WIRELESS communication technology has gained widespread

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1 616 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 4, NO. 6, NOVEMBER/DECEMBER 2005 Dstrbuted Far Schedulng n a Wreless LAN Ntn Vadya, Senor Member, IEEE, Anurag Dugar, Seema Gupta, and Paramvr Bahl, Senor Member, IEEE Abstract Farness s an mportant ssue when accessng a shared wreless channel. Wth far schedulng, t s possble to allocate bandwdth n proporton to weghts of the packet flows sharng the channel. Ths paper presents a fully dstrbuted algorthm for far schedulng n a wreless LAN. The algorthm can be mplemented wthout usng a centralzed coordnator to arbtrate medum access. The proposed protocol s derved from the Dstrbuted Coordnaton Functon n the IEEE standard. Smulaton results show that the proposed algorthm s able to schedule transmssons such that the bandwdth allocated to dfferent flows s proportonal to ther weghts. An attractve feature of the proposed approach s that t can be mplemented wth smple modfcatons to the IEEE standard. Index Terms Medum access control, wreless networks, weghted farness, dstrbuted protocols. æ 1 INTRODUCTION WIRELESS communcaton technology has ganed wdespread acceptance n recent years. Wreless local area networks have come nto greater use wth the advent of the IEEE standard and the avalablty of several commercal products based on ths standard. Farness s an mportant ssue when accessng a shared wreless channel. Wth far schedulng, dfferent flows wshng to share the wreless channel can be allocated bandwdth n proporton to ther weghts. Ths paper presents a dstrbuted medum access control (MAC) protocol for far schedulng n a wreless LAN (operated n an ad hoc mode). Although IEEE wreless MAC s not far (partcularly on short tme-scales), the proposed protocol s derved from the Dstrbuted Coordnaton Functon (DCF) n IEEE An attractve feature of the proposed approach s that t can be mplemented wth smple modfcatons to IEEE In general, medum access control (MAC) protocols can be dvded nto two types: centralzed and dstrbuted. In centralzed protocols, a desgnated host (often referred to as base staton or access pont) coordnates access to the wreless medum. Pont Coordnaton Functon (PCF) n IEEE s an example of the centralzed approach. In dstrbuted protocols, a coordnator s not needed to arbtrate access to the wreless medum. For nstance, n the CSMA (carrer sense multple access) protocol, a node wshng to transmt a packet does so only f t does not hear another on-gong transmsson. CSMA protocol s fully dstrbuted snce each node ndependently determnes. N. Vadya s wth the Department of Electrcal and Computer Engneerng and the Coordnated Scence Laboratory, Unversty of Illnos at Urbana- Champagn, 1308 West Man St., Urbana IL E-mal: nhv@crhc.uuc.edu.. A. Dugar s wth OPNET Technologes Inc., 7255 Woodmont Avenue, Bethesda, MD E-mal: anurag_dugar@yahoo.com.. S. Gupta s wth Csco Systems Inc., 510 McCarthy Blvd, Mlptas, CA E-mal: segupta@csco.com.. P. Bahl s wth Mcrosoft Research, One Mcrosoft Way, Redmond, WA E-mal: bahl@mcrosoft.com. Manuscrpt receved 22 Aug. 2003; revsed 21 May 2004; accepted 12 July 2004; publshed onlne 28 Sept For nformaton on obtanng reprnts of ths artcle, please send e-mal to: tmc@computer.org, and reference IEEECS Log Number TMC whether to transmt a packet or not. Dstrbuted Coordnaton Functon (DCF) n IEEE s an example of the dstrbuted approach. Ths paper develops a dstrbuted approach for far schedulng. Much research has been performed on far queung algorthms for achevng a far allocaton of bandwdth on a shared lnk [2], [4], [14], [20]. Consder the system shown n Fg. 1, where a node mantans several queues (or flows) whch store packets to be transmtted on an output lnk. A far queung algorthm s used to determne whch flow to serve next so as to satsfy a certan farness crteron. By desgn, these far queung algorthms are centralzed snce they are executed on a sngle node (for nstance, a swtch or router) whch has access to all nformaton about the flows. Far queung algorthms n the lterature typcally attempt to approxmate the Generalzed Processor Sharng (GPS) dscplne [20]. When usng the GPS dscplne, a server serves, say, n flows, each characterzed by a postve weght; let denote the weght assocated wth flow ( ¼ 1; ;n). Let W ðt 1 ;t 2 Þ be the amount of flow traffc served n the nterval ½t 1 ;t 2 Š. Then, for a GPS server [20], f flow s backlogged 1 throughout ½t 1 ;t 2 Š, the followng