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IEEE COMMUNICATIONS LETTERS, VOL. 14, NO. 7, JULY 2010
COMIC: Intelligent Contention Window Control for Distributed Medium Access Subodh Pudasaini, Moonsoo Kang, Seokjoo Shin, and John A. Copeland
Abstract—In this letter, a scheme for Collision Mitigation with Intelligent Contention Window Control (COMIC) is proposed for backoff based collision resolution algorithm. COMIC intelligently mitigates collisions by probabilistically maximizing the selection likelihood of relatively less collision-probable contention slots over the backoffed contention window. A unified Markovian model for the Distribution Coordination Function (DCF) that incorporates COMIC, DCF𝑐𝑜𝑚𝑖𝑐 , is formulated for the performance analysis. The performance results show that DCF𝑐𝑜𝑚𝑖𝑐 outperforms the conventional DCF in both throughput and average packet delay due to the significant reduction in packet collisions. Index Terms—Backoff, collision mitigation, COMIC, DCF.
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I. I NTRODUCTION
ANDOM access schemes in distributed packet radio networks are always supplemented with algorithms for resolving packet collisions, since packet collisions frequently happen when uncoordinated stations contend for the shared broadcast channel. In order to resolve packet collisions, Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) combined with simple Binary Exponential Backoff (BEB) has been having huge popularity in Wireless Local Area Networks (WLANs). However, the simplicity of BEB adds momentous overheads associated with collision resolution [1]. The overhead gets magnified by increased network load and, hence, the overall MAC protocol operates far below the theoretical protocol throughput limit [2]. Schemes suggested in [2]- [4] that replace the uniform probability distribution of Contention Slot Selection (CSS) over an exponentially increasing contention window (BEB in CSMA/CA based MAC), with a non uniform distribution of CSS over a constant optimal-size contention window, are capable of reducing overheads, and may increase the throughput. Those schemes, however, are not attractive for practical consideration because they are complex (since they need to estimate the total contenders in the network in real time to derive optimal constant window size), and they also require major modifications in the standard MAC protocols. COMIC requires neither contender estimation nor major revision in the standard MAC protocols. It can easily be incorporated in the existing IEEE 802.11 distributed MACs simply by having a minor modification in BEB. The modification needed is only to the operational procedure for
Manuscript received February 18, 2010. The associate editor coordinating the review of this letter and approving it for publication was M. Dohler. S. Pudasaini and M. Kang are with the Department of Computer Engineering, Chosun University, Gwangju, Republic of Korea. S. Shin (corresponding author) and J. A. Copeland are with the Department of Electronics and Computer Engineering, Georgia Institute of Technology, USA (e-mail:
[email protected]). This study was supported by research funds from Chosun University, 2005. Digital Object Identifier 10.1109/LCOMM.2010.07.100287
defining CSS distribution, while the functional procedure for contention window expansion and contraction upon collision and success can be kept intact as in BEB. The modification to the operational procedure is initiated by a simple new technique of backoff sensing. Backoff sensing is an ability to determine the overlapped contention slots in the adjacent contention windows (collided and backoffed window) based on the immediate-past backoff value. These overlapped contention slots are more collision prone [5] while the other slots are relatively less collision prone. Hence it is wise to restrict the contention slot selection in an overlapped region. COMIC intelligently determines overlapped contention slots and probabilistically minimizes their selection chances. COMIC can be applied to all kinds of distributed MACs equipped with backoff based collision resolution algorithms like DCF, EDCA, etc. In the current work we present the analysis for COMIC adapted DCF, i.e. DCF𝑐𝑜𝑚𝑖𝑐 . II. COMIC: C OLLISION M ITIGATION WITH I NTELLIGENT C ONTROL A. Operational Mechanism The contention window expanision/reset procedure of the COMIC is same as in BEB [1] but there is a subtle modification in the CSS distribution. The uniform CSS distribution of BEB over [0, 𝑊𝑖 − 1] for contention stage 𝑖 ∈ [0, 1, ... , 𝑚] is replaced with a dynamic non uniform distribution, 𝑔𝑖 (𝑘) 𝑘 ∈ [0, 𝑊𝑖 − 1], where 𝑊𝑖 is the window size for i-th stage and 𝑚 is the maximum retry limit. We consider 𝑔𝑖 (𝑘) to be a truncated normal distribution. It can be accurately represented with quad-tuples (𝜇𝑖 , 𝜎𝑖 , 𝑇i,l , 𝑇i,r ), where 𝜇𝑖 is mean, 𝜎𝑖 is standard deviation, 𝑇i,l is left truncation point, and 𝑇i,r is right truncation point. The first two tuples characterize the shape while the last two characterize the range of 𝑔𝑖 (𝑘). In COMIC, for every 𝑖 the range is determined as per [ the BEB rules. Thus, ]𝑇i,l is zero for all 𝑖 and 𝑇i,r = 𝑚𝑖𝑛 (2𝑖 ⋅ 𝑊0 ) − 1, 𝑊𝑚𝑎𝑥 − 1 = 𝑊𝑖 −1, where 𝑊0 and 𝑊𝑚𝑎𝑥 are the initial and maximum contention window size, respectively. So, 𝑔𝑖 (𝑘) can be expressed as ⎧ 𝑓𝑖 (𝑘) ⎨ , 0 ≤ 𝑘 ≤ 𝑊𝑖 − 1, (1a) ∫ 𝑊𝑖 −1 𝑔𝑖 (𝑘) = 𝑓𝑖 (𝑘)𝑑𝑘 ⎩ 0 0, else where, (1b) 1 √
−
(𝑘−𝜇𝑖 )2 2𝜎2 𝑖
, −∞ ≤ 𝑘 ≤ ∞ is the normal where 𝑓𝑖 (𝑘) = 𝜎 ⋅ 2𝜋 𝑒 𝑖 probability distribution function. Function 𝑓𝑖 (𝑘) is normalized ∫ 𝑊 −1 ∑𝑊𝑖 −1 with 0 𝑖 𝑓𝑖 (𝑘) so as to make the expression 𝑘=0 𝑔𝑖 (𝑘) always reach to 1. For each 𝑖, shape of 𝑔𝑖 (𝑘) is intelligently tuned based on the backoff value 𝑗 ∈ [0, 𝑊𝑖−1 − 1] previously selected in
c 2010 IEEE 1089-7798/10$25.00 ⃝
PUDASAINI et al.: COMIC: INTELLIGENT CONTENTION WINDOW CONTROL FOR DISTRIBUTED MEDIUM ACCESS jx = 0
j
contention 0 stage i-1
Wi-1-1
Ψ i = 0.0 0
63
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W i -1
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W i -1
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g i (k) PDF of CSS
Ψ i = 1.0
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W i -1
(a)
0 Overlapped slots in adjacent contention stages
63
CSS distribution in conventional scheme
(b)
Fig. 1. Basic operation of COMIC: (a) probability density functions (PDFs) of CSS in the conventional BEB and COMIC when collision occurs in j-th slot of stage (𝑖 − 1); (b) an example of 𝑔𝑖 (𝑘) assignments in COMIC for the contention stage 𝑖 according to the 𝑗 selected in stage (𝑖 − 1).
(𝑖 − 1)-th contention stage such ] [ that slot selection likelihood in the non overlapped region ( 𝑊2𝑖 − (𝑗 + 1)), 𝑊𝑖 − 1 of the backoffed window is maximized. A schematic diagram of such tuning is presented in Fig. 1 (a). Such tuning is achieved by updating 𝜇𝑖 and 𝜎𝑖 based on 𝜓𝑖 as follows
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ellipse) which are exclusive of the slots already selected by previous 𝑦 stations (since the slots selected by 𝑦 stations could only be within the range covered by the shaded rectangular box in the figure). At the same time, since 𝜎 is large enough 𝑥 stations may choose different values even though 𝜇 is same for them. Similarly for the three different cases when 𝑗𝑥 is 0, 23, and 31, 𝜓 and 𝜇 are (0, 0.74, 1) and (63, 16, 0), respectively, and the resulting CSS distributions are as shown in Fig. 1(b). By comparing the CSS distribution for all different cases of 𝑗𝑥 , it can be seen that most probable slot to be selected by different sub-groups (marked by dotted ellipses in the figure) are sufficiently separated over the contention window. This minimizes the chances of inter-sub group collision. COMIC contributes to collision mitigation and results delay-fair access among contending stations by auto-balancing the backoff delay. i.e. stations collided at higher 𝑗𝑥 are probabilistically provisioned earlier access in the next contention stage and vice-versa.
