predicts and punishes the selfish users avoiding them to deviate from the assigned network parameters. I. INTRODUCTION. The IEEE 802.11 WLAN uses the ...
A FICA Based Contention Scheme for WLAN with Non Cooperation Tanmay K Sarkar IIT Bombay, INDIA Abstract—The data rates of IEEE 802.11 WLAN (Wireless local area network) have increased from an initial 1Mbps to 600 Mbps leading to smaller packet transmission time. However the overheads used to facilitate this packet transmission have remained more or less the same thereby decreasing the efficiency of 802.11. We focus on improving this loss in efficiency. We develop on the idea of partitioning the 802.11 bandwidth into multiple sub-channels and allow multiple nodes to transmit on these sub-channels using OFDM (Orthogonal frequncy division multiplexing) technology. We consider a frequency domain contention scheme instead of the traditional time domain contention and provide some analysis. We also address the presence of selfish users in the system. We design a penalty scheme where the AP predicts and punishes the selfish users avoiding them to deviate from the assigned network parameters.
I. I NTRODUCTION The IEEE 802.11 WLAN uses the CSMA/CA protocol to infer whether the channel is busy or idle and to avoid packet collision. Each node with a packet to transmit, performs carrier sensing and transmits its packet when the channel is sensed idle. To take care of packet collisions, the RTS (Request To Send) and CTS (Clear To Send) handshake is used. The 802.11 WLAN protocol also uses the binary exponential backoff (BEB) scheme to avoid multiple users from transmitting simultaneously. If the channel is idle, the node waits for a backoff period of c slots, followed by a wait of duration equal to DIFS (DCF Interframe space), before transmitting the RTS to the Access Point (AP). On successfully receiving the RTS, the AP sends a CTS to the requesting node and this node can now transmit the data packet. Also the channel remains idle for an SIFS duration each time the node or the AP switches from receiving to the transmitting mode. It is clear that the total overhead duration toverhead of the idle spaces such as the DIFS, SIFS (Short Interframe space), backoff period is significant compared to the data transmission time tdata . Refer Fig. 1 to compare the overhead duration with the data transmission time. As a result, the 802.11 WLAN tdata has a low efficiency η where η = . Further, tdata + toverhead as the PHY data rates improve because of better modulation schemes and with improved coding techniques, η decreases with the decrease in tdata . For e.g. the efficiency of WLAN has decreased from over 80% at 1 Mbps to under 10% at 1 Gbps (802.11ac). Several schemes have been proposed to improve the efficiency of 802.11 WLAN, some of which are now outlined. Wifi-Nano, proposed in [1] is a system where the 802.11 WLAN efficiency is improved by reducing the 978-1-4673-5952-8/13/$31.00 © 2013 IEEE
Tejas Bodas IIT Bombay, INDIA
DIFS
Backoff Period
Fig. 1.
RTS CTS SIFS SIFS
DATA
ACK SIFS
IEEE 802.11 frame timing diagram
slot times from the current 9 µ sec to 800 ns. The slot time refers to the unit of time used in the backoff algorithm. They propose a ‘Speculative Preamble Transmission’ where the node transmit the data preamble immediately after the backoff counter expires unlike the traditional 802.11 WLAN. A similar ‘Speculative ACK’ reduces the overhead period on the frame. FLUID, proposed in [2] is a design of 802.11 WLAN which uses flexible channel widths. While current 802.11 WLAN have fixed channel widths and centre frequencies, with dynamic spectrum access networks and cognitive wireless networks the advantages of using a flexible channel width becomes apparent. In [3], nodes aggregate multiple packets from higher layers into a single MAC layer frame. This increases tdata for the same overhead duration, thus improving the efficiency. However, a node has to generate enough data before transmission, making the model less desirable for delay sensitive traffic. [4] proposes a modification to the existing binary exponential backoff (BEB) algorithm. In the current backoff algorithm, the contention window is doubled on collision and is reset to a value CWmin after a successful packet transmission. Thus the BEB does not remember the collision information and resets the contention window after a successful packet transmission regardless of network congestion. Their proposed algorithm halves the contention window instead of going back to CWmin thereby preventing the successful nodes from suffering multiple collisions during subsequent packet transmission. Note that all the above schemes improve the 802.11 WLAN efficiency by making suitable changes to the PHY. Following are some schemes which amortize the effect of overheads by using OFDM and OFDMA (Orthogonal frequency division multiple access). [5], [6] provide a scheme that performs channel contention in the frequency domain instead of time domain where the channel remains idle when the nodes perform backoff. They consider the 802.11 implementation of OFDM with a number of multiple sub-carriers where nodes randomly pick a sub-carrier and a node with the lowest subcarrier frequency wins the contention and is awarded the channel.