condton holds: W ðt 1 ;t 2 Þ W j ðt 1 ;t 2 Þ ; 8j: j Equalty holds above f flow j s also backlogged n nterval ½t 1 ;t 2 Š. Note that the above condton s vald regardless of how small the nterval ½t 1 ;t 2 Š. Ths mples that the GPS server can nterleave data from dfferent flows wth an arbtrarly fne granularty. The GPS dscplne cannot be accurately mplemented n practce snce data transmtted on real networks s packetzed. Ths observaton led to the development of several packet far queung algorthms whch approxmate GPS under the constrant that each 1. A queue (or flow) s sad to be backlogged f t s not empty /05/$20.00 ß 2005 IEEE Publshed by the IEEE CS, CASS, ComSoc, IES, & SPS

2 VAIDYA ET AL.: DISTRIBUTED FAIR SCHEDULING IN A WIRELESS LAN 617 Fg. 1. A node wth several flows sharng a lnk. packet must be transmtted as a whole [2], [4], [14], [20]. These protocols are centralzed by desgn, as noted above. There has been some work on achevng farness n wreless networks (e.g., [3], [12], [16], [17], [27], [26]). Some of the past work on ncorporatng farness nto dstrbuted protocols has been lmted n that these protocols attempt to provde an equal share of bandwdth to dfferent nodes (essentally, node weghts are mplctly assumed to be equal). Other researchers have developed protocols that take nto consderaton multhop network topology to acheve farness. For nstance, Luo et al. [16] have developed mechansms that acheve weghted farness whle also tryng to maxmze the throughput. They proposed an nterestng approach based on the noton of a flow contenton graph that takes nto account the topology of the network. They have also developed a topologyndependent model for far queung [17]. The protocol proposed n ths paper s relatvely smple, but wth relatvely modest goals compared to the work of Luo et al. In recent years, researchers have also consdered the use of far queung n the wreless cellular envronment llustrated n Fg. 2a. Although exstng centralzed algorthms may be appled to the wreless envronment (wth the base staton actng as the coordnator), t has been observed that farness acheved by these algorthms may suffer n the presence of locaton-dependent errors [19]. Wth locaton-dependent errors, whle error-free transmsson may be possble between a gven host and the base staton, transmssons between another host and the base staton may be corrupted by errors. In ths case, some mechansm to compensate hosts whose packets are corrupted by errors should be ncorporated. Many approaches for mprovng farness n the presence of locaton-dependent errors have been developed [15], [18], [19], [21]. These approaches are centralzed and requre the base staton to coordnate access to the wreless channel, whereas the proposed protocol s dstrbuted. There has also been work on dstrbuted protocols that takes prortes nto account when performng medum access control [1], [25], [23], [24]. For nstance, Aad and Castellucca [1] present servce dfferentaton mechansms for wreless networks. Ther mechansm allows a host to pck a backoff nterval as a functon of ts prorty, larger backoff ntervals beng used for lower prorty. Our proposed far schedulng mechansm uses a smlar mechansm, but wth the goal of achevng weghted far schedulng, not prorty schedulng. Our related work [22] proposed a dstrbuted MAC protocol for wreless networks to support prortzed schedulng along wth a weghted far sharng of the bandwdth among the users belongng to the same prorty level. Interestng work on a dstrbuted schedulng algorthm for real-tme traffc on a wreless LAN has also been performed [23]. Ths work, however, assumes that a flow transmts packets wth a constant rate. Such assumptons cannot be made when performng far schedulng. The rest of ths paper s organzed as follows: Secton 2 dscusses some background on the SCFQ far queung protocol and IEEE The proposed protocol s dscussed n Secton 3. An approach to mprove performance of the proposed protocol s presented n Secton 4 and an adaptve protocol n Secton 5. Secton 6 makes some nterestng observatons about the proposed method. Performance evaluaton s presented n Secton 7. Fnally, conclusons are presented n Secton 8. 2 PRELIMINARIES The objectve behnd ths work was to develop a far schedulng MAC protocol for a wreless LAN (llustrated n Fg. 2b), wth the followng propertes: 1) The protocol must Fg. 2. Wreless envronments. (a) In centralzed approaches, the base staton coordnates medum access. (b) In dstrbuted approaches, all nodes have dentcal responsbltes.

