Keywords weighted fairness,WLAN, EDCF

--- This work was published in IEEE VTC-Fall 2003, Orlando, Florida.

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I. I

In order to provide differentiated QoSs in Wireless LAN (WLAN), it is essential to have a method that can allocate bandwidth for classes of stations (STAs) according to their priorities. A weighted fairness is achieved if the bandwidth could be allocated according to a predetermined goal.

In IEEE 802.11, two mechanisms are defined to access the channel: a contention-based distributed coordinator function (DCF) and a polling-based point coordinator function (PCF). In order to support different priorities, enhanced DCF (EDCF) mode is further defined in 802.11e. DCF is based on CSMA/CA protocol with slotted binary exponential backoff scheme. In DCF and EDCF modes, the bandwidth is shared by all of the STAs and the probability for a STA to access the WLAN is depended on the number of active stations, the contention window (CW) size, and the inter-frame space (IFS) time. The major difference between EDCF and DCF is that the CW and IFS are the same for all STAs in DCF but could be different in EDCF.

Several algorithms were proposed for investigating the behavior of DCF mode. Bianchi, Fratta, and Oliveri [1] proposed a mechanism to adaptively adjust the CW according to the estimated contending stations.

It showed that a better throughput is achieved as the increased of network loading. Cali, Conti, and Gregori [2]

proposed a dynamic tuning of the backoff algorithm to achieve a theoretical throughput limit. In [3], the authors designed a throughput enhancement mechanism for DCF by adjusting the contention window-resetting scheme. In these papers, the authors were focused only on the behavior of a single class. Vaidya, Bahl, and Gupta [4] presented a distributed packet scheduling algorithm. The bandwidth of different flows was allocated in proportion to their weights. Banchs and Perez [5] proposed an extension of the DCF function to provide weighted fairness by tuning the CW. However, these two schemes only focused on fairness and did not consider the enhancement of channel utilization. Qiao and Shih [6] attempted to deal with both weighted fairness and maximized utilization simultaneously by analytical method, but their model did not consider backoff mechanism and cannot be backward-compatible to DCF mode.

In this paper, we propose a method to achieve weighted fairness for two classes of services operating under EDCF mode. We derive the relationship between throughput, conditional collision probability, and channel busy probability, for high- and low-class stations, respectively. The rest of the paper is organized as follows. In Section II, basic concepts of DCF and EDCF modes are described. Section III presents the analytical results of the weighted fairness problems for two classes of services in EDCF mode. In Section IV,

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numerical examples and simulation results are presented to verify the effectiveness of the analysis. Finally, the concluding remarks are given in Section V.

II. B

In this section, we briefly review some background information on 802.11. Basic concepts of DCF and EDCF modes will be introduced.

The time interval between frames, named InterFrame Spaces (IFSs), are used to control the priority for accessing the channel in 802.11. Three types of IFSs are defined in 802.11: Short IFS (SIFS), the Point coordination function IFS (PIFS), and the Distributed coordination function IFS (DIFS). SIFS is the shortest interval and is used for transmission of acknowledgments (ACKs), polling responses in point coordination function (PCF) mode, and fragments belonging to the same MAC service data unit (MSDU). The PIFS, which is greater than SIFS but smaller than DIFS, is used to initiate the Contention Free Period in PCF mode.

In DCF mode, a STA with a new packet is allowed to transmit only if the channel is sensed to be idle for DIFS. Otherwise, the transmission is deferred and the exponential backoff procedure is invoked. The exponential backoff procedure is implemented via using a backoff counter C calculated by

C=Rand(0,w-1), (1)

where w is set to be equal to CWmin, at the first transmission attempt and is doubled after each unsuccessful transmission until it reaches a maximum value CWmax = 2m CWmin. C is decreased whenever the channel is sensed idle for , is frozen when any packet transmission is detected, and is reactivated when the medium is sensed idle for DIFS again. The STA transmits immediately when C reaches to zero. At the end of the receiving packet, the destination STA immediately acknowledges the successful reception by transmitting an ACK after SIFS. Since the SIFS is shorter than DIFS, the other STAs will not detect the channel as idle until the end of ACK. The originating STA assumes that the transmission is failed if it does not receive ACK within a pre-defined period or it detects packets transmitted by other STAs. For the failed transmission, the originating STA will reschedule the packet according to the backoff procedure described above.