Contention Band
Sub Channel
A. Overview of FICA Fine grained channel access (FICA) proposed in [7] is a recent work based on OFDM that improves the 802.11 WLAN efficiency by dividing the channel into multiple orthogonal sub-channels to be simultaneously used by several nodes. Each sub-channel has multiple orthogonal subcarrier frequencies. Nodes contend for a particular sub-channel by contending for the sub-carriers corresponding to that particular subchannel. This is done using a specially designed OFDM symbol called Multi-tone RTS. As the contention for sub-channel access is in the frequency domain, multiple successful nodes share the same overhead while transmitting simultaneously in different sub-channels amortizing the overheads. While tdata for each node in a sub-channel increases, toverhead remains fixed thus increasing the efficiency η. The FICA model of [7] forms the main motivation for our work. We build on the idea of partitioning the channel into multiple sub-channels as proposed in [7] using OFDM technology. We consider a new frequency domain contention scheme for accessing the sub-channels which is scalable with the number of users. In this contention scheme, the orthogonal sub-carriers are grouped into what are called as contention bands. The number of contention bands (m) is much larger than the number of sub-channels (s). A node contends for a sub-channels by transmitting RTS in each of the contention band with an attempt probability p. A node has a successful RTS transmission on a contention band if no other node transmits RTS on the same band. If RTS from multiple nodes are successful over different contention bands, the sub-channels could be allocated to nodes based on some predefined rule. Clearly, while the expected number of nodes with successful RTS increases with the number of contention bands, a large number of contention bands reduce the RTS transmission rate thereby increasing the system overhead such as tRT S , tCT S . In this work, we consider this trade-off and find the optimum number of contention bands required by the system. Note that the RTS attempt probability p is an important network parameter of the system. A small value of p may lead to insufficient nodes with successful contention bands resulting in unoccupied sub-channels. On the other hand, if the value of p is large, this may cause RTS collisions resulting in sub-channel wastage. In this work, we calculate the optimal RTS attempt probability p∗ which maximises the probability of successful sub-channel allocation. Note that while the system may prescribe an attempt probability p∗ to all its users as part of the network parameters, nodes have an incentive to increase their attempt probability p as this increases the expected number of successful RTS thereby increasing its probability of subchannel allocation. In this paper, we also consider such a non-cooperative system where nodes selfishly deviate from the prescribed network parameter p∗ . To make the system robust to selfish users, we propose a penalty scheme where the AP imposes penalty on a selfish user discouraging the node from deviating. [8], [9], [10], [11] are some related game theoretic papers which analyze the impact of selfish users in different ALOHA and
DIFS
RTS
SIFS
CTS SIFS
DATA
Fig. 2.