3 618 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 4, NO. 6, NOVEMBER/DECEMBER 2005 be fully dstrbuted n that no sngle node should have any specal responsblty. 2) Each node should be able to ndependently determne when to transmt a packet, wthout knowng the state of (or exstence of) flows at other nodes the state of a flow ncludes nformaton such as the weght of the flow, whether the flow s backlogged or not, and the tme of the arrval of packets on the flow. 3) Mantan compatblty or close resemblance to an exstng wreless MAC standard, to make t easer to mplement the proposed protocol. The next two sectons descrbe a centralzed far queung algorthm and the IEEE MAC protocol, whch together form the bass for the proposed far schedulng protocol. 2.1 Self-Clocked Far Queung (SCFQ) The algorthm proposed here was desgned n an attempt to emulate Self-Clocked Far Queung (SCFQ) n a dstrbuted manner. Two mportant ssues are worth notng here: 1) The proposed technque to mplement dstrbuted far schedulng can also be extended to other far queung algorthms, such as Start-Tme Far Queung (SFQ) [14]. 2) Although our ntenton was to emulate SCFQ, the dstrbuted mplementaton behaves somewhat dfferently, as dscussed later n Sectons 6.1 and 6.4. Now, we brefly descrbe the centralzed SCFQ algorthm [13] whch assumes the archtecture shown n Fg. 1. A vrtual clock s mantaned by the central coordnator, and vðtþ denotes the vrtual tme at real tme t. Let P k denote the kth packet arrvng on flow. Let A k denote the real tme at whch packet P k arrves. Let L k k denote the sze of packet P. A start tag S k and a fnsh tag F k are assocated wth each packet P k, as descrbed below. Let F 0 ¼ 0; On arrval of packet P k, the packet s stamped wth start tag S k, calculated as S k ¼ maxmumfvða k Þ;Fk 1 g: Also, F k k, the fnsh tag of P, s calculated as F k ¼ S k þ Lk. 2. Intally, the vrtual clock s set to 0,.e., vð0þ ¼0. The vrtual tme s updated only when a new packet s transmtted. When a packet begns transmsson on the output lnk, the vrtual clock s set equal to the fnsh tag of that packet. 3. Packets are transmtted on the lnk n ncreasng order of ther fnsh tags. Tes are broken arbtrarly. As noted n Step 1 above, n the SCFQ algorthm (and, also n other algorthms, such as SFQ [14], WFQ [4], WF2Q [2], etc.), the start and fnsh tags are calculated when a packet arrves n a flow. An alternatve approach s to calculate the start tag when a packet reaches the front of ts flow; that s, for a packet P k n flow, start and fnsh tags are calculated only after all packets that arrved n flow before packet P k have been servced. If ths approach were to be used, then calculaton of the start tag above should be modfed as follows: Let f k denote the real tme when packet P k reaches the front of ts flow. If P k arrves on an empty flow, then f k ¼ A k ; else, fk wll denote the real tme when P k 1 fnshes servce. On arrval of packet P k at the front of ts flow, the packet s stamped wth start tag S k, calculated as S k ¼ vðf k Þ: The fnsh tag s calculated as before, as F k ¼ S k þ Lk =.It s a smple exercse to verfy that, for the SCFQ algorthm, ths new procedure and the earler procedure result n the same start and fnsh tags for all packets. In our dstrbuted mplementaton, however, we emulate the latter procedure. 