[IEEE 2006 6th International Conference on ITS Telecommunications - Chengdu, China...

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2006 6th International Conference on ITS Telecommunications Proceedings A TXOP-based Scheduling Algorithm for Video Transmission in IEEE 802. e Networks Qianhua Deng, Anni Cai School of Telecommunication Engineering, Beijing University of Posts and Telecommunications, 100876, P.R.China Abstract-The IEEE 802.11e proposes new features to support Quality-of-Service (QoS) in Wireless Local Area Network (WLAN). It provides several configurable parameters for four Access Categories (AC) to achieve differentiated service in the enhanced distributed channel access (EDCA) mechanism. However it is no longer effective when diverse burst flows present in the same AC. In this paper, an adaptive transmission opportunity (TXOP) allocation method, called Surplus TXOP Diverter (S1XD), is designed to improve the performance of variable bit rate (VBR) video transmission. Through our simulation study, we demonstrate the STXD can provide good delay guarantee for burst video transmission without violating the long-term fairness. In multi-rate scenario, the STXD can solve the performance anomaly and guarantee time-fairness. I. INTRODUCTION The IEEE 802.1 le [1] defines two different access mechanisms, one of which is the enhanced distributed channel access (EDCA). It is a contention-based channel access mechanism and introduces four Access Categories (ACs). Each AC uses different configurable parameters: minimum contention window (CWmin), maximum contention window (CWmax), arbitrary inter-frame space (AIFS), and transmission opportunity (TXOP) limit. Currently most works focus on priority differentiation to ensure better services of voice or video by assigning smaller CWmin, CWmax and AIFS, but adaptive adjusting TXOP is seldom studied. However when VBR streams with miscellaneous peak and mean bit rates aggregate in the same AC, a fixed parameter for one AC cannot satisfy all flows' requirements. Most notable papers restrict the study to saturation throughput [2], without providing practical solutions. Moreover, the 802.11 PHY layer multi-rate option poses new challenges for network protocol design in the context of wireless packet scheduling, because there is a mismatch between the amount of service that a user receives and the amount of time that a user actually utilizes. In this paper, we propose a Surplus TXOP Diverter (STXD) scheduling algorithm. It can let each flow fully exploit its granted TXOP time to reduce the delay when burst packets arrival. In large time scale, because granted-slot waste is avoided, it can maintain the long-term time-fairness, and resolve the performance anomaly of 802.11 in face of multi- rate. The rest of this paper is organized as follows: Section II introduces the IEEE 802.1 le and identifies the limitations of 802.11 e EDCA mechanism. Section III describes the principle of STXD. Section IV evaluates STXD through simulations and compares it with other related work and the results are analyzed. Section V concludes the paper. 11. BACKGROUND A. Fairness Scheduling and QoS Fairness is an important issue when accessing a shared wireless channel. However, 802.11e does not elaborate on using fair queuing scheduling in providing QoS. Banchs [5] and Vaidya [6] proposed some mechanisms which modified only one parameter, such as the CWmin , the AIFS or the frame size. These mechanisms ignore the wireless channel intrinsic location-dependent channel capacity and can not solve the unfairness problem in multi-rate environment. On the other hand, fairness is a measure of how the network assigns resources during periods of congestion, which cannot be perceived by users directly; so it cannot equal a guarantee of good service quality. We contend that a good scheduling discipline should strive to maximize the quality that the users can perceive especially in video transmissions rather than focus on providing absolute fairness of which the users are unaware. B. Multi-rate Problem Description We carry out an experiment to show the EDCA only provides a fair channel access opportunity for flows belong to the same AC, and two nodes use different PHY rates can lead to unfair throughput (e.g. Fig 1). In the IBSS, four wireless workstations (in the rest of the paper we call them wkstn 1, wkstn_2, wkstn_3 and wkstn_4) belonging to AC2 are located around an AP and transmit VBR streams (mean 2.3Mb/s per- node) to it. Background traffic belonging to ACO is constant at 1.5Mb/s. Wkstn 1 starts a flow from beginning of the simulation time, and the other three stations are joined to the AP every other 15 sec. The TXOP operation is not used and no channel error and hidden stations occur. From Fig. 1 (a) we can see when all stations use the same bit rate (11 Mb/s), the system throughput approaches the maximum utilization after the third station joins (at the 30th sec). This illustrates one problem that the access delay increases remarkably due to the burst of VBR flows, so the legacy EDCA is not effective to provide absolute QoS guarantee for delay-sensitive traffics. Figure 1 (b) illustrates the results of multi-rate scenario in which wkstn 1 maintains 11 Mb/s, but other three decline their rate to 5.5 Mb/s, 2 Mb/s and 1 Mb/s respectively. As is shown, the aggregated throughput is pulled down by the This work is supported by Lenovo Corporate R&D. 0-7803-9586-7/06/$20.00 C2006 IEEE. 573

Transcript of [IEEE 2006 6th International Conference on ITS Telecommunications - Chengdu, China...

