Supporting Deadline Monotonic Policy over 802.11
Average Service Time Analysis
Inès El Korbi
Ecole Nationale des Sciences de l’Informatique
Laboratoire Cristal
Université de la Manouba, 2010 Tunisia
ines.korbi@gmail.com
Abstract
In this paper, we propose a real time scheduling policy over 802.11 DCF protocol called Deadline Monotonic
(DM). We evaluate the performance of this policy for a
simple scenario where two stations with different delay
constraints contend for the channel. For this scenario a
Markov chain based analytical model is proposed. From the
mathematical model, we derive expressions of the average
medium access delay called service time. Analytical results
are validated by simulation results using the ns-2 network
simulator.
1. Introduction
The IEEE 802.11 wireless LANs [2] become more and
more reliable to support applications with Quality of Service (QoS) requirements. Indeed, the IEEE 802.11e standard [3] was recently proposed to offer service differentiation over 802.11.
In the absence of a coordination point, the IEEE 802.11
defines the Distributed Coordination Function (DCF) based
on the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol. In the DCF protocol, a station shall ensure that the channel is idle when it attempts
to transmit. Then it selects a random backoff in the contention window [0, CW − 1] , where CW is the current window size and takes its values between the minimum and the
maximum contention window sizes. If the channel is sensed
busy, the station suspends its backoff until the channel becomes idle for a DIFS period after a successful transmission or an EIFS period after a collision. When the backoff
reaches 0, the packet is transmitted. A packet is dropped if
it collides after maximum retransmission attempts.
The IEEE 802.11e standard proposes the Enhanced Distributed Channel Access (EDCA) as an extension for DCF.
978-1-4244-1890-9/07/$25.00 ©2007 IEEE
Leila Azouz Saidane
Ecole Nationale des Sciences de l’Informatique
Laboratoire Cristal
Université de la Manouba, 2010 Tunisia
leila.saidane@ensi.rnu.tn
With EDCA, each station maintains four priorities called
Access Categories (ACs). Each access category is characterized by a minimum and a maximum contention window sizes and an Arbitration Inter Frame Spacing (AIFS).
Although IEEE 802.11e classifies the traffic into four prioritized ACs, there is still no guarantee of real time transmission service due to the lack of a satisfactory scheduling
method for various delay-sensitive flows. Different analytical models have been proposed to evaluate the performance
of 802.11e standard [9],[4], all inspired from Bianchi’s
model [1] that calculates saturation throughput of 802.11
DCF.
In this paper, we focus on delay sensitive flows and propose to introduce the Deadline Monotonic (DM) scheduling policy over 802.11 to satisfy the delay requirements
of such flows. Indeed DM is a real time scheduling policy that assigns static priorities to flow packets according
to their deadlines; the packet with the small deadline being assigned the highest priority [7]. Supporting the DM
policy over 802.11, requires a distributed scheduling and a
new medium access backoff policies.
Distributed scheduling over 802.11 was early introduced
in [5] to allow stations maintaining the priority of the Head
Of Line (HOL) packets (highest priority packet) of all other
stations. Thus, stations can have a vision of the packets being transmitted in the network and adjust their backoff accordingly. Using a distributed scheduling mechanism similar to [5], we introduce in this paper a new medium access
backoff policy to support DM over 802.11, where the backoff value is inferred from the deadline information.
We then propose a Markov chain based analytical model
to evaluate the performance of DM for a simple scenario
where two stations with different deadline constraints contend for the channel. This configuration will reflect the behavior of DM over 802.11 and the mathematical model can
be extended for more complex scenarios. For the considered configuration, we evaluate for each station the average
medium access delay called average service time. Analytical results will be validated against simulation results using
the ns-2 simulator [8].
The rest of this paper is organized as follows. In section II, we present the distributed scheduling and the new
medium access backoff policy to support DM over 802.11.
In section III, we present the mathematical model based on
the Markov chains analysis. Section IV present analytical
and simulation results of the average service time. Finally,
we conclude the paper and present our future work in Section V.
2. Supporting DM policy over 802.11
Using the DM policy within a node means that the packets are sorted by increasing order of their deadlines such
as the HOL packet has the shortest delay bound. With the
DCF, all the stations share the same transmission medium
and the HOL packets of all the stations will contend for
the channel with the same priority even they have different
deadlines.
