Contention Free Burst (CFB) is a promising burst transmission scheme defined in the IEEE 802.11e Medium Access Control (MAC) protocol to achieve differentiated Quality of Service (QoS) and improve the utilization of the wireless scarce bandwidth. Although modeling and performance analysis of the IEEE 802.11e network have attracted tremendous research efforts from both the academia and industry, most existing analytical models do not give attention to the CFB QoS parameter. In this paper, we aim to propose a simple analytical model of the IEEE 802.11e Enhanced Distributed Channel Access (EDCA) function including mainly the CFB, in order to study its effect on the improvement of the achievable throughput of Video and Voice Access Categories (ACs). Therefore, we propose a new two-dimensional Markov chain model of the IEEE 802.11e EDCA function with CFB. Then, we develop a mathematical model to derive the saturation throughput. Finally, performance analysis has allowed us to estimate the maximum sustainable throughput with CFB in an IEEE 802.11e-EDCA network under infinite load conditions.
The IEEE 802.11 standard is currently one of
the most popular wireless access technologies. It
allows for quick and simple configuration of local,
broadband networks at home, in offices, or in public
places and greatly facilitates Internet access
(KosekSzott et al. (2011)). With the increasing demand of
Wireless Local Area Networks (WLANs), especially
of the IEEE 802.11 (IEEE 802.11 Standard (1999)),
the support of differentiated Quality of Service (QoS)
has become one of the recent critical challenges
for the success of IEEE 802.11 Medium Access
Control (MAC) protocols for the future wireless
communications. It is important to develop a new
medium access scheme that can support the
differentiated QoS requirements over IEEE 802.11
WLANs, which is specified by the IEEE 802.11e
(IEEE 802.11e Standard (2005)). The IEEE 802.11e
standard specifies differentiated service classes in
the MAC layer to enable different kind of packet
priorities and have drawn tremendous interest
from both industry and academia. IEEE 802.11e
defines the Hybrid Coordination Function (HCF)
access mechanism, which uses two mechanisms
for the support of QoS differentiation. They are
Enhanced Distributed Channel Access (EDCA) and
HCF Controlled Channel Access (HCCA) (
The EDCA function defines several QoS
enhancements to the legacy IEEE 802.11 Distributed
Coordination Function (DCF). EDCA operation is based
on different priority levels through the definition of
Access Categories (ACs). There are four ACs (Voice
– VO, Video – VI, Best Effort – BE, and Background
– BK), each with a separate queue. To provide traffic
differentiation, the following medium access
parameters are defined for each AC: the Contention Window
minimum (CWmin) and maximum (CWmax) size, the
Arbitration Inter-Frame Space Number (AIF SN ),
and the Contention Free Burst (CFB). The functions
of the access parameters are as follows: CWmin and
CWmax determine the initial size of the contention
window and the maximum possible backoff value,
respectively. AIF SN determines the minimum
number of idle slots before a frame transmission may
begin. The CFB allows consecutive frame
transmissions after gaining channel access (
After the new EDCA function was defined, the
previously proposed analytical models of the IEEE
802.11 DCF became unsatisfactory because they
lacked traffic differentiation. However, they were
a solid starting point for further research. Most
of all, they resolved the complicated problem
of representing multiple states of the channel
access procedure by using Markov chains
(KosekSzott et al. (2011)). In this area,
In this paper, we propose a simple analytical model of the IEEE 802.11e EDCA function with Contention Free Burst. Therefore, we use a two-dimensional Markov chain to model the behavior of a single access category. Then, we develop a mathematical model to derive the saturation throughput of a given access category.
The remainder of this paper is organized as
following: an overview of the CFB scheme is given
in section 2. In section 3, we describe the proposed
analytical model of the IEEE 802.11e ECDA function
with CFB. The obtained analytical results about the
sustainable overall throughput in an IEEE
802.11eEDCA network, are presented in section 4. In section
5, we conclude the paper.