2.2 IEEE MAC: Dstrbuted Coordnaton Functon The medum access control protocol specfed n the IEEE standard cannot perform far allocaton, partcularly on short tme scales, (even f we assume that all flows have equal weghts). However, usng a mechansm smlar to the Dstrbuted Coordnaton Functon (DCF) n IEEE , the proposed protocol s able to acheve sgnfcantly better farness. We now brefly present salent features of the Dstrbuted Coordnaton Functon (DCF) n IEEE A CSMA/CA (collson avodance) mechansm s ncorporated n DCF. A smlar mechansm s also used n the proposed protocol. When a node wshes to transmt a packet, t chooses a backoff nterval equal to B slots. 2 Specfcally, B s chosen unformly dstrbuted n the nterval ½0;cwŠ, where cw s the sze of the so-called contenton wndow. cw at node s reset to a value CW mn at the begnnng of tme and also after each successful transmsson of a data packet by node. Now, f the transmsson medum s not dle, node wats untl t becomes dle. Then, whle the medum s dle, B s decremented by 1 after each slot tme. 3 If the medum becomes busy whle B s nonzero, then B s frozen whle the medum s busy. B s decremented agan when the medum becomes dle. Eventually, when B reaches 0, node transmts a Request-to-Send (RTS) packet for the ntended destnaton of the packet. The destnaton node, on recevng the RTS, sends a Clear-to-Send (CTS) packet. Node, on recept of the CTS packet, transmts the data packet. The recever node, on recept of data, sends an acknowledgment (ACK). Now, t s possble that two nodes, say and j, may choose ther backoff ntervals such that they both transmt ther RTS packets smultaneously, causng a collson between the RTS packets. In ths case, node wll not receve a CTS, therefore, t wll not be able to send the data packet. When a CTS s not receved, node doubles ts contenton wndow sze cw, pcks a new B unformly dstrbuted over ½0;cwŠ, and repeats the above procedure. 3 DISTRIBUTED FAIR SCHEDULING (DFS) PROTOCOL The proposed Dstrbuted Far Schedulng (DFS) protocol s based on the IEEE MAC and SCFQ: 2. A slot s a fxed nterval of tme defned n IEEE Actually, node wats for an nterval known as an nterframe spacng, before startng to decrement B. We wll omt such detals n ths dscusson. However, our smulaton model does mplement these detals accurately. ð1þ

4 VAIDYA ET AL.: DISTRIBUTED FAIR SCHEDULING IN A WIRELESS LAN 619. The DFS protocol borrows SCFQ s dea of transmttng the packet whose fnsh tag s the smallest, as well as SCFQ s mechansm for updatng the vrtual tme.. A dstrbuted approach for determnng the smallest fnsh tag s employed, usng the backoff nterval mechansm from IEEE MAC. The essental dea s to choose a backoff nterval that s proportonal to the fnsh tag of the packet to be transmtted. Several mplementatons of ths dea are possble, as dscussed below. We now descrbe the proposed approach. In our dscusson and smulatons, we assume that all packets at a node belong to a sngle flow the proposed algorthm can be easly extended when multple queues are mantaned at each node (as dscussed later n Secton 6.2). Each node mantans a local vrtual clock, v ðtþ, where v ð0þ ¼0. Now, P k represents the kth packet arrvng at the flow at node on the LAN.. Each transmtted packet s tagged wth ts fnsh tag.. When, at tme t, node hears or transmts a packet wth fnsh tag Z, node sets ts vrtual clock v equal 4 to maxmumðv ðtþ;zþ.. Start and fnsh tags for a packet are not calculated when the packet arrves. Instead, the tags for a packet are calculated when the packet reaches the front of ts flow. When packet P k reaches the front of ts flow at node, the packet s stamped wth start tag S k, calculated as (smlar to (1) for the SCFQ algorthm) S k ¼ vðf kþ, where fk denotes the real tme when packet P k reaches the front of the flow. Fnsh tag F k s calculated as follows, where the approprate choce of the Scalng_Factor allows us to choose a sutable scale for the vrtual tme: F k ¼ S k þ Scalng Factor Lk ¼ vðf k ÞþScalng F actor Lk :. The objectve of the next step s to choose a backoff nterval such that a packet wth a smaller fnsh tag wll deally be assgned a smaller backoff nterval. Ths step s performed at tme f k. Specfcally, node pcks a backoff nterval B for packet P k, as a functon of F k and the current vrtual tme v ðf kþ,as follows: B ¼ F k vðf k Þ slots: ð2þ Now, observe that, snce F k ¼ vðf k ÞþScalng F actor Lk ; 4. The vrtual clock update mechansm n DFS dffers somewhat from that n SCFQ. Due to potental collson between packets n the dstrbuted mplementaton, occasonally a packet wth a larger fnsh tag may be transmtted before a packet wth a smaller fnsh tag. To ensure that vrtual clocks are nondecreasng, maxðv ðtþ;zþ s used n ths step. Incdentally, as dscussed later n Secton 6.1, DFS can be mplemented wthout mantanng vrtual clocks at the nodes. the above expresson reduces to: B ¼ Scalng F actor Lk : ð3þ Fnally, to reduce the possblty of collsons, we randomze the B value chosen above as follows: B ¼ b B c; ð4þ where s a random varable wth mean 1. In our smulatons, s unformly dstrbuted n the nterval ½0:9; 1:1Š. When ths step s performed, a varable named CollsonCounter s reset to 0.. Collson handlng: If a collson occurs (because backoff ntervals of two or more nodes count down to 0 smultaneously), then the followng procedure s used. 5 Let node be one of the nodes whose transmsson has collded wth some other node(s). Node chooses a new backoff nterval as follows: - Increment CollsonCounter by 1. - Choose new B unformly dstrbuted n 1; 2 CollsonCounter 1 CollsonWndow, where CollsonW ndow s a constant parameter. The above procedure tends to choose a relatvely small B (n the range ½1; CollsonWndowŠ) after the frst collson for a packet. The motvaton for choosng small B after the frst collson s as follows: The fact that node was a potental wnner of the contenton for channel access ndcates that t s node s turn to transmt n the near future. Therefore, B s chosen to be small to ncrease the probablty that node wns agan soon. However, to protect aganst the stuaton when too many nodes collde, the range for B grows exponentally wth the number of consecutve collsons. The above protocol has two potental shortcomngs:. The DFS protocol can exhbt short-term unfarness for some nodes when ther packets collde. For nstance, assume that, at the begnnng of tme, nodes 1, 2, and 3 pck backoff ntervals of 25, 25, and 26 slots, respectvely. Nodes 1 and 2 would collde when ther backoff ntervals count down to 0 (the backoff nterval of node 3 would count down to one slot by ths tme). After collson, nodes 1 and 2 pck new backoff ntervals of, say, 2 and 3 slots, respectvely. In ths case, node 3 would end up transmttng a packet before nodes 1 and 2, even though these two nodes should have transmtted earler (snce ther orgnal backoff ntervals were smaller). To elmnate such unfarness, a collson resoluton protocol whch guarantees colldng statons access pror to access by any other node (or a 5. Recall that, when the backoff nterval reaches 0, a node transmts an RTS (request-to-send) packet, smlar to IEEE When two or more nodes count down backoff ntervals to 0 smultaneously, ther RTS packets would collde.