The idea of introducing DM over 802.11 is to allow
stations having packets with short deadlines to access the
channel with higher priority than those having packets with
long deadlines. Providing such a QoS requires a distributed
scheduling and a new medium access policy.
2.1. Distributed Scheduling
To realize a distributed scheduling over 802.11, we introduce a broadcast priority mechanism similar to [5]. Indeed
each station maintains a local scheduling table with entries
for HOL packets of all other stations. Each entry in the
scheduling table of node Si comprises two fields (Sj, Dj)
where Sj is the source node MAC address (Address 2 field
in DATA packet and RA field in the ACK packet) and Dj
is the deadline of the HOL packet of Sj. To broadcast the
HOL packet deadlines, we propose to use the DATA/ACK
access mode. The deadline information requires two additional bytes to be encoded in DATA and ACK packets.
When a node Si transmits a DATA packet, it piggybacks
the deadline of its HOL packet. The nodes hearing the
DATA packet add an entry for Si in their local scheduling
tables by filling the corresponding fields. The receiver of
the DATA packet copies the priority of the HOL packet in
the ACK and sends it back. All the stations that did not hear
the DATA packet add an entry for Si using the information
in the ACK packet.
In the following, we propose a new medium access policy, where the backoff value is inferred from the packet
deadline.
2.2. DM medium access backoff policy
Let’s consider two stations S1 and S2 transmitting two
flows with the same deadline D1 (D1 is expressed as a number of 802.11 slots). The two stations having the same delay bound can access the channel with the same priority using the native 802.11 DCF. Now, we suppose that S1 and
S2 transmit flows with different delay bounds D1 and D2
such as D1 < D2, and generate two packets at time instants t1 and t2. If S2 had the same delay bound as S1,
its packet would have been generated at time t20 such as
t20 = t2 + D21, where D21 = (D2 − D1). At that time
S1 and S2 would have the same priority and transmit their
packets according to the 802.11 protocol.
Hence, when S2 has a packet to transmit, it selects a
802.11 backoff, but suspends this backoff during D21 idle
slots. The D21 slots elapsed, 802.11 backoff can therefore
be decremented.
Thus to support DM over 802.11, each station uses a new
backoff policy where the backoff is given by:
• The random backoff selected in [0, CW −1], according
to 802.11 DCF, called BAsic Backoff (BAB).
• The DM Shifting Backoff (DM SB): corresponds to
the additional backoff slots that a station with low priority (the HOL packet having a large deadline) adds to
its BAB to have the same priority as the station with
the highest priority (the HOL packet having the shortest deadline).
Whenever a station Si sends an ACK or hears an ACK
on the channel its DM SB is reevaluated as follows:
DM SB(Si) = Deadline(HOL (Si)) − DTmin (Si) (1)
Where DTmin (Si) is the minimum of the HOL
packet deadlines present in Si scheduling table and
Deadline(HOL (Si)) is the HOL packet deadline of node
Si.
Hence, when Si has to transmit its HOL packet with a
delay bound Di, it follows this procedure:
1- It selects a BAB in the contention window [0, CW − 1].
2- The WHole Backoff (WHB) is computed as:
W HB(Si) = DM SB(Si) + BAB(Si)
3- If ( the channel is idle) Then
Decrement W HB(Si).
(2)
Else If ( DATA packet heard ) Then
Update the scheduling table
If (Si is the receiver) Then
Copy the packet priority in ACK
Reevaluate DM SB(Si) before
4) We suppose that we are in stationary conditions, i.e.
the two stations have already sent one packet to each
other. Thus, the two stations have the same scheduling
table.
Each station Si will be modeled by a Markov Chain representing the whole backoff (WHB) process.
sending ACK
End If
Else
If (ACK is heard) Then
Update the scheduling table
Reevaluate DM SB(Si);
End If
End If
Repeat steps 2) and 3)
3.1. Markov chain modeling station S1
Figure 1 represents the Markov Chain modeling station
S1. The states of this Markov chain are described by the
following quadruplet (R, i, i − j, −D21) where:
• R : takes two values S2s and S2c . When R = S2s ,
station S2 is decrementing its shifting backoff (its
DM SB) during D21 slots and wouldn’t contend for
the channel. When R = S2c , the D21 slots were
elapsed and S2 will contend for the channel at the
same time as S1.