Page 1: [IEEE 2006 6th International Conference on ITS Telecommunications - Chengdu, China (2006.06.21-2006.06.23)] 2006 6th International Conference on ITS Telecommunications - A TXOP-based

2006 6th International Conference on ITS Telecommunications Proceedings

A TXOP-based Scheduling Algorithm for Video

Transmission in IEEE 802. e NetworksQianhua Deng, Anni Cai

School of Telecommunication Engineering,Beijing University of Posts and Telecommunications, 100876, P.R.China

Abstract-The IEEE 802.11e proposes new features to supportQuality-of-Service (QoS) in Wireless Local Area Network(WLAN). It provides several configurable parameters for fourAccess Categories (AC) to achieve differentiated service in theenhanced distributed channel access (EDCA) mechanism.However it is no longer effective when diverse burst flowspresent in the same AC. In this paper, an adaptive transmissionopportunity (TXOP) allocation method, called Surplus TXOPDiverter (S1XD), is designed to improve the performance ofvariable bit rate (VBR) video transmission. Through oursimulation study, we demonstrate the STXD can provide gooddelay guarantee for burst video transmission without violatingthe long-term fairness. In multi-rate scenario, the STXD cansolve the performance anomaly and guarantee time-fairness.

I. INTRODUCTION

The IEEE 802.1 le [1] defines two different accessmechanisms, one of which is the enhanced distributed channelaccess (EDCA). It is a contention-based channel accessmechanism and introduces four Access Categories (ACs).Each AC uses different configurable parameters: minimumcontention window (CWmin), maximum contention window(CWmax), arbitrary inter-frame space (AIFS), andtransmission opportunity (TXOP) limit. Currently mostworks focus on priority differentiation to ensure betterservices of voice or video by assigning smaller CWmin,CWmax and AIFS, but adaptive adjusting TXOP is seldomstudied. However when VBR streams with miscellaneouspeak and mean bit rates aggregate in the same AC, a fixedparameter for one AC cannot satisfy all flows' requirements.Most notable papers restrict the study to saturation throughput[2], without providing practical solutions. Moreover, the802.11 PHY layer multi-rate option poses new challenges fornetwork protocol design in the context of wireless packetscheduling, because there is a mismatch between the amountof service that a user receives and the amount of time that auser actually utilizes.

In this paper, we propose a Surplus TXOP Diverter (STXD)scheduling algorithm. It can let each flow fully exploit itsgranted TXOP time to reduce the delay when burst packetsarrival. In large time scale, because granted-slot waste isavoided, it can maintain the long-term time-fairness, andresolve the performance anomaly of 802.11 in face of multi-rate.

The rest of this paper is organized as follows: Section IIintroduces the IEEE 802.1 le and identifies the limitations of802.11 e EDCA mechanism. Section III describes the principleof STXD. Section IV evaluates STXD through simulations

and compares it with other related work and the results areanalyzed. Section V concludes the paper.

11. BACKGROUND

A. Fairness Scheduling andQoSFairness is an important issue when accessing a shared

wireless channel. However, 802.11e does not elaborate onusing fair queuing scheduling in providing QoS. Banchs [5]and Vaidya [6] proposed some mechanisms which modifiedonly one parameter, such as the CWmin , the AIFS or theframe size. These mechanisms ignore the wireless channelintrinsic location-dependent channel capacity and can notsolve the unfairness problem in multi-rate environment. Onthe other hand, fairness is a measure of how the networkassigns resources during periods of congestion, which cannotbe perceived by users directly; so it cannot equal a guaranteeof good service quality. We contend that a good schedulingdiscipline should strive to maximize the quality that the userscan perceive especially in video transmissions rather thanfocus on providing absolute fairness of which the users areunaware.