5 620 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 4, NO. 6, NOVEMBER/DECEMBER 2005 Fg. 3. Functon : Threshold, K 1, and K 2 are constant parameters. In our smulatons, we use K 1 ¼ T hreshold. protocol whch ensures ths wth hgh probablty) must be used. Protocols for collson resoluton n a wreless LAN have been proposed [7], [22]. Analogous approaches may be used n conjuncton wth our algorthm as well. For performance evaluaton, we consder the DFS algorthm presented above wthout usng a perfect collson resoluton algorthm.. Observe that, n DFS, the duraton of the backoff nterval s drectly proportonal to the Scalng F actor and nversely proportonal to the weght of a flow. When the weghts of backlogged flows are small or the Scalng Factor s chosen to be large, the duraton of the backoff ntervals can become large. Ths leads to long duratons of dle tme when the nodes are countng down the backoff ntervals to 0. To address ths problem, we now present two solutons. In one of these solutons, we use mappng schemes to compress the backoff ntervals. In ths soluton the Scalng F actor s constant and predefned. In the other soluton, we use an adaptve scheme to dynamcally choose the Scalng F actor as a functon of contenton for the channel. 4 MAPPING SCHEMES We wll refer to the scheme presented above for calculatng the backoff nterval as the lnear scheme (or lnear mappng). From (2) and (3), observe that, n the lnear scheme, backoff nterval B s a lnear functon of fnsh tag and drectly proportonal to (1/flow weght). Ths can make the backoff ntervals large when flow weghts are small, as noted above. We consder an alternatve approach to obtan the backoff nterval as a functon of the fnsh tag usng some mappng schemes as follows (other alternatves are also possble). 4.1 Exponental Mappng Scheme Let denote the backoff nterval obtaned n (4) usng the lnear scheme descrbed above. When usng the exponental scheme, we apply another functon ðþ to obtan the actual backoff nterval B to be used for medum access. Functon ðþ s defned n Fg. 3. In the defnton of ðþ n Fg. 3, note that Threshold, K 1, and K 2 are constant parameters. Use of the functon has the mpact of compressng large values nto a smaller range; ths has an advantage and a dsadvantage:. The advantage s that the tme spent n countng down backoff ntervals s reduced, potentally mprovng performance when weghts of backlogged flows are small. Example 1. Consder an example of two flows wth weghts 0.01 and 0.02, respectvely. It may be the case that there are several other flows; however, let us assume that the other flows are not backlogged presently. Wth the lnear approach, backoff ntervals would be nversely proportonal to the weghts. Wth packets of sze 1,000 bytes and Scalng F actor ¼ 1=100, the lnear approach may yeld backoff ntervals of 1,000 slots and 500 slots, respectvely, for the two flows. Now, for the exponental scheme, suppose T hreshold ¼ 80, K 1 ¼ 80, and K 2 ¼ 0:002. Then, the correspondng exponentally mapped backoff nterval would be ð1; 000Þ ¼147 and ð500þ ¼125 slots, respectvely. Thus, the backoff nterval of flow 2 would count down to 0 much sooner wth the exponental mappng, as compared to the lnear mappng.. The dsadvantage s that, snce a larger range of lnear backoff ntervals s compressed nto a smaller exponental range, the lkelhood of collsons can ncrease wth the exponental scheme. For nstance, ð990þ ¼ð1; 000Þ ¼147; therefore, two nodes whch smultaneously begn countng down from ntal backoff ntervals of 990 and 1,000 slots when usng the lnear scheme would nstead both start countng down from 147 slots when usng the exponental scheme. If the lnear scheme were to be used, these two nodes would not collde, however, wth the exponental mappng scheme, they would collde. To reduce the possblty of such addtonal collsons, when defnng we ntroduced Threshold as a lower bound (on backoff nterval) below whch the exponental functon s not appled; thus, the fnal value of B may belong to the lnear range (between 1 and Threshold) or the exponental range (above Threshold). A small Threshold may result n better throughput but poorer farness, dependng upon the network condtons. On the other hand, a larger Threshold would yeld better farness but poorer throughput. Thus, by choosng the approprate Threshold, a trade-off between farness and throughput can be obtaned. The above exponental mappng scheme needs to be augmented to ncorporate a recalculaton procedure, as dscussed below Recalculaton of Backoff Intervals Unlke the case of lnear mappng, addtonal care needs to be taken to ensure far allocaton n the case of the exponental mappng; n partcular, the backoff ntervals must be recalculated after each packet transmsson to mantan farness. Let us explan ths usng the followng example.