• i : the value of the BAB selected by S1 in [0, W − 1].
4- If (W HB(Si) = 0) Then transmit.
• j : the current backoff value of S1. So (i − j) corresponds to the remaining backoff slots before reaching
0.
The steps 1-4 are repeated until the packet is correctly
transmitted or dropped. The contention window CW is doubled at each retransmission attempt until it reaches CWmax.
• D21 : corresponds to D2 − D1. We choose the
negative notation −D21 for S1 to express the fact
that S2 has a positive DM SB equals to D21 and
DM SB (S1) = 0.
End If
3. Mathematical Model of the DM policy over
802.11
In the hereby section, we propose a mathematical model
to evaluate the performance of the DM policy using Markov
chains analysis [1]. We consider the following assumptions:
1) The system under study comprises two stations S1 and
S2, such as Si transmits a flow F i having a deadline
Di and D1 < D2. We define D21 = (D2 − D1) as
the difference between the two delay bounds.
2) We operate in saturation conditions: each station has
immediately a packet available for transmission after
the service completion of the previous packet [1].
3) A station selects a BAB in a contention window
[0, W − 1]. We consider that each station selects a
802.11 backoff in the same contention window of size
W independently of the transmission attempt. This is
a simplifying assumption to limit the complexity of the
mathematical model.
Initially S1 selects a random BAB and is in one of the
states (S2s , i, i, −D21) , i = 0..W − 1. During (D21 − 1)
slots, S1 decrements its backoff with the probability 1
and moves to one of the states (S2s , i, i − j, −D21), i =
0.. (W − 1), j = min(max(0, i − 1), D21 − 1). Indeed during these slots, S2 is decrementing its DM SB
and wouldn’t contend for the channel. When S1 decrements its D21th slot it knows that henceforth, S2 can contend for the channel (the D21 slots were elapsed). Hence,
S1 moves to one of the states (S2c , i, i − D21, −D21),
i = D21..W − 1. If the BAB initially selected by S1
is smaller than D21, then S1 transmits when its backoff
reaches 0. If S2 transmits before S1 backoff reaches 0, the
next packet of S2 will decrement another DM SB and S1
will see the channel free again for D21 slots.
3.2. Markov chain modeling station S2
Figure 2 represents the Markov Chain modeling station
S2. Each state of S2 Markov chain is represented by the
quadruplet (i, k, D21 − j, D21) where:
Figure 1. Markov Chain modeling station S1
• i : refers to the BAB value selected by S2 in
[0, W − 1].
the explanations above, each station Markov chain states
can be divided in two groups:
• k : refers to the current BAB value.
- ξ1 : the set of states of S1 for which S2 will not contend
(states colored in blue in figure 1).
n
o
ξ1 = (S2s , i, i − j, −D21)i=0..W −1,j=0.. min(max(0,i−1),D21−1) .
• D21 − j : refers to the current DM SB of S2, j ∈
[0, D21].
• D21 : corresponds to (D2 − D1).
When S2 selects a BAB, its DM SB equals D21 and
is in one of states (i, i, D21, D21), i = 0..W − 1. If S2
observes the channel idle during D21 slots, it moves to
one of the states (i, i, 0, D21), i = 0..W − 1, where it ends
its shifting backoff. At that time, S2 begins decrementing its basic backoff. If S1 transmits, S2 re-initializes
its shifting backoff and moves again to one of the states
(i, i, D21, D21), i = 1..W − 1.
3.3. Blocking probabilities in the Markov
chains
We notice from figure 1 that when S1 is in one of
the states (S2s , i, i − j, −D21), i = 0..W − 1, j =
min (max (0, i − 1) , D21 − 1), it decrements its backoff
with the probability 1. That means that when S1 is in
one of these states, it knows that S2 is decrementing its
DM SB and is in one of the states (i, i, D21 − j, D21),
i = 0..W − 1, j = 0.. (D21 − 1).