The access mechanism of 802.11e EDCF, as shown in Fig. 1, is similar to that of DCF. Four different priorities, called access categories (ACs), are supported in EDCF. Each AC has its associated values of CWmin, CWmax, and arbitration IFS (AIFS). The AIFS for the i-th AC, denoted by AIFSi, is defined by

AIFS_i=SIFS+Li × σ, for 1≦i≦4, (2)

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where Li is an integer ranging from 1 to 255. Specifically, AIFSi is PIFS and DIFS for Li equal to 1 and 2, respectively. One should note that an AC with a smaller CWmin or AIFS implies a higher priority to access the channel. In EDCF, the backoff counter for priority i, denoted by ci, is modified as

ci = Rand (0,wi-1) + X, for 1≦i≦4, (3)

where wi is the CW for priority i; X is equal to 1 if Li=1, otherwise, it’s set to be 0. X is introduced to ensure

that operation of EDCF mode will not disturb the PCF mode.

Figure 1. Basic access mechanism under 802.11e EDCF MAC protocol.

III. T

A

In this section, we investigate the weighted fairness of 802.11 under EDCF mode. We consider a system with NL low-class STAs and NH high-class STAs, each STA adopts a full queue traffic model [7]. For backward compatible to DCF, AIFSH=PIFS and AIFSL=DIFS are assigned for the two classes. An ideal channel condition without hidden terminals and with error-free transmission is assumed. We adopted the weighted fairness function given by [6]

, (4) high- and low-class STAs, respectively. We assumed that the average frame length for both classes is the same. Therefore, the traffic flows for each class may share the channel according to the pre-defined weights and the weighted fairness is then achieved if Eq. (4) can be guaranteed.

A. System Parameters and Observation Points

According to the backoff procedure, the decrement of backoff counter is stopped if the channel is sensed busy. Therefore, the time interval between two consecutive backoff counter decrements is not fixed. Due to the fact that AIFSH<AIFSL, we define a slot time as the (variable) time interval between two consecutive

AIFSj

Select Slot and Decrement Backoff as long SIFS

Select Slot and Decrement Backoff as long SIFS

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backoff counter decrements for the high-class STAs. The observation points are then selected at the end of each time slot such that the backoff counter for either low- or high-class STAs can only be decreased at the observation points.

Let c n_L( ) and c n_H( ) be the stochastic processes representing the backoff counter of a given low- and high-class STA saw at the observation point n, respectively. The first property we found is that the c n_H( ) is always decreased but c n_L( ) could be frozen for any observation point n. Since AIFSH=PIFS, the new backoff counter for high-class STAs is initially chosen in range of (1,WH ) after a successful or a collided _i transmission. However, the selection of initial backoff counter of a high-class STA must be done in a slot and should be decreased by 1 at the observation point. Thus, we have the second property that c n_H( )will fall into the range of (0,WH -1). _i

L( )

c n and c n_H( ) are non-Markovian because the backoff counter depends also on its retransmission history. Therefore, we adopt the definition of “backoff stage,” which is defined as the number of retransmission attempts for a frame, to account for the retransmission history [8]. Let M_L (M_H) and WL ₀ (WH ) be the maximum backoff stage and the CWmin of the low-class (high-class) STAs, respectively. We ₀ can calculate the CW of the low-class (high-class) STAs at the i-th backoff by WL =2i×_i WL (₀ WH _i

= 2ⁱ×WH ), where i is called the backoff stage and i≦₀ M_L (M_H).

B. Behavior of a Single Station with Different AIFS

Lets n_L( ) and s n_H( ) be the stochastic processes representing the backoff stage for a given low-class (high-class) STA at time n, respectively. We first consider the behavior of a single low-class STA with c n_L( ) and s n_L( ) at observation point n. Similar to the approximation adopted in [8], we assume that at each transmission attempt, each frame (of a low-class STA) collide with a constant and independent probability PLregardless of the number of retransmissions. P_L is referred to as conditional collision probability of a low-class STA, meaning that a collision seen by a frame (of a low-low-class STA) being transmitted on the channel.

In other words, it is the probability that at least one of the other STAs (i.e. N_H high-class STAs and N_L-1 low-class STAs) counts down to zero while the low-class STA transmits. We further assume that a low-class STA with nonzero backoff counter may sense the channel as busy with a constant and independent probability q. q is referred to as channel busy probability sensed by a low-class STA. In other words, it’s the probability that at least one of other STAs (i.e. N_H high-class STAs and N_L-1 low-class STAs) transmits

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while the low-class STA has nonzero backoff counter. Therefore, q is independent of the number of retransmissions.

Once independence is assumed, and P_L and q are supposed to be constant values, it is possible to model the bi-dimensional process {s n_L( ),c n_L( )} with the discrete-time Markov chain as depicted in Fig. 2. Here, we assumed that the CW of a frame originates from a low-class (high-class) STA will be reset to WL (₀ WH ) ₀ if has been retransmitted for M_L (M_H ) times. In this Markov chain, the non-null one-step transition probabilities of a single low class station are

0 0

Figure 2. Markov chain model for the backoff counter with AIFSL=DIFS.