2. OVERVIEW OF THE CFB SCHEME
In DCF, the system efficiency is considerably
affected by various overheads referred to as Physical
(PHY) layer headers, control frames, backoff, and
inter-frame space. The overhead problem becomes
more serious as the data rate increases. To mitigate
the impact of the overheads and improve the system
efficiency, the TXOP scheme has been proposed in
the IEEE 802.11e protocol (
SIFS
CFB
SIFS DATA
DATA ACK
SIFS
DATA
SIFS ACK
SIFS
ACK
AIFS
CW
Different from DCF where a station can transmit only one frame after winning the channel, the TXOP scheme allows a station gaining the channel to transmit the frames available in its buffer successively provided that the duration of transmission does not exceed a certain threshold, namely the CFB. As shown in Figure 1, each frame is acknowledged by an ACKnowledgement (ACK) after a Short Inter-Frame Space (SIFS) upon receiving this ACK. If the transmission of any frame fails, the burst is terminated and the station contends again for the channel to retransmit the failed frame. The TXOP scheme is an efficient way to improve the channel utilization because the contention overhead is shared among all the frames transmitted in a burst. Moreover, it enables service differentiation between multiple traffic classes by virtue of various CFBs. Another advantage of using the TXOP scheme is that the channel occupation time in multi-rate WLANs can be fairly distributed by the packets available in its queue consecutively, provided that the duration of transmission does not exceeds the specific CFB. 2. We assume a fixed number of wireless stations, where each access category h always having a packet available for transmission. In other words, we operate in saturation conditions. 3. The collision probability of a packet of any access category h is constant and is independent of the number of retransmissions. 3.2. Packet Transmission Probability We study the behavior of a single access category h with a Markov chain model, and we obtain the stationary probability [h] that the AC[h] transmits a packet in a generic slot time. This probability will be used to determine the saturation throughput of the IEEE 802.11e-EDCA network.
1 1 1 0, - TL[h]+1 ...
1 1, - TL[h]+1 ...
1
allocating the larger CFB to faster stations. The slow
stations, therefore, no longer severely degrade the
performance of those with the higher rate (
Number of stations in the network.
Maximum backoff stage of the AC[h].
Minimum contention window of the AC[h].
Maximum contention window of the AC[h].
Contention window size of the AC[h] at ith transmission attempt.
Maximum number of packets can be transmitted in burst during the CF B[h] of the AC[h].
Packet payload length.
Time of a packet payload transmission.
Time of a MAC layer header transmission.
Time of a PHY layer header transmission.
Time of an acknowledgment transmission.
Time interval of AIFS of the AC[h].
Time interval of SIFS.
Time of a signal propagation.
An empty slot time. 1. All packets are of the same length. Each station that gains the channel access transmits 1 m[h],-TL[h]+1 ...
1 m[h], -1 m[h], 0 m[h], 1
Let S[h](t) be the stochastic process representing the backoff stage i (i = 0; 1; : : : ; m[h]) of the AC[h] at the time t.
Let B[h](t) be the stochastic process representing either the backoff time counter j (j = 0; 1; : : : ; Wi[h]) or the kth transmitted packet (k = 0; 1; : : : ; T L[h]+1) during the CF B[h] for a given AC[h].
For a given AC[h], the Wi[h] and the T L[h] are given by the Equations 1 and 2, respectively. P[h] P[h]
i, 0
P[h]
P[h] ..1.. 0, W0[h]- 1 .... 1, W1 [h]- 1 1 .... 1
i, Wi[h]- 1
..1.. m[h],Wm[h]- 1
We can now express the probability [h] that an
AC[h] transmits in a random chosen slot time. It is
the sum of all the steady-state probabilities of states
i;k, i = 0; 1; m[h], and k = 0; 1; T L[h] + 1.
In these states, an AC[h] attempts to transmit its
packets. Thus:
(1)
(5)
(6)
(7)
Once the key approximation in Bianchi’s Markov
chain model (
Thus, by the relation (4), all the values i;k are expressed as a function of the value 0;0 and packet collision probability P [h]. 0;0 is finally determined by imposing the normalization condition, that can be simplified as follows: P fi; k=i; k + 1g = 1; i 2 (0; m[h]); k 2 ( T L[h] + 1; 2): P fi; k=i; k + 1g = 1; i 2 (0; m[h]); k 2 (0; Wi[h] 2): P fi; 1=i; 0g = 1 P f0; k=i; T L[h] + 1g =
P [h]; i 2 (0; m[h]):
1
W0[h] P fi; k=i 1; 0g = P fm[h]; k=m[h]; 0g =
P [h] ; i 2 (1; m[h]); k 2 (0; Wi[h] 1): Wi[h]
P [h] Wm[h] ; k 2 (0; Wm[h] 1): ; i 2 (0; m[h]); k 2 (0; W0[h] 1): Let i;k = limt→∞P fS[h](t) = i; B[h](t) = kg, i 2 (0; m[h]), k 2 ( T L[h]+1; Wi[h] 1) be the stationary distribution of the chain. The closed-form solution for this Markov chain is: 0;0; 0;0; 0;0; i 2 (0; m[h] 1); k 2 (0; Wi[h] 1);
i = m[h]; k 2 (0; Wi[h] 1); 0;0; i 2 (0; m[h] 1); k 2 ( 1; T L[h] + 1); i = m[h]; k 2 ( 1; T L[h] + 1): (4)
From the viewpoint of a wireless station, the probability that the wireless station accesses the channel is given by the Equation 8, where the access categories VO, VI, BE and BK are represented by the priorities 3, 2, 1 and 0, respectively. (3a)
[h] = Where, 4 = 2 (1 = = m[h] T L[h]−1 ∑ ∑ i=0 k=1 T L[h] (1 1 m[h] ∑ i;−k +
i=0 P [h]) + P [h] P [h]
i;0; 4 1 + 2 + 3 (T L[h] 1) : 0;0; 2P [h]) (T L[h] (1
P [h]) + P [h]) The probability P [h] that a transmitted packet of a given AC[h] encounters a collision, is the probability that, in a time slot, at least one of n 1 remaining wireless stations transmits, or at least one of AC[i] (i > h) of the same wireless station transmits. i > h means that, AC[i] has higher priority than AC[h]. Hence, we have: i>h Equations 7, 8 and 9 form a set of nonlinear equations. It can be solved by means of numerical methods. All the transition probabilities and steadystate probabilities can be obtained. 3.3. Saturation Throughput (T H[h]) We study the events that can occur within a generic slot time, and we express the saturation throughput of a given AC[h] in an IEEE 802.11e-EDCA network, as a function of the computed value [h].