However, when S1 is in one of the states
(S2c , i, i − D21, −D21), i = D21.. (W − 1), S2
has already decremented its DM SB and can now
contend for the channel by decrementing its basic
backoff. In this case, S2 will be in one of the states
(i, i, 0, D21)i=0..W −1 ∪ (i, i − 1, 0, D21)i=2..W −1 . From
- γ1 : the set of states of station S1 for which S2 can contend and decrements its BAB (states colored in pink in
figure 1).
γ1 = (S2c , i, i − D21, −D21)i=D21..W −1 .
- ξ2 : the set of states of S2 where S2 does not contend for
the channel (states colored in blue in figure 2).
n
o
ξ2 = (i, i, D21 − j, D21)i=0..W −1,j=0..D21−1 .
- γ2 : the set of states of S2, where S2 contends for the
channel (states colored in pink in figure 2).
γ2 = (i, i, 0, D21)i=0..W −1 ∪ (i, i − 1, 0, D21)i=2..W −1
Thus when S1 is in one of the states of ξ1 , S2 is obligatory in of the states of ξ2 . Similarly, when S1 is in one of
the states of γ1 , S2 is obligatory in of the states of γ2 .When
the station S2 is in one states of ξ2 , S2 is blocked with the
probability τ11 , this probability corresponds to the probability that S1 transmits knowing that it is in one of the states
of ξ1 . So:
τ11 =Pr [S1 transmits /ξ1 ]
=
W −1
P
i=0
(S2s ,0,0,−D21)
π1
min(max(0,i−1),D21−1)
(S2s ,i,i−j,−D21)
π1
j=0
P
(3)
Figure 2. Markov Chain modeling station S2
(R,i,i−j,−D21)
where π1
is the probability of the state
(R,
i,
i
−
j,
−D21)
in
the
stationary conditions and Π1 =
n
o
(R,i,i−j,−D21)
π1
is the probability vector of S1. We also
define τ12 , the probability that S2 is blocked knowing that
station S1 is in one of the states of γ1 . So:
3.4. Transition probability matrix of S1
Let P1 be the transition probability matrix of S1 and
P1 {i, j} is the probability to transit from state i to state
j. The transitions probabilities of station S1 are:
(S2c ,D21,0,−D21)
τ12 = Pr [S1 transmits /γ1 ] =
π1
(4)
W −1
P
(S2c ,i,i−D21,−D21)
π1
i=D21
In the same way, when S2 is in one of the states of ξ2 ,
S1 will decrement its backoff with the probability 1. Indeed,
no one of the ξ2 states corresponds to a transmission state
(those states describe the shifting backoff decremented by
S2). However, when S2 is in one of the states of γ2 , it contends for the channel and S1 is blocked with the probability
τ22 , such as:
τ22 =Pr [S2 transmits /γ2 ]
(i,0,0,D21)
= W −1
P
π2
(i,i,0,D21)
π2
i=0
W −1
+
P
(5)
(i,i−1,0,D21)
π2
P1 {(S2s , i, i − j, −D21) , (S2s , i, i − (j + 1) , −D21)} = 1,
i = 2..W − 1, j = 0.. min (max (0, i − 2) , D21 − 2)
P1 {(S2s , i, i − D21 + 1, −D21) , (S2c , i, i − D21, −D21)} = 1,
(8)
i = D21..W − 1
P1 {(S2s , i, 1, −D21) , (S2s , 0, 0, −D21)} = 1,
i = 1.. min (W − 1, D21 − 1)
(9)
P1 {(S2c , i, i − D21, −D21) , (S2c , (i − 1), (i − 1 − D21), −D21)}
= 1 − τ22 , i = D21 + 1..W − 1
(10)
c
s
P1 {(S2 , i, i − D21, −D21) , (S2 , (i − D21), (i − D21), −D21)}
= τ22 , i = D21 + 1..W − 1
(11)
P1 {(S2s , 0, 0, −D21) , (S2s , i, i, −D21)} =
1
W
, i = 0..W − 1 (12)
If (D21 < W ) then :
P1 {(S2c , D21, 0, −D21) , (S2s , i, i, −D21)} =
i=2
1
W
, i = 0..W − 1
(13)
(i,k,i−j,D21)
where π2
is the probability of the state
(i,
k,
i
−
j,
D21)
in
the
stationary
conditions and Π2 =
n
o
(i,k,i−j,D21)
π2
is the probability vector of S2. The blocking probabilities described above allows deducing the transition state probabilities and having the transition probability matrix Pi , for each station Si. Therefore, we can evaluate the state probabilities by solving the following system
[6]:
(
Π
i Pi = Πi
P
j
πi = 1
j
(6)
(7)
By replacing P1 and Π1 in (6) and solving the resulting
(R,i,i−j−D21)
system, we can express π1
as a function of τ22 ,
where τ22 is given by (5).