𝜇𝑖 =⌊(𝑊𝑖 − 1) ⋅ (1 − 𝜓𝑖 )⌋, 𝜓𝑖 ∈ [0, 1], 𝑖 ∈ [0, 1, ... , 𝑚], (2) 𝜎𝑖2 =𝑊𝑖 ⋅
{
1+2⋅𝜓𝑖 4 3−2⋅𝜓𝑖 4
0 ≤ 𝜓𝑖 ≤ 0.5 0.5 < 𝜓𝑖 ≤ 1,
III. A NALYSIS OF DCF𝑐𝑜𝑚𝑖𝑐 (3)
𝑗
where 𝜓𝑖 = 𝑊𝑖−1 −1 for 𝑖 ∈ [1, 2, ..., 𝑚]. For the initial access, 𝑖 = 0, there is no history information available and hence 𝜓0 is taken as 0.5. It is note worthy to mention that Eqn. (3) can be changed to any other function or can be be assigned some constant value. The selection of 𝜎𝑖2 , however, has a significant impact on the performance of the COMIC. After tuning 𝜇𝑖 and 𝜎𝑖 now the shape of 𝑔𝑖 (𝑘) in Eqn. (1) is determined. B. Collision Mitigation: Explanatory Example COMIC minimizes collisions in two intelligent ways. Firstly, less collision-prone contention slots in the non] [ overlapped portion ( 𝑊2𝑖 − (𝑗 + 1)), 𝑊𝑖 − 1 of the backoffed window are provisioned maximum likelihood of being selected. Secondly, a group of contending stations in a single collision-domain are autonomously portioned into smaller subgroups having separated collision-domain with reduced intersubgroup collision probability. These features are elaborated next with an example. Let us assume that a group of saturated stations want to access the channel at a time following the CSMA/CA rules. Let’s say 𝑥 ≥ 2 number of stations from the group select same slot 𝑗𝑥 and the rest 𝑦 stations select their slots larger than 𝑗𝑥 for their initial access over the window [0, 𝑊0 ]. In such scenario, collisions occur at 𝑗𝑥 . After collision, the 𝑥 stations determine the slot for the next access in such a way that the chances of collision with the previous 𝑦 stations is significantly reduced as illustrated below. For the case when 𝑊0 is 32 and 𝑗𝑥 is 7, 𝜓 for the re-access after collision is 7/(32−1) = 0.22 and hence according to Eqn. (2) and Eqn. (3), 𝜇 and 𝜎 are 49 and 23.04, respectively. For the calculated 𝜇 and 𝜎, the shape of the CSS distribution can be obtained as per Eq. (1) which is shown in Fig. 1 (b) (second from the top). According to this newly tuned CSS distribution, 𝑥 stations might probably select their new contention slots near the mean value of 49 (marked with dotted
In what follows, we assume that the reader is familiar with DCF operation. We replace the conventional collision resolution algorithm in DCF with COMIC and analyze the new DCF𝑐𝑜𝑚𝑖𝑐 . For the analysis, firstly, we study the behavior of a single station (tagged station) by formulating a Markovian model for DCF𝑐𝑜𝑚𝑖𝑐 based on Bianchi’s model, incorporating the correction offered in [6]. With the aid of the formulated model, the probability 𝜏 that the tagged station transmits in a randomly chosen slot is derived. Secondly, we express the performance metrics like throughput and delay as a function of the 𝜏 . As in [6], we assume that 1) the probability 𝑝 that a transmitted packet collides is independent of the contention stage of the station, and 2) there are 𝑁 saturated stations in the system. Let 𝑏(𝑡) and 𝑠(𝑡) be the stochastic process representing the contention window size and contention stage for the tagged station at a slot time 𝑡. For DCF𝑐𝑜𝑚𝑖𝑐 , the bi-dimensional stochastic process {𝑠(𝑡), 𝑏(𝑡)} is simply an integer-valued Markov process and hence can be characterized with a discrete-time Markov chain (Fig. 5, in [6]). The state transition for DCF𝑐𝑜𝑚𝑖𝑐 remains the same with DCF presented in [6] but with new values of state transition probabilities. By adopting the conventional notation for one-step transition probabilities, 𝑃 {𝑖1 ,𝑘1 ∣𝑖0 ,𝑘0 }=𝑃 {𝑠(𝑡+1)=𝑖1 ,𝑏(𝑡+1)=𝑘1 ∣𝑠(𝑡)=𝑖0 , 𝑏(𝑡)=𝑘0 }, the only non null one-step transition probabilities for the chain can be represented as 𝑃 {𝑖, 𝑘∣𝑖, 𝑘 + 1} = 1
𝑘 ∈ [0, 𝑊𝑖 − 2] 𝑖 ∈ [0, 𝑚]
𝑃 {0, 𝑘∣𝑖, 0} = (1 − 𝑝) ⋅ 𝑔0 (𝑘) 𝑘 ∈ [0, 𝑊0 − 1] 𝑖 ∈ [0, 𝑚 − 1] 𝑃 {𝑖, 𝑘∣𝑖 − 1, 0} = 𝑝 ⋅ 𝑔𝑖 (𝑘) 𝑘 ∈ [0, 𝑊𝑖 − 1] 𝑖 ∈ [1, 𝑚] 𝑃 {0, 𝑘∣𝑚, 0} = 1 ⋅ 𝑔0 (𝑘)
𝑘 ∈ [0, 𝑊0 − 1].