The average length of a slot time E[ ], is obtained by considering that:
With the probability (1
3 ∑Ps[h]), the slot time h=0
contains a collision; 3 With the probability Ptr ∑Ps[h], the slot time h=0 contains T L[h] packets successfully transmitted. We express the elementary parameters of T H[h]:
Let Tc be the time that the channel is sensed busy by a collided transmission of the first packet of any AC[h]: Tc = minfAIF S[h]g + TMAC + TP HY + TP + (12)
AIF S[h] = AIF SN [h] + SIF S: (13)
Let Ts[h] be the time that the channel is sensed busy by a successful transmission of all the packets of the AC[h]:
Ts[h] =AIF S[h] + T L[h] [TMAC + TP HY + TP + 2SIF S + 2 + ACK]
SIF S: (14) We define EI [h], as the average amount of useful information successfully transmitted by the AC[h] in a slot time. It is given as follows: Now, we are able to express the saturation throughput (T H[h]) of a given AC[h], as the ratio of the average amount of useful information successfully transmitted EI [h] to the average length of a slot time E[ ]:
T H[h] = 4. SATURATION THROUGHPUT ANALYSIS In this section, we present and analyze the obtained analytical results about the overall throughput of the IEEE 802.11e-EDCA network. These results are obtained after solving and programming the analytical model described in section 3 under Matlab software. The numerical values of parameters used to get the below figures, are listed in Tables 3 and 4. The throughput analysis of the IEEE 802.11e-EDCA network provided in this section, is done with different BER values, packet lengths and network sizes, in cases of aggregated and non-aggregated packets. This analysis is original and leads to new conclusions that could not be intrusively expected. In Figure 3, we compare the overall throughput of AC[VO] and AC[VI] obtained with and without CFB according to the number of stations in the network. We observe that, the overall throughput of both AC[VO] and AC[VI] is decreasing with the increase of the network size. This due to the number of collisions which increases with the increase of the number of stations in the network. We note on Figure 3 that, the use of CFB allows significant channel utilization improvement of both AC[VO] and AC[VI].
We also note that, when CFB is used, the overall throughput obtained with AC[VI] is greater than the one obtained with AC[VO]. This is due to the number of consecutive MPDUs sent by the AC[VI] which is greater than the one sent by the AC[VO].
In Figure 5, we analyze the overall throughput of AC[VO] and AC[VI] according to the number of MPDUs in cases of middle and maximum packet length (1500 bytes and 2312 bytes, respectively). We show clearly that, the overall throughput of both AC[VO] and AC[VI] increases with the increase of the number of MPDUs allowed to be transmitted during a CFB. We also note that, increasing the packet length allows to increase the efficiency of CFB. Through the presented analytical results, we can affirm that, the CFB is a promising burst transmission scheme which allows to enhance the utilization of the bandwidth and to achieve QoS differentiation.
In Figure 4, we compare the overall throughput of both AC[VO] and AC[VI] obtained with and without CFB according to the packet length. We show on this figure that, on one hand, the use of CFB permits considerably to improve the channel utilization compared to the case without CFB. On other hand, with CFB the overall throughput of AC[VO] and AC[VI] increases considerably with the increase of packet length. When the CFB is used, the collision can occur only on the first packet in burst and the other packets are spared from collision related losses. This is why the throughput in case of CFB increases significantly with the increase of the packet length.
In this paper, we have proposed a simple analytical model of the IEEE 802.11e-EDCA network taking into account the CFB. So, we have proposed a new two dimensional discrete time Markov chain model. Then, we have developed a mathematical model to compute the saturation throughput with CFB of a given AC[h]. The obtained analytical results have allowed us to estimate the maximum throughput of the IEEE 802.11e-EDCA network with CFB. Particularly, the presented analytical results show how the Contention Free Burst permits to increase significantly the throughput of video and voice access categories.