Let_{bi k,} =_{limn→∞Pr{ ( )s nL} =_{i c n, ( )L} =_{k i},} ∈_(0,ML),k∈_(0,WLi−₁₎ be the steady-state probability of the low-class STA. We

Then, by using the normalization condition for stationary probabilities, we have

29 assumed that at each transmission attempt, each frame (of a high-class STA) collide with a constant and independent probability P_H regardless of the number of retransmissions. P_H is referred to as conditional collision probability of a high-class STA, meaning that a collision seen by a frame (of a high-class STA) being transmitted on the channel. In other words, it’s the probability that at least one of the other STAs (i.e.

NH–1 high-class STAs and NL low-class STAs) counts down to zero while the high-class STA transmits.

PH is supposed to be a constant value because of the independence assumption. It is also possible to model the bi-dimensional process {s n_H( ),c n_H( )} with the discrete-time Markov chain as depicted in Fig. 3.

Similarly, the non-null one-step transition probabilities are

0 0

Figure 3. Markov chain model for the backoff counter with AIFSH=PIFS.

Here, we do not have P{i,k|i,k} as in Eq.(5) due to the first observed property that c n_H( ) is always decreased but c n_L( ) could be frozen for any observation point n. Also, the range of c n_H( ) (i.e. k) has to be modified to (0,WHi-1) according to the second observed property.

Let d_{i k,} =lim_n→∞Pr{ ( )s n_H =i c n, _H( )=k i}, ∈(0,M_H),k∈(0,WH_i−1) be the steady-state probability of the high-class STA.

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C. Frame Transmission Probabilities with Different AIFS

Denote τ as the transmission probability that a high-class STA transmits in a randomly chosen time slot, _H τ can be obtained by summarizing of the state probability dH i,0 found in (18) as

,0

Since AIFSH<AIFSL, the low-class STA may not affect the high-class STA. Therefore, τ is equal to the _H probability that more than one high-class STA that choose the same backoff counter. Similarly, we can derive the probability that more than one low-class STA that choose the same backoff counter value, denoted by τ'L, as

The transmission probability that a low-class STA transmits in a randomly chosen time slot, denoted by τL, is the sum of bi,0 found in (10) and is given by ready-to-transmit high-class STA collides with any of the NH-1 high-class STAs or NL low-class STAs. q is the probability that the channel is sensed busy by a low-class STA with nonzero backoff counter. The channel will be busy if any of the NH high-class STAs or NL-1 low-class STAs transmits at the same time. PL is the

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probability that a ready-to-transmit low-class STA collides with any of the NH high-class STAs or NL–1 low-class STAs. In this case, the transmission probability for low-low-class STAs is τ'L because the counter of the ready-to-transmit low-class STA is zero. Then we can have,

1

Finally, we can easily derive successful transmission probabilities of high-class and low-class STAs, respectively, as

Comparing with Eq. (4), we can use the numerical method to find the relationship between WH0 and WL0

from Eqs.(22), (23), (24), and (25) that can satisfied with Eqs. (4) and (26) by fixing the values of φH, φL, NH, NL, MH, and ML.

IV.

To validate the analysis, simulations were performed based on MATLAB. The values of PHY-related parameters were referred to IEEE 802.11b [9]. The symbol transmission rate was set to 11 Mbps. The frame format was the one defined by the 802.11e MAC specifications, and the PHY header and IFS intervals were those defined for 802.11b PHY. The PHY overhead time including preamble and header length is 196 µs, σ is 20 µs, SIFS is 10 µs, and the propagation delay is 1 µs. The length of the MAC header and ACK packet is 36 and 14 bytes, respectively. Unless otherwise specified, a constant frame payload size of 1028 bytes, which includes 1000 bytes application data payload, 20 bytes IP header, and 8 bytes UDP header, were used in the simulations. The full queue traffic model was assumed to apply to all stations. The maximum backoff stage MH and ML were both set to be equal to 5 throughout this section. Unless otherwise specified, the numerical results were depicted in solid and dash lines and the simulation results were depicted with hollow and full symbols.

The accuracy of the analysis is verified by simulation results. In the following examples, we fix the sum of NH and NL to be 10 and set WL0 to be 32. The effect of high- and low-class STAs (i.e. NH and NL, respectively) for different values of WH0 was investigated. In Fig.4, the transmission probabilities of the two classes (i.e. τH and τL) were depicted for different NH and WH0. It was found that the larger NH would lead to smaller transmission probabilities for both classes because the high-class STAs have more chances to access the

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channel. It was observed that, if WL0 was fixed, a small WH0 resulted in a high τH but a low τL. Fig. 5 showed the weighted fairness, STH/STL, for different cases. It was showed that STH/STL was highly depended on the selection of (WH0, WL0). The smaller WH0 would lead to the larger STH/STL when WL0 was fixed. Moreover, the growth of NH might lead to the decrease of STH/STL. Moreover, it was found that, the STH/STL could be greater than one even if WH0=WL0. The differentiation of throughput was achieved by setting different AIFSs.