SIFS ACK
The FICA model
802.11 based systems. B. Notation and Preliminaries We now introduce some of the notations to be used throughout the paper. n denotes the number of nodes in the system. As our model exploits OFDM, the channel is divided into M small and partially overlapping signal-carrying frequency bands called sub-carriers. We assign a group of these subcarriers to a user for transmitting data. During data transmission period, the channel is divided into s sub-channels each consisting of M/s sub-carriers. Refer Fig. 2. During the contention period, the channel is divided into m contention bands each consisting of M/m sub-carriers, with m > s. Clearly, a sub-channel is used for transmitting a data packet while a contention band is used for transmitting an RTS packet for requesting a sub-channel. p denotes the access probability with which a node transmits RTS in each of the contention band. The sub-channel allocation rule to be used to assign nodes to sub-channels is as follows. The contention bands are first scanned in the decreasing order of their frequency. A node with a successful contention band is allocated an available subchannel if it has not been allocated in the present slot. As there are s sub-channels, the first s unique nodes with successful contention bands are chosen. Rest of the paper is organized as follows. In Section II we calculate the optimal attempt probability with which the nodes must attempt RTS in the contention bands. Next in Section III we describe the trade-off in determining the optimal number of contention bands that the system can accommodate and provide a numerical example for the same. Finally in Section IV we consider the impact of selfish users on the system and propose a penalty scheme that discourages selfish behavior. II. O PTIMAL ATTEMPT P ROBABILITY Recall that in this system, a node sends an RTS in a contention band with attempt probability p which is a network parameter provided by the AP to all the nodes of the system. An RTS transmission by a node is either successful or it suffers collision. If the RTS is successful, then the node is allocated a sub-channel only if the number of unique nodes with successful RTS transmission on the higher contention bands is less than s. Here higher contention band means a contention band with higher frequency. Clearly, the probability that a node is allocated a sub-channel is a function of p. In this section, we obtain the optimal attempt probability p∗ which
0.2 0.18 0.16 0.14
s
0.12 Pi
the AP should inform to all nodes such that the probability that a node is allocated a sub-channel is maximised. Let Psi denote the probability of a particular node i obtaining one of the s sub-channels. Let α denote the probability of successful transmission of an RTS packet in a contention band. Then α = np(1 − p)
n−1
(1)
0.1 0.08 0.06
Let αr denote the probability that there are r successful contention bands out of m bands. We have m r αr = α (1 − α)m−r (2) r The AP scans the contention bands in decreasing order of their constituent frequency bands. A node i is allocated a subchannel, if its RTS appears for the first time in say the lth successful contention band and of the (l − 1) higher frequency contention bands, there are at most (s − 1) unique RTS. Here 1 ≤ l ≤ m. This implies that a node is considered for allocation only once, subject to the availability of an unallocated sub-channel. Let al denote the probability that an RTS of node i is received for the first time in the lth successful contention band. Clearly, (n − 1)l−1 (3) nl Probability bl that there were less than s unique RTS in previous (l − 1) successful contention bands conditioned on none of them being of node i is as follows 1 l s ((n−1)+(l−1)−1 ) (n−1)−1 al =
This is arrived by using Eq-3.2.6 of [12] - when we draw l balls with replacement, the number of ways of having less than i+[(l−1)−i]−1 or equal to i unique balls is given by i+l−1 i−1 . i−1 corresponds to the number of combinations of having i unique RTS packets out of (l − 1). Probability dr that node i is allocated given that there are r successful RTS packets is given by r X ( a l · bl ) (5) dr =
0.04 0.02 0
0
0.2
0.4
0.6
0.8
1
p
Fig. 3.