(4)
Let 𝑏𝑖,𝑘 = 𝑙𝑖𝑚𝑡→∞ 𝑃 {𝑠(𝑡) = 𝑖, 𝑏(𝑡) = 𝑘}, 𝑖 ∈ (0, 𝑚) be the stationary distribution of the chain. Note that 𝑏𝑖,0 =𝑝𝑖 ⋅ 𝑏0,0 for 0 ≤ 𝑖 ≤ 𝑚. Since the chain is regular, for every 𝑘 ∈ [0,𝑊𝑖 −1],
IEEE COMMUNICATIONS LETTERS, VOL. 14, NO. 7, JULY 2010
𝑏𝑖,𝑘 =
𝑊 𝑖 −1 ∑
𝑔𝑖 (𝑙) ⋅ 𝑏𝑖,0
𝑓 𝑜𝑟
𝑙=𝑘+1
Applying the normalization condition for the expression in (7) yields 𝑏0,0 = ∑
𝑚 𝑖=0
𝑝𝑖
0 ≤ 𝑖 ≤ 𝑚.
∑𝑚 ∑𝑊𝑖 −1 𝑖=0
𝑘=0
1 [ ]. ∑𝑊𝑖 −1 ∑𝑘 ⋅ 𝑊𝑖 − 𝑘=0 𝑔 (𝑙) 𝑖 𝑙=0
(7)
𝑏𝑖,𝑘 = 1 (8)
Now, transmission probability 𝜏 that a station transmits in a randomly chosen slot can be expressed as 𝜏=
𝑚 ∑
𝑏𝑖,0 =𝑏0,0 ⋅
𝑖=0
1−𝑝𝑚+1 . 1−𝑝
(9)
Then, the conditional collision probability, 𝑝, can be expressed as 𝑁 −1 𝑝= 1 − (1−𝜏 ) . (10) Equation (9) and (10) represent two non-liner equations in two unknowns, 𝜏 and 𝑝, which can be solved using numerical techniques to get a unique solution pair. When 𝜏 and 𝑝 are obtained, the normalized throughput and packet delay can be calculated. Normalized throughput can be calculated as in [6]. The average packet delay, duration from the instant when a packet is the Head-of-Line packet in a MAC queue to the instant when acknowledgement is received, can be calculated using 𝐸[𝐷] = 𝐸[𝑋]×𝐸[𝑠𝑙𝑜𝑡], where 𝐸[𝑠𝑙𝑜𝑡] is the average length of slot time, which is equal to the denominator in [6, eq. (13)] and 𝐸[𝑋] is the average number of slot times required for a successful transmission. Mathematically, 𝐸[𝑋] is a product of the number of slots the packet is delayed in each contention stage (𝜇𝑖 ), and the probability that a packet which is not dropped reaches the i-th backoff stage (𝑞𝑖 ). It can ∑𝑚 𝑖 −𝑝𝑚+1 be represented as 𝐸[𝑋]= 𝑖=0 𝜇𝑖 ⋅ 𝑞𝑖 , where 𝑞𝑖 = 𝑝1−𝑝 𝑚+1 for 𝑖 ∈ [0, 𝑚]. Hence, 𝐸[𝐷] can be obtained as 𝐸[𝐷] = 𝐸[𝑠𝑙𝑜𝑡] ×
𝑚 ∑ 𝑖=0
𝜇𝑖 ⋅
𝑝𝑖 −𝑝𝑚+1 1−𝑝𝑚+1
(11)
IV. P ERFORMANCE R ESULTS We evaluate the performance numerically considering a WLAN where every station is operating according to DCF𝑐𝑜𝑚𝑖𝑐 . The physical and MAC layer parameters are set according to the IEEE 802.11b specifications. Among the three available channel rates, 1Mbps is selected. Payload size is chosen to be of 1,024bytes. We observe that the COMIC significantly reduces collisions. Because of collision reduction, the average channel time
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𝑏𝑖,𝑘 can be represented as { ∑𝑊𝑖 −1 𝑔𝑖 (𝑙)[⋅ 𝑏𝑖,0 0