3.5. Transition probability matrix of S2
Let P2 be the transition probability matrix of S2. The
transitions probabilities of S2 are:
P2 {(i, i, D21 − j, D21) , (i, i, D21 − (j + 1), D21)} = 1 − τ11 ,
i = 0..W − 1, j = 0.. (D21 − 1)
(14)
P2 {(i, i, D21 − j, D21) , (i, i, D21, D21)} = τ11 ,
(15)
i = 0..W − 1, j = 0..(D21 − 1)
[4],[1]. TD is the time required to transmit the two bytes
deadline information and Tp is the time required to transmit the data payload. If we consider a constant size packets
for both stations, we have Ts = Tc .
As Te is the smallest duration event, the duration of all
events will be given by d Tevent
Te e.
P2 {(i, i, 0, D21) , (i, i − 1, 0, D21)} = 1 − τ12 ,
i = 2..W − 1
(16)
4.1. Z-transform of S1 service time
P2 {(1, 1, 0, D21) , (0, 0, 0, D21)} = 1 − τ12
(17)
P2 {(i, i, 0, D21) , (i, i, D21, D21)} = τ12 , i = 1..W − 1
(18)
P2 {(i, i − 1, 0, D21) , (i − 1, i − 1, D21, D21)} = τ12 ,
i = 2..W − 1
(19)
P2 {(i, i − 1, 0, D21) , (i − 1, i − 2, 0, D21)} = 1 − τ12 ,
i = 3..W − 1
(20)
To evaluate the Z-transform of station S1 service time
T S1 (Z), we define:
H1(R,i,i−j,−D21) (Z) : The Z-transform of the time already elapsed from the instant S1 selects a basic backoff in
[0, W − 1] (i.e. being in one of the states (S2s , i, i, −D21))
to the time it is found in the state (R, i, i − j, −D21) .
P2 {(0, 0, 0, D21) , (i, i, D21, D21)} =
1
W
, i = 0..W − 1
(21)
Replacing P2 and Π2 in (6) and solving the resulting sys(i,k,D21−j,D21)
tem, we can express π2
as a function of τ11
and τ12 given respectively by (3) and (4). Moreover, by re(R,i,i−j,D21)
(i,k,D21−j,D21)
placing π1
and π2
by their values,
in equations (3), (4) and (5), we obtain a system of non linear equations as follows:
We compute H1(R,i,i−j,−D21) , for each state of S1
Markov chain as follows:
H1(S2s ,W −1,W −1−j,−D21) (Z) =
H1(S2s ,i,i,−D21) (Z) =
1
Z, i = (W − D21) .. (W − 2)
W
H1(S2s ,i,i,−D21) (Z) = τ22 Z
1
+W
1 j
Z , j = 0..D21
W
T
d T se e
(24)
(25)
H1(S2c ,i+D21,i,−D21) (Z)
, i = 1.. max (0, (W − 1 − D21))
(26)

τ11 = f (τ22 )



τ12 = f (τ22 )
τ22 = f (τ11 , τ12 )


under the constraint:

τ11 > 0, τ12 > 0, τ22 > 0, τ11 < 1, τ12 < 1, τ22 < 1
H1(S2s ,i,i−j,−D21) (Z) = Z j H1(S2s ,i,i,−D21) (Z) ,
i = 1..W − 2, j = 1.. min(i − 1, D21 − 1)
Solving the above system (22), allows deducing the expressions of τ11 , τ12 and τ22 , and deriving the state probabilities
of S1 and S2 Markov chains.