B. Multi-rate Problem DescriptionWe carry out an experiment to show the EDCA only

provides a fair channel access opportunity for flows belong tothe same AC, and two nodes use different PHY rates can leadto unfair throughput (e.g. Fig 1). In the IBSS, four wirelessworkstations (in the rest of the paper we call them wkstn 1,wkstn_2, wkstn_3 and wkstn_4) belonging to AC2 are locatedaround an AP and transmit VBR streams (mean 2.3Mb/s per-node) to it. Background traffic belonging to ACO is constantat 1.5Mb/s. Wkstn 1 starts a flow from beginning of thesimulation time, and the other three stations are joined to theAP every other 15 sec. The TXOP operation is not used andno channel error and hidden stations occur. From Fig.1 (a) wecan see when all stations use the same bit rate (11 Mb/s), thesystem throughput approaches the maximum utilization afterthe third station joins (at the 30th sec). This illustrates one

problem that the access delay increases remarkably due to theburst of VBR flows, so the legacy EDCA is not effective toprovide absolute QoS guarantee for delay-sensitive traffics.Figure 1 (b) illustrates the results of multi-rate scenario inwhich wkstn 1 maintains 11 Mb/s, but other three declinetheir rate to 5.5 Mb/s, 2 Mb/s and 1 Mb/s respectively. As isshown, the aggregated throughput is pulled down by the

This work is supported by Lenovo Corporate R&D.

0-7803-9586-7/06/$20.00 C2006 IEEE. 573

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5 5 f 5- AP Throughput 5

2 ~~~~~~~4 4M4De Y 4M

(a) All stations in 11 Mb/s (b) Every station in various PHY rateFigure 1. Throughput and delay of AC2 in multi-rate scenario

slowest station dramatically and the delayis deterioratedgreatly.Under multi-rate environment the guarantee of fairness is

more difficult. Sadeghi [3] introduced the Opportunistic AutoRate (OAR) to opportunistically exploit high quality channelsvia the transmission of multiple back-to-back packets inproportion to the ratio of the achievable data rate over thebase rate. Fallah [4] proposed the Distributed AdaptivelyConfigured EDCA (DACE-T) algorithm, which monitors thecollision in the network and adjusts the TXOP accordingly.Hence this gives us the motivating that the fairness should bebuilt based on the amount of channel time that a user utilizesinstead of the amount of throughput the user receives.

III. SURPLUS TXOP DIVERTER (STXD)

In this section we propose a scheme called Surplus TXOPDiverter (STXD). In table I we list the notations used in thispaper.

The fundamental of STXD is to regulate TXOP limitduring runtime according to the per-flow arrival behavior toprovide absolute delay guarantee of VBR flows. Each flow'ssurplus TXOP time can be diverted to next round, so it canavoid wasting the slots granted to a flow. In large time scale,it can maintain an acceptable long-term fairness; in short timescale, it makes the best of transmission time to satisfy thedelay bound of video flows. Another metric of the STXD isthat it can solve the performance anomaly of 802.11 in multi-rate scenario due to time-fair scheduling mechanism. TheTXOP is a new concept introduced in 802.11e. The TXOPlimit is defined for per-AC but not for per-flow. For CBRflows the arrival rate is relative smooth, and under thecondition that the packet length matches the TXOP length, itcan consume the granted consecutive time and the delay iscontrollable. However it is inevitable that some TXOP iswasted. Figure 2 (a) gives an example. For VBR flows, thepacket size and arrival interval may widely vary, and agranted constant TXOP limit is not sufficiently. The STXDuses a similar principle to Deficit Round Robin (DRR) [7][8]scheduling algorithm. The DRR can provide throughput-fairness and maintain only 0(1) work. We have illustratedthat throughput-fairness principle does not works efficientlyin multi-rate wireless networks, so the time-based quantumwill be more effective than the byte-based. In the STXD, eachflow is associated with a time quantum (TQd and aTXOP() both in terms of gsec. The TQi denotes the time-share in each round robin the flow should be allocated andthe TXOP(i) is used to count the accumulated unused portion

TABLE I. NOTATIONSAbbr. DescriptionQ(t)s |The length of queue i at time t.TQ A granted initial TXOP limit value for flow i

TQi The required TXOP limit value for flow i

TXOP (i) The surplus TXOP time in current round, including theTQi allocated for current round

TXOP(i)'ls The surplus TXOP time in last round

TXOP()fore The forecasted TXOP(i) value after current round

TXOP() last The forecasted TXOP(i) value for last round

rPHY the PHY layer bit rate adopted by payload transmissionThe base bit rate adopted by PHY header and ACK frames,rb etc. It is 1 Mb/s.