Psi v/s p for the case of n = 5, m = 9 and s = 1
Proof: Note from Eq. 5 that dr is an increasing function in r which is independent of p. Also note that αr follows Binomial distribution with parameter (m, α). Therefore Eq. 6 will be maximized if the Binomial distribution αr has more mass towards the right where dr is maximum. A(j, α), the tail of this binomial distribution with parameter (m, α) given by m X m r α (1 − α)m−r αr = A(j, α) = r r=j r=j m X
Differentiating w.r.t α we have m − 1 j−1 A′ (j, α) = m α (1 − α)m−j > 0 j−1 Since the derivative is positive, A(j, α) is strictly increasing with α. Therefore as α increases, the mass of the binomial distribution shifts to the right. Therefore Psi is maximized for maximum value of α. Differentiating Eq. 1 w.r.t p, and equating to 0 we see that p = 1/n maximizes α. This completes the proof. For the case of n = 5, m = 9 and s = 1 Fig 3 shows thats Psi is maximised when p = p∗ = 0.2. III. O PTIMAL N UMBER OF C ONTENTION BANDS
l=1
where l is the index of the lth highest frequency successful contention band in which RTS of node i is transmitted. Clearly, from the definition of dr and αr , the probability Psi that node i is allocated a sub-channel is m X dr · α r (6) Psi = r=1
Psi
Now note that is a function of the attempt probability p since αr is a function of p. We are now interested in choosing a p which maximizes Psi . We call this the optimal attempt probability p∗ . We have the following theorem. Theorem 1: p = 1/n maximizes Psi .
The number of contention bands used in the system affects the system performance. Increasing the number of contention bands in the system increases the expected number of successful sub-channels. However it also increases tRT S thus increasing the system overhead. This tradeoff must be considered while designing the optimal number of contention bands for the system. Let D (Mbps) denote the channel data rate while L (Bytes) denote the average data packet size. P (i|j) denotes the conditional probability that there are i unique RTS out of j. Now n i+(j−i)−1 P (i|j) =
i
i−1 n+j−1 n−1
(7)
Fig. 4.
Throughput efficiency vs m for s = 10
βi , the probability of i unique RTS is given by P m j=1 P (j)P (i|j) where 1 ≤ i ≤ m. Thus, n i+(j−i)−1 m X m j i−1 m−j i (8) α (1 − α) βi = n+j−1 j n−1 j=1
Let X be a random variable denoting the number of subchannels utilized per slot. The expected number of successful sub-channels E(X) is given by E(X) =
s X i=1
max(M,n)
βi · i +
X
βi · s
(9)
i=s+1
If T denotes the total slot duration, then T = tDIF S +tRT S +tSIF S +tCT S +tSIF S +tdata +tSIF S +tACK
As in the IEEE 802.11 standard, we consider the RTS size of and 20B and CTS and ACK size of 14B. Also tRT S = 20·8·m D tCT S = tACK = 14·8·s . The data rate of one sub-channel is D L·8 D/s. Therefore tdata = D/s . Now the throughput efficiency η is given by L · 8 · E(X) η= D·T Note that E(X) and T are a function of m and hence η depends on m. However differentiating η w.r.t m is not easy and closed form expression to obtain the optimal m is difficult. Instead we provide a numerical example giving the optimal number m of contention bands for the values of parameters D, RTS size, Ack and CTS size as per the IEEE 802.11 standard. We consider the case of s = 10. Figure 4 shows the optimal m which maximizes η. The x-axis indicates the number of contention band m while the y-axis is the efficiency η. It is clear from the example that the efficiency for the 802.11 WLAN system is small when the number of contention bands are small. On the other hand, if m is large, the efficiency η decreases due to an increase in tRT S and tCT S . IV. P ENALTY SCHEME FOR SELFISH USERS It is often possible for a node to increase its utility beyond the assigned share by changing the network parameters assigned by the AP. In our model, such a selfish node can increase its RTS attempt probability so as to improve its chances of getting a sub-channel. If the selfish node does get