H1(S2c ,i,i−D21,−D21) (Z) = Z D21 H1(S2s ,i,i,−D21) (Z)
+ (1 − τ22 ) ZH1(S2c ,i+1,i+1−D21,−D21) (Z) , i = D21..W − 2
(28)
1
H1(S2s ,0,0,−D21) (Z) =
W
min(W −1,D21−1)
+
4. Average Service time computation
X
H1(S2s ,i,1,−D21) (Z)
(29)
i=1
In this section, we evaluate the average MAC layer service time of S1 and S2 using DM policy. The service time
is the time interval from the time instant that a packet becomes at the head of the queue and starts to contend for
transmission to the time instant that either the packet is acknowledged for a successful transmission or dropped [10].
We propose to evaluate the Z-Transform of the MAC layer
service time [4] to derive an expression of the average service time. The average 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], [4]. We have:
If the station S1 transmission state is (S2s , 0, 0, −D21) ,
the transmission will be successful since S2 was decrementing its shifting backoff. Whereas when the station S1 transmission state is (S2c , D21, 0, −D21), the transmission occurs successfully only if S2 doesn’t transmit with the probability (1 − τ22 ). Otherwise S1 selects another backoff and
tries another transmission. After m retransmissions, if the
packet is not acknowledged, it will be dropped. So:
T S1 (Z) =
d
τ22 Z
Tc
e
Te
m+1
H1(S2c ,D21,0,−D21) (Z)
Ts =(TP HY + TM AC + Tp + TD ) + SIF S
+(TP HY + TACK + TD ) + DIF S
(27)
(22)
+ H1(S2s ,0,0,−D21) (Z) + (1 − τ22 ) H1(S2c ,D21,0,−D21) (Z)
(23)
m P
Tc
i
τ22 Z d T e e H1(S2c ,D21,0,−D21) (Z)
Z
d Ts e
Te
i=0
Where TP HY , TM AC and TACK are the durations of the
PHY header, the M AC header and the ACK packet
(30)
4.2. Z-transform of S2 service time
In the same way, we define T S2 (Z), the Z-transform of
station S2 service time. We have:
H2(i,k,D21−j,−D21) (Z): The Z-transform of the time
already elapsed from the instant S2 selects a basic
backoff in [0, W − 1] (i.e. being in one of the states
(i, i, D21, D21)) to the time it is found in the state
(i, k, D21 − j, −D21) , and:
H2(i,i,D21,D21) (Z) =
H2(i,i,D21,D21) (Z) =
1
, i = 0 and i = W − 1
W
1
W
+ τ12 Z
T
e
d Ts e
(31)
H1(i+1,i,0,D21) (Z) ,
i = 1.. W − 2
+ (1 − τ12 ) Z
m P
τ12 Z
0
Tdec
(Z)=1
j
Tdec
(33)
(1 − τ11 ) Z
(Z)=
1 − τ11 Z
T
e
d Ts e
, j = 1..D21
j−1
Tdec
(Z)
(34)
So:
T
T
e
d Ts e
d T ce e
H2(0,0,0,D21) (Z)
(40)
i
H2(0,0,0,D21) (Z)
i=0
4.3. Average service time
From equations (30) and (40), we can derive the average
service time of both stations S1 and S2. The average service time of station Si will be denoted by Xi and is given
by:
(32)
j
To compute H2(i,i,D21−j,D21) (Z) , we define Tdec
(Z) ,
such as:
m+1
Tc
T S2 (Z) = τ12 Z d T e e H2(0,0,0,D21) (Z)
(1)
Xi = T Si
(1)
(41)
(1)
T Si
Where
(Z) , is the derivate of the service time Ztransform of station Si [6].