Di Delay bound for flow iPackSize(i) abbr. P Packet size for flow in Total station numbers in the IBSSO(H) Per-packet overhead ofPHY head, MAC head and ACK

rPHY under the rate rPHY

of the granted channel time after each scheduling round. Onceflowi gets an access opportunity, a number of backloggedpackets can be transmitted back-to-back if the time occupiedby the successful transmission is less than the sum ofTXOP(i)a"t and TQi. After the transmission, the sum isupdated by subtracting time spent by the packets that aresuccessfully transmitted, and the surplus portion is diverted tonext round. Accordingly the TXOP(i) is updated to record thesurplus. The difference of work mechanisms between thefixed TXOP and the STXD is illustrated in Figure 2. To bebrief, the work procedure of STXD consists of two maincomponents: Delay Bound Estimate module (DBE) andRegulate TXOP module (RTX).

A. Delay BoundEstimate module (DBE)DBE is a monitor process. It monitors the current flow

arrival behavior and the delay bound. Once flow i gets anaccess chance at time t, it examines its queue length Q(t)i.Assume there are m packets in the queue i, then Q(t)i=mPackSize(i). In the current round the granted slot time forqueue i is (TQi + TXOP(i)). If the Eq. (1) is true, this indicatesthat not all the m packets can be scheduled in current round.

Q(t)X IrpHy > TQ i + TXOP(i) (1)Let j denote the maximum number of packets that can bescheduled for current round, then,

TQi + TXOP(i) (2)PackSize (i)lrpHy + O(H)pHY j

We examine whether the left (m-j) packets will violate theirdelay bound if they are left to the next round. If the Eq. (3) istrue, this indicates the alarm ofbeyond delay bound Di.

jPackSize [i

+O(H)r, (m -j)PackSize (1)n (3)PHY rPHY *TQ / TQ

The denominator of the second component represents theequivalent bit rate if all these left packets will be scheduleduntil next round. To reduce the amount of late packets, weshould enter the next module to regulate the TQi for the

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Access Opportunity

I\Idle sloto Payload ACKC used by others C Y A

Diverted Overhead X Wasted

W astedW sted

Mlnn M0 nn-1 k

TXOP TXOP

(a) In fixed TXOP, surplus slots are wasted

Figure 2. T>

Diverted Diverted

j '-, '. m ~~~~~~~~1.5 1ft

A~~~~~~IAeTXOP(i TXOP(i ) -r-----------

(b) In STXD, the TXOP(i) is length-varying and °surplus slots are diverted to next round

WOP vs. STXD

0.15

0.1

0.05

0 5 10 15 20 25 30 35 40 45 50 55 60

(a) Delay in EDCA Time (s)

- wkstn_lI(VBR)- wkstn_2

A-wkstn 3

0 5 10 15 20 25 30 35 40 45 50 55 60

(b) Delay in STXD Time (s)

3 5-l-owkstn_ I1(VBR)

2; - n--wkstn 2 |

2.5- -A-wkstn -3 N o, AI -~~~wkstn 44

F u15 20 25 30 35 40 45 50 55T im e (s)

Figure 3. Arrival rates of flows

0.25-1 V BR delay inDACE-T

02--o VBR delay in STXD bi lcs

;E9.15 -_ Average CBR delay in

nu DACE-To0.1 Average CBR delay in

STXD 00.05 s

00 5 10 15 20 25 30 35 40 45 50 55 60

Time (s)

Figure 4. Delay in STXD vs. in EDCA

TABLE II. PARAMETERLISTParameters Values Parameters Values Time

PHY rate rPHY (Mb/s) 1,2, 5.5, 11 PLCP Header 4 Bytes 32 psSIFS T Ios PLCP Preamble 12 Bytes 96 ps

slot time 20p ACK Frame 14Bytes 112sMAC Header Size 30 Bytes CRC size 4 Bytes ----

Min per-frame overhead (11Mb/s) 412.7 !sMin per-frame overhead (5Mb/s) 437.5 !sMin per-frame overhead (2Mb/s) 524 !sMin per-frame overhead (1Mb/s) 660 !s