a slightly better throughput, it is at the cost of the cooperative nodes. Also, if the number of such selfish nodes with high RTS attempt probabilities is large there may not be sufficient successful RTS requests and some sub-channels may remain idle lowering system throughput. As an example, consider the system with only two nodes, one subchannel and one contention band. The first node is a selfish nodes with RTS attempt probability p = 1 while the second node is cooperative with RTS attempt probability p. While the probability of successful RTS for the cooperative node is 0, it is 1 − p for the selfish node. If however both the nodes were cooperative, the probability of successful RTS for each node would have been p(1 − p). Clearly a node has an incentive to deviate from the prescribed parameter p. We now come up with a scheme to suitably penalize such selfish nodes. To make the system robust to selfish users, we propose a scheme where the AP imposes penalty to a selfish user, so that a node does not have any incentive to deviate from a given attempt probability. The AP observes the number of successful RTS contentions for each node in a slot, and gives priority for sub-channel allocation to the user with least number of successful contention bands. To avoid selfish users from being biased towards higher frequency contention bands, we consider allocation of sub-channels to randomly selected successful requests. Thus the AP no longer scans the contention bands from the higher frequency while deciding the subchannel allocation. We further consider a threshold θ on the maximum number of successful contention bands that a node can obtain. Thus a node with the number of successful contention bands greater than θ will not be considered for subchannel allocation. We now analyze the effect of this penalty scheme on the node’s strategy of choosing a transmission probability. Let n be the number of cooperative users with attempt probability p. We consider only one selfish user labeled S1 which has an RTS attempt probability p1 . To make the analysis simple, we assume that s = 1. Let ni denote the number of users who successfully transmits i RTS. The selfish node successfully transmits an RTS in a contention band with probability PS1 = p1 (1 − p)n . The probability of success for a cooperative node say S is given by PS = p(1 − p)n−1 (1 − p1 ) A contention band is wasted with probability given by PF = 1 − [np(1 − p)n−1 (1 − p1 ) + p1 (1 − p)n ] Let P (x; n1 , n2 , ....nm ) denote the joint probability that the selfish user successfully transmits x RTS and ni other users transmit P i RTS, i = 1 . . . m. Here x and ni are such that x + i ini ≤ m. Now as the AP allocates a sub-channel to a user with minimum number of RTS not exceeding θ, the probability that a selfish user is allocated a sub-channel is Psuccess =
θ X X
1/(nx + 1)P (x; n1 , n2 , ....nm )
¯ x=1 n
where n ¯ represents all possible combinations of the m+1 tuple (x; n1 , n2 , . . . nm ) such that n1 = 0, n2 = 0, . . . , nj−1 = 0
Pi−1 Y nY m i −1 Pm Pm n m − kn − ij − x m k k=0 P ( k=1 knk ) P m−( k=1 knk )−x P (x; n1 , n2 , ...nm ) = PSx1 Pm S F i x k=1 nk i=1 j=0
0.26 0.24 0.22
P
Success
0.2 0.18 0.16 0.14 0.12 0.1 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
1
Fig. 5.
Psuccess vs p1 for m = 5 and n = 3
when x = j. Note that the term 1/(nx + 1) indicates that all nodes with the same least number of successful RTS are equally likely to be allocated a sub-channel. The general expression for P (x; n1 , n2 , ...nm ) is given by Eq. 10. Note from the that the values of x, ni must Pexpression m be such that m − ( k=1 knk ) − x ≥ 0. We will now give an example for the penalty scheme method which should also motivate the expression for P (x; n1 , n2 , ...nm ). Consider the case with two cooperative nodes i.e n = 2 and one selfish node. We assume θ = 1. The selfish node uses attempt probability p1 while the cooperative nodes attempt an RTS with p. Assume that the number of contention bands m = 5, and the number of sub-channel is 1. For this case, !