For Numerical results, S1 and S2 transmit 512
bytes data packets using 802.11.b MAC and PHY layers’parameters with a data rate equal to 11Mbps. For simulation scenarios, the transmission range of each node covers
250m and the distance between S1 and S2 is 5m. Figure 3
represent the average service time of both stations S1 and
S2 as a function of the contention window size W for different values of D21 = (D2 − D1) (D21 is given in slots).
j
H2(i,i,D21−j,D21) (Z) = H2(i,i,D21−j+1,D21) (Z) Tdec
(Z) ,
i = 0..W − 1, j = 1..D21
(35)
H2(i,i−1,0,D21) (Z) =
(1−τ12 )ZH2(i,i,0,D21) (Z)
Ts
d
e
1−τ12 Z Te T D21 (Z)
i = 2..W − 1
,
dec
(36)
(37)
We also have :
H2(i,i−1,0,D21) (Z)= (1 − τ12 ) Z H2(i+1,i,0,D21) (Z)
+H2(i,i,0,D21) (Z) , i = 2..W − 2
and:
H2(W −1,W −2,0,D21) (Z) = (1 − τ12 ) ZH2(W −1,W −1,0,D21) (Z)
(38)
Figure 3. Average Service Time vs Contention Window Size
According to figure 2 and using (31), we have:
H2(0,0,0,D21) (Z) =
(1−τ12 )ZH2(1,1,0,D21) (Z)
Ts
d
e
1−τ12 Z Te T D21 (Z)
dec
(39)
+H2(0,0,0,D21) (Z)
Therefore, we can derive an expression of S2 Ztransform service time as follows:
Figure 3 also compares the average service time of S1
and S2 to the one obtained with 802.11. It shows that all
the curves of the average service time of S1 are below the
of one of 802.11 and the curves of the average service time
of S2 are above the one of 802.11. In figure 4, we represent
X1 and X2 as a function of D21, (W = 128). We notice
that the average service time of station S1 flow decreases
as D21 increases. The opposite scenario happens for S2
flow. We can therefore conclude that compared to 802.11,
the DM policy offers better delay guarantees for the flow
with the small deadline.
[3] IEEE 802.11 WG, ”Draft Supplement to Part 11:
Wireless Medium Access Control (MAC) and physical layer (PHY) specifications: Medium Access Control (MAC) Enhancements for Quality of Service
(QoS)”, IEEE 802.11e/D13.0, Jan. 2005.
[4] Engelstad, P.E. and Osterbo O.N., ”Queueing Delay Analysis of 802.11e EDCA”, Proceedings of
The Third Annual Conference on Wireless On demand Network Systems and Services (WONS 2006),
France, Jan. 2006.
[5] Kanodia, V., Li, C., ”Distribted Priority Scheduling and Medium Access in Ad-hoc Networks”, ACM
Wireless Networks, Volume 8, Nov. 2002.
[6] Kleinrock, L., “Queuing Systems,Vol. 1”, John Wiley,
1975.
[7] Leung, J. Y. T., Whitehead, J, “On the Complexity
of Fixed-Priority Scheduling of Periodic, Real-Time
Tasks”, Performance Evaluation (Netherlands), pp.
237-250, Dec. 1982.
Figure 4. Average Service Time vs D21
5. Conclusion
In this paper we proposed to support the DM policy over
802.11 protocol. Therefore, we used a distributed scheduling algorithm and introduced a new medium access policy.
Then we proposed a mathematical model to evaluate the
performance of the DM policy for a scenario where two stations with different delay bounds contend for the channel.
Analytical and simulation results show that the station with
the shortest deadline has the shortest medium access delay.
We can hence conclude that DM performs service differentiation over 802.11 and offers better guaranties in terms of
average service time for the flow having the small deadline.
In future works, we intend to generalize the deadline monotonic analytical model to n contending stations transmitting
real time flows with different deadline constraints.
References
[1] Bianchi, G., ”Performance Analysis of the IEEE
802.11 Distributed Coordination Function”, IEEE JSAC Vol. 18 N. 3, Mar. 2000, pp. 535-547.
[2] IEEE 802.11 WG, ”Part 11: Wireless LAN Medium
Access Control (MAC) and Physical Layer (PHY)
specification”, IEEE 1999.
[8] McCanne, S., Floyd, S., The network simulator - ns-2,
http://www.isi.edu/nsnam/ns/.
[9] Xiao, Y., ”Performance analysis of IEEE 802.11e
EDCF under saturation conditions”, Proceedings of
ICC, Paris, France, June 2004.
[10] Zhai, H., Kwon, Y., Fang, Y., ”Performance Analysis of IEEE 802.11 MAC protocol in wireless LANs”,
Wireless Computer and Mobile Computing, 2004.