Figure 5. Delay in STXD vs. in DACE-T

TABLE III. ARRIVAL RATE OF FLOWS IN ExPERIMENT 1Station Video Time (s) Arrival Rate MeanRate

ON/Pareto (0.005,1.3)0.02 40 OFF/Pareto (0.003,1.7)

wkstn 1 VBR Interval (0.005 s) 1.5Mb/sON/Pareto (0.005,1.3)41 60 OFF/Pareto (0.003,1.7)

Interval (0.002 s)wkstn 2 CBR 0.02 60 Interval (0.005333 s) 1.5Mb/swkstn 3 CBR 0.02 60 Interval (0.005333 s) 1.5Mb/swkstn 4 CBR 0.02 60 Interval (0.005333 s) 1.5Mb/s

purpose of providing absolute delay guarantee to more

packets in current round instead of waiting them to bediscarded in the next round.

B. Regulate TXOP module (RTX)We can enlarge TQi so that urgent packets can be

transmitted as many as possible. Although a small quantity ofthem may have some large delays, if they are deferred to nextround, the probability of being discarded due to overtime isalmost 1. Assume in the queue i maximum k packets can betransmitted before their delay bound, that is,

k.( PackSize (i) + O(H) ) = D (4)rPHY

This means the TQi should be regulated toTQ i = Di -TXO P (Olast (5)

If Eq. (5) holds for all time, it can maximize delivery ofdelay-guaranteed packets regardless of the range of theregulated TQ1. In presence of ill-behaved flows, the updatedTQi will increase arbitrarily and long-term fairness will bebroken. We can use the exponential smoothing technique to

perform the TXOP(i)fore prediction by recursive updatingformula. The predicted surplus time can represent the flow'slong-term arrival behavior, and if it is used to constrain the

range of TQ,, the long-term fairness can be maintained in a

sense. The recent observations are given relatively more

weight in forecasting than the older observations. This is verysimilar to the dependency characteristic between video frames.The formula takes the form:

TXOP(i)'- = a TXOP(i)-" + (1- a) . TXOP(i)l"t (6)

where a is the weighingfactor, 0. cx 1 .

We perform lots of experiments and choose the best valuea =0.2, which results in the smallest MSE. Then, if the Eq. (7)is true, we deem the regulated TQi can be accepted and it doesnot deviate from the long-term fairness.

TXOP(i) re+ TQ > TQ (7)

Else let the inequation get equal, and only part of theregulated TQ- can be accepted.

The regulation of the TXOP according to the burst of flowscan affect the short-term fairness, but short-term fairness isless appealing than instantaneous QoS to video users. Thusthe cost is worthy. This approach allows delay sensitive flowsto burst occasionally as long as it does not violate long-termfairness.

IV. PERFORMANCE EVALUATION

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In this section, we study the performance of STXD incomparison with the legacy EDCA, DACE-T [4], and OAR [3]schemes.The simulation is performed through the simulator tool

Opnet. We configure an IBSS with an AP connected to awired video server, and four stations, wkstn 1, 2, 3, and 4distributed around the AP. The only bottleneck is the wirelessaccess domain. Since we are not concerned about thedifferentiated access mechanism of the EDCA in this article,for simplicity of comparison, assume there is only one flow ineach station and all flows belong to the same priority (e.g. inAC2) with the same packet size of 1000 bytes. The schemecan be easily extended to support multiple flows and varying-length packets. We describe the parameter configuration intable II. The arrival rates of flows are described in table III,and are plotted accordingly in Fig 3. The provisional delaybound is 100 msec, and the TXOP is 6.016 msec. Thesimulation time lasts 60 sec.