! ! 4 2 PS0 PF5−1 1 1
P (1; 0, 0, 0, 0, 0) =
5 1 PS1 1
P (1; 1, 0, 0, 0, 0) =
! ! ! 4 2 5 1 PS1 PF5−2 PS1 1 1 1
P (1; 0, 1, 0, 0, 0) =
! ! ! 4 2 5 1 PS2 PF5−3 PS1 2 1 1
P (1; 2, 0, 0, 0, 0) =
! ! ! 4 2 5 1 PS2 PF5−3 PS1 2 2 1
Now Psuccess is given by Psuccess
=
1 ∗ (P (1; 0, 0, 0, 0, 0) + P (1; 0, 1, 0, 0, 0))
+
1/2 ∗ P (1; 1, 0, 0, 0, 0) + 1/3 ∗ P (1; 2, 0, 0, 0, 0)
Clearly Psuccess is a function of the attempt probability p. A small value of p may not guarantee a successful RTS while a large p may result in multiple successful RTS which may not translate to a subchannel allocation due to the penalty scheme proposed. Figure 5 for the selfish node gives the probability Psuccess as a function of the attempt probability p1 . Clearly the penalty scheme prevents the selfish user from arbitrarily increasing its attempt probability.
(10)
V. S UMMARY We have considered an OFDMA based system where the nodes contend for sub-channel by randomly transmitting RTS over contention bands. We provide the optimal RTS attempt probability p∗ which the AP announces to maximize the probability of successful sub-channel allocation. Although not intuitive, it is shown that p∗ = 1/n. We have also considered the problem of determining the optimal number of contention bands that the system should support. While the explicit expression for this number is difficult to obtain, with the help of an example we calculate the optimal number of contention bands required by the model. Finally we consider the case where selfish users being myopic choose a different value of the network parameter p than the one prescribed by the AP. To penalize or discourage such selfish behavior we describe a penalty scheme to be used by the AP such that there is no incentive for selfishness. ACKNOWLEDGEMENTS The authors would like to thank Prof. D. Manjunath, IIT Bombay for numerous useful discussions on this problem and also for motivating the problem. The authors would like to acknowledge the support of the Bharti Centre for Communication, IIT Bombay. R EFERENCES [1] E. Magistreti, K. K. Chintalapudi, B. Radunovic, and R. Ramjee, “WiFiNano: Reclaiming wifi efficiency through 800ns slots,” in Proc. of ACM MobiCom, 2011. [2] S. Rayanchu, V. Shrivastava, S. Banerjee, and R. Chandra, “FLUID: improving throughputs in enterprise wireless LANs through flexible channelization,” in Proc. of ACM MobiCom, 2011. [3] Y. Kim, S. Choi, K. Jang, and H. Hwang, “Throughput enhancement of IEEE 802.11 WLAN via frame aggregation,” in Proc. of V.T.C., 2004. [4] P. Chatzimisios, A. Boucouvalas, V. Vitsas, A. Vafiadis, A. Oikonomidis, and P. Huang, “A simple and effective backoff scheme for the IEEE 802.11 MAC protocol,” in Proc. of CITSA, 2005. [5] S. Sen, R. Roy Choudhury, and S. Nelakudti, “Listen (on the frequency domain) before you talk,” in Proc. of ACM HotNets, 2010. [6] S. Sen et.al, “No time to countdown: Migrating backoff to the frequency domain,” in Proc. of ACM Mobicom, 2011. [7] K. Tan, J. Fang, Y. Zhang, S. Chen, L. Shi, J. Zhang, and Y. Zhang, “Fine-grained channel access in wireless LAN,” in Proc. of ACM SIGCOMM, INDIA, 2011. [8] Z. Han, Z. Ji, and K. J. Ray Liu, “Non-cooperative resource competition game by virtual referee in multi-cell OFDMA networks,” IEEE J.S.A.C., vol. 25. 2007. [9] E. Altman, R. El Azouzi, and T. Jiminez, “Slotted Aloha as a game with partial information,” Computer Networks, vol. 45. 2004. [10] Y. Jin and G. Kesidis, “Equilibria of a non cooperative game for heterogeneous users of an ALOHA network,” IEEE Comm Letters, vol. 6, 2002. [11] H. inaltekin and S. B. Wicker, “The analysis of Nash equilibria of the one-shot random-access game for wireless networks and the behavior of selfish nodes,” IEEE Trans on Networking, vol. 16, 2008. [12] K. L. Chung and Farid AitSahlia, Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance, Springer Verlag.
