1 Pidle : the probability that the channel is idle.
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
PIdle Te Ps T s 1 PIdle
i i ,s
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.
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
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 , . 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
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
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
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
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 , ,. As Te is the smallest
duration event, the duration of all events will be
given by event .
6.1 Z-Transform of the MAC layer service time
6.1.1 Service time Z-transform of a category
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
the contention window size (different D 21 values)
H 1R ,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:
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
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
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 1R ,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.
1 11 Te
6 SERVICE TIME ANALYSIS H 1~ C2 ,i ,i , D21 Z Psuc Z
In this section, we evaluate the average MAC
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
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
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 .
We propose to evaluate the Z-Transform of the Where:
MAC layer service time , ,  to derive an
Ubiquitous Computing and Communication Journal - 10 -
H 1C ,i D ,i , D Z H 1C ,i D ,i , D Z
1 p11 H 1~ C ,0 ,0 , D
TS1 Z Z Z
2 21 21 2 21 21
if i D 21 W 1 (39) 2 21
ˆ m c
H 1C2 ,i D21 ,i , D21 Z 0 Otherwise
1 p12 H 1C2 ,D21 ,0 , D21 Z Te
Z p11H 1~C ,0 ,0 , D Z
We also have:
p12 H 1C 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
Z e p11 H 1~ C2 ,0 ,0 , D21 Z p12 H 1C 2 ,D21 ,0 , D21 Z
11 Te 11 T
1 Psuc Z p11 Psuc Z e
i 2..W 1, j 1..mini 1, D21 1
1 p11 Z D21 H 1~ C2 ,i ,i , D21 Z 6.1.2 Service time Z-transform of a category
H 1C2 ,i ,i D21 , D21 Z C2 station:
In the same way, let TS 2 Z be the service
1 Psuc Z Te p11 11 T
Psuc Z e
1 p12 ZH 1C2 ,i 1,i 1 D21 , D21 Z ,i D21 ..W 2 time Z-transform of a station S 2 of category C 2 .
H 2i ,k ,D21 j ,D21 Z : The Z-transform of the
H 1C2 ,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
Ts Tc states i , i , D 21 , D 21 ) to the time it is found in the
1 Psuc Z
p11 Psuc Z
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 p11 Z H 1
~ C 2 ,i ,1, D21 Z
W Psuc n1 11 1 11 n1 1
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
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 2i ,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:
H 2i ,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 2i ,i ,D21 ,D21 Z Psuc Z
Thus, the Z-transform of station S 1 service time is: W
H 2i 1,i ,0 ,D21 Z , i 1..W 2
p 22 Psuc
Ubiquitous Computing and Communication Journal - 11 -
To compute H 2i ,i ,D21 j ,D21 Z , we define Tc
Tdec Z , such as:
j TS 2 Z p 22 Z Te H 2
0 ,0 ,0 ,D21 Z
Tdec Z 1
(49) Ts Tc
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
j i 0
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
station). The average service time of a category C i
station is given by:
H 2i ,i ,D21 j ,D21 Z H 2i ,i ,D21 j 1,D21 Z j
Tdec Z ,
X i TS i1 1 (56)
i 0..W 1, j 1..D21 , i , j 0 , D 21
Where TS i1 Z , is the derivate of the service
H 2i ,i 1,0 ,D21 Z 1 p 22 ZH 2i 1,i ,0 ,D21 Z time Z-transform of a category C i station .
1 p 22 ZH 2i ,i ,0 ,D21 Z By considering the same configuration as in
Ts Tc figure 3, we depict in figure 5, the average service
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 2W 1,W 2 ,0 ,D21 Z fairness of DM in serving stations of the same
1 p 22 ZH 2W 1,W 1,0 ,D21 Z category.
Ts Tc (53)
1 Psuc Z p 22 Te T D21 Z
22 Psuc Z dec
According to figure 2 and using equation (51),
H 20 ,0 ,0 ,D21 Z H 20 ,1,0 ,D21 Z Tdec Z
1 p 22 ZH 21,1,0 ,D21 Z
Ts Tc (54)
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 :
Figure 9: Complementary service time distribution
~ 1 TS i Z for different values of D21 ( W 64 )
X i Z (56)
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
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
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
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
Distribution of IEEE 802.11e EDCA and
G. Bianchi: Performance Analysis of the IEEE 802.11 DCF, in the proceeding of 25th IEEE
802.11 Distributed Coordination Function, International Performance Computing and
IEEE J-SAC Vol. 18 N. 3, (March 2000). Communications Conference (IPCCC’06),
H. Wu1, Y. Peng, K. Long, S. Cheng, J. Ma: (April 2006), USA.
Performance of Reliable Transport Protocol The network simulator ns-2,
over IEEE 802.11 Wireless LAN: Analysis and http://www.isi.edu/nsnam/ns/.
Enhancement, In Proceedings of the IEEE Y. Xiao: Performance analysis of IEEE 802.11e
INFOCOM’02, June 2002. EDCF under saturation conditions, Proceedings
H. Zhai, Y. Kwon, Y., Fang: Performance Analysis of International Conference on
of IEEE 802.11 MAC protocol in wireless Communication (ICC’04), Paris, France, (June
LANs, Wireless Computer and Mobile 2004).
Computing, (2004). V. Kanodia, C. Li: Distribted Priority Scheduling
I. Aad and C. Castelluccia: Differentiation and Medium Access in Ad-hoc Networks”,
mechanisms for IEEE 802.11, In Proc. of IEEE ACM Wireless Networks, Volume 8,
Infocom 2001, (April 2001). (November 2002).
IEEE 802.11 WG: Part 11: Wireless LAN Medium
Access Control (MAC) and Physical Layer
Ubiquitous Computing and Communication Journal - 16 -