Based on the results observed above, we might choose a suitable WL0 based the given NH, NL, MH, and ML. Then we may adopt any numerical method to find the WH0 based on the desired weighted goal φH/φL. In the simulations, WH0 was initially set to be equal to WL0. For a given WH0, STH/STL was calculated. The new value of WH0 was decreased if STH/STL < φH/φL and was increased otherwise. The iteration continued until

|STH/STL-φH/φL| was minimized.

In the following, we show that the fairness is achieved using the proposed method. A total of 10 STAs are considered. The weighted goal φH/φL is 2 and the WL0 is fixed to be 32. WH0 is then chosen based on the weighted goal for different combination of (NH, NL). Fig. 6 showed that the weight goal was achieved for different combination of high- and low-class STAs. Due to the constraint that WH0 was an integer, therefore, it resulted in a little fluctuation of STH/STL.

V.

In this paper, we proposed an analytical method to obtain parameters required to achieve weighted fairness for services operating under the enhanced distributed coordinator function (EDCF) mode. A system with full queue traffic model and supported two classes of services was considered. Specifically, the length of AIFS was set to be DIFS and PIFS for low- and high-class stations, respectively, to backward compatible with 802.11. In the queueing analysis, a discrete-time Markov-chain was adopted to model the behavior of backoff counters for the two classes and the steady-state probabilities were derived. We further explored the relationship between throughput, conditional collision probability, and conditional busy medium probability for the two classes. With the information, the size of the contention window was adjusted to achieve the weighted goal. The accuracy of the analytical solution is verified by simulation for different number of active stations. It can conclude that, for different combination of high- and low-class STAs, the weighted fairness is easily achieved by employing the proposed method.

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REFERENCES

[1] G. Bianchi, L. Fratta, and M. Oliveri, “Performance Evaluation and Enhancement of the CSMA/CA MAC Protocol for 802.11 Wireless LANs,” IEEE PIMRC, Taipei, Taiwan, Oct. 1996, pp. 407-411.

[2] F.Cali, M.Conti, and E.Gregori, “Dynamic Tunig of the IEEE 802.11 Protocol to Achieve a Theoretical Throughput Limit,”

IEEE/ACM Trans. on Networking, vol. 8, no. 6, Dec. 2000.

[3] H. Wu, S. Cheng, Y. Peng, K. Long, and J. Ma, “IEEE 802.11 Distributed Coordination Function (DCF) Analysis and Enhancement,” IEEE ICC, vol. 1,pp. 605-609, 2002.

[4] N. H. Vaidya, P. Bahl, and S. Gupta, “Distributed Fair Scheduling in Wireless LAN,” IEEE MOBICOM, Boston, MA, Aug.

2000, pp. 167-178.

[5] A. Banchs and X. Perez, ”Distributed Weighted Fair Queuing in 802.11 Wireless LAN,” IEEE ICC, vol. 5 , pp. 3121 -3127, 2002.

[6] D. Qiao and K.G. Shin, ”Achieving Efficient Channel Utilization and Weighted Fairness for Data Communications in IEEE 802.11 WLAN under the DCF ” Tenth IEEE International Workshop on Quality of Service, pp. 227 -236, 2002.

[7] 3GPP TSG-RAN-1, Nortel Networks, “Nortel Networks’ reference simulation methodology for the performance evaluation of OFDM/WCDMA in UTRAN”, Document R1-03-0518, Meeting #32, Paris, France, May 19-23, 2003.

[8] G. Bianchi, “Performance Analysis of the IEEE 802.11 Distributed Coordination Function,” IEEE Journal on Selected Area in Communications, vol.18, no.3, pp. 535-547, Mar. 2000.

[9] “IEEE Standard for Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Higher-Speed Physical Layer Extension in the 2.4 GHz Band,” IEEE Std 802.11b-1999, Sep. 1999.

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Number of high-class STAs (total STAs=10)

Transmission probability

Figure 4. Transmission probability: analytical versus simulation results.

1 2 3 4 5 6 7 8 9

Number of high-class STAs (total STAs=10)

WH₀=16,WL₀=32 WH₀=24,WL₀=32 WH₀=32,WL₀=32

Figure 5. The STH/STL: analytical versus simulation results.

1 2 3 4 5 6 7 8 9

Number of high-class STAs (total STAs=10) STH/STL

ideal weighted numerical results

Figure 6. Performance of STH/STL under a total 10 STAs: φ_H/φ_L=2

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A Joint Power and Rate Assignment Algorithm