A. Performance ImprovementFigure 4 shows the comparison of delay in EDCA vs. in

STXD. We observe in Fig.4 (a) that the delay goes over 100msec at the time the VBR bursts in EDCA. The delay isreduced remarkably in (b) with STXD. This is because thediverted surplus service time can accommodate more burstpackets before their delay bound. One may notice the delay ofCBR flows increases a little in Fig .4 (b); this is because theextended transmission time ofVBR enlarges the waiting timeof CBR. However we also observe the delays of CBR flowsstill stay within 100 msec all the time, which is acceptable forfamiliar VOD applications. One should be warned not to setthe TXOP too long as it will increase the delay experiencedby other traffic types. Figure 5 shows the comparison ofSTXD and DACE-T. The DACE-T causes a reduction incollision consequently in the average delay of the whole AC.However, it is only suitable for priority differentiationbetween ACs, because the collision noise perceived by thestations in one IBSS is equal. The VBR with heavy burst isallocated the same TXOP as CBRs, so the channel cannot befully utilized. On the other hand, the threshold of DACE-T isa pre-set limit, and cannot adapt to flow's runtimecharacteristic. Our scheme adjusts the per-flow TXOP to trackthe arrival of the flow, and a specific QoS parameter isconsidered as a restriction, when a flow becomes temporarilyburst, it can get a rational portion of compensation.

B. FairnessIn Fig. 6 we compare the fairness ofEDCA, OAR, and our

Figure 6. Fairness of STXD

2.048 6.144 10.240 14.336 18.432TQi(ms)

Figure 7. Saturation throughputvs. burst length

scheme in multi-rate environment to resolve the anomalyproblem illustrated in Fig. 1. The parameters are the same as inthe first experiment. As is shown, EDCA without TXOP isonly throughput-fair, and the system utilization is degradedgreatly. Our scheme is comparable to OAR that gets muchpublic praise of time-fairness.

C. The Effect ofTQi Length on ThroughputIn the above experiments, what we have discussed is the

system in heavy loaded scenario. The saturation throughput Swith STXD can be extended from Bianchi's Markovian model[2]:

PP rE[P]S =s tr []_p1 1 (1 p) =n(l-)"' (8)

(1-P )±+P PT +P (1-P )T str tr s s tr S C tr

We can rewrite Eq. (8) usingT's , T'c to substitute for Ts and

T7 respectively when different rPHYemployed.

TP, = TQ, + AIFS +S, T' = O(H)1

r and TQi are

PackSize(i) -SIFS - T - S+ SJFS T~~~A k(9)

I I , I r AiHWPHY IIU

In present of burst transmission, we can regard the framesexchanged in one round as a large packet P* excluding theadditional heads, and S can be modified as S .

* ~~~TQ,p = E[P] T S(T - DIFS + SIFS)

(10)I+- Pt (y+-PT'T'+ Pr+ T '

~PP' P~

In Fig. 7 we plotted the results of above analysis. As is seen,when the TQi increases beyond 10.24 ms, the systemapproaches the maximum utilization. Considering thecompromise of the throughput maximization and the delay ofother low priority flows, we bound the TQi below 10.24 ms.

V. CONCLUSION

Through simulation and comparison we demonstrate thatwith the long-term fairness restriction, the STXD scheme canprovide absolute delay support for delay-sensitive traffics viaallocating the bursting periods dynamically. At the same time,in multi-rate scenario the STXD can guarantee time-fairnessand the throughput gain is remarkable.

REFERENCES

[1] IEEE 802. 1 e/D4.0, Draft Supplement to Part 1 1, November 2002.[2] G. Bianchi, "Performance analysis of the IEEE 802.11 Distributed

Coordination Function," IEEE Journal of Selection Areas inCommunications, vol.18, no.3, March 2000.

[3] B. Sadeghi, V. Kanodia, A. Sabharwal, and E.Knighlty, "OpportunisticMedia Access for Multi-rate Ad Hoc Networks", Proc. of ACMMobiCom'02, Atlanta, Giorgia, September 2002.

[4] Y.P.Fallah and H.M.Alnuweiri, "Enhanced controlled-access andcontention-based algorithms for IEEE 802.1l e Wireless LANs,"WNCMC'05, Volume 1, 13-16 June 2005 Page(s): 409 - 414.

[5] A. Banchs, and X. Perez, "Distributed weighted fair queuing in 802.11wireless LAN," ICC, April 2002.

[6] N. H. Vaidya, P. Bahl, and S. Gupta, "Distributed fair scheduling in awireless LAN," Proceedings ofACM MOBICOM, pp. 167-178, 2000.

[7] M.H. Kim and H.S. Park, "Scheduling self-similar traffic in packet-switching systems with high utilization," IEE Proc.-Commun., Vol. 151,No. 5, October 2004, pp. 429 - 437.

[8] M. Shreedhar and G. Varghese, "Efficient fair queuing using deficitround-robin," IEEEIACM Transactions on Networking, 1996.

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