6 VAIDYA ET AL.: DISTRIBUTED FAIR SCHEDULING IN A WIRELESS LAN 621 Fg. 4. Recalculaton procedure. Example 2. Consder two flows, flow 1 at node 1 and flow 2 at node 2, wth weghts 1.0 and 0.05, respectvely. Assume that both flows begn wth several queued packets of dentcal sze at tme 0. Let the packet sze be 1,000 bytes and the Scalng F actor be Then, Scalng F actor packetsze=flow weght wll be 10 slots for flow 1 and 200 slots for flow 2. For smplcty, let us assume that the random multpler (.e., ) used for all packets s 1.0 n ths example. Therefore, flow 1 wll pck a backoff nterval of 10 slots for all ts packets and flow 2 wll pck a backoff nterval of 200 slots for all ts packets. 6 As a result, on average, flow 2 wll transmt one packet for every 20 packets transmtted by flow 1 ths s consstent wth the assgned weghts. Now, f the exponental scheme were to be used wth Threshold ¼ 80 slots, K 1 ¼ 80, and K 2 ¼ 0:002, then flow 1 wll contnue to use a backoff nterval of 10 slots, but flow 2 wll pck a backoff nterval of ð200þ ¼97. Now, unless some precauton s taken, flow 2 wll transmt a packet after approxmately 9 or 10 packets transmtted by flow 1, on average ths s nconsstent wth the assgned weghts. The above example llustrates that, unless modfed, the exponental mappng scheme presented above can result n unfar bandwdth allocaton. To avod such unfarness, the backoff ntervals n the exponental range must be recalculated after each packet transmsson on the wreless channel. We now descrbe our recalculaton procedure. When usng the recalculaton procedure, the value for a gven pendng packet may be recalculated many tmes. Consder a packet P that s beng transmtted on the channel presently. Let the most recent value of for ths packet be current. Then, to allow recalculatons to be performed, when packet P s transmtted, we tag t wth the value current. For nstance, n Example 2 above, node 1 mght tag ts transmtted packet wth current ¼ 10. Now, when some node hears a packet transmtted by node j, node updates the and B for ts pendng packet (f any), as shown n Fg. 4. The fnal step n Fg. 4 recalculates the backoff nterval. Node then begns to count down from ths new value of B. In Example 2, flows 1 and 2 ntally set to 10 and 200 slots, respectvely, and the backoff ntervals to 10 and 97 slots, respectvely, as dscussed above. Now, when flow 1 transmts ts packet after countng down the backoff nterval from 10 to 0, t tags the transmtted packet wth current ¼ 10. On hearng ths packet, node 2 updates ts 6. In realty, due to randomzaton, the backoff ntervals wll not be constant for a gven flow. as ¼ 190 and recalculates the backoff nterval as ð190þ. (Now, for the packet on flow 2, current ¼ 190.) In the above example, snce the backoff nterval of flow 1 was n the lnear range, for ts transmtted packets, the most recently calculated values of and the chosen backoff nterval are equal however, n general, ths may not be the case. For nstance, f only flow 2 was backlogged n the above example (.e., flow 1 does not attempt to transmt), then flow 2 wll start wth a backoff nterval of 97 slots and ¼ 200 slots and eventually transmt a packet. Ths packet would then have been tagged wth ts current ¼ Other Mappngs In general, any ncreasng functon can be used to map values to backoff ntervals, smlarly to the exponental mappng functon defned earler. Note that, although the lnear and exponental mappng functons are ncreasng, they are not strctly monotoncally ncreasng functons due to the fact that backoff ntervals must be ntegers. Ths can result n many values beng mapped to the same backoff nterval. The frequency of such occurrences depends on how much compresson s performed by the mappng functon. Observe that the exponental functon results n a sgnfcantly greater compresson than the lnear mappng. As a compromse between these two possbltes, n our evaluaton, we also consder another mappng, ðþ, defned n Fg. 5. We wll refer to the mappng n Fg. 5 as the square-root mappng. The procedure for usng the squareroot mappng s dentcal to that for exponental mappng, except that ðþ s used nstead of ðþ. The recalculaton procedure s also smlar to that for the exponental mappng, wth the only dfference beng that ðþ s used nstead of ðþ. Fg. 6 llustrates the three mappngs consdered n ths paper. Clearly, many other alternatves for the mappng are also possble. In ths paper, however, only the above mappngs are evaluated. 5 ADAPTIVE DFS The performance of DFS depends on the Scalng F actor chosen and the weghts assgned to varous flows. In the earler dscusson n ths paper, we had chosen a statc Scalng Factor and had assgned statc weghts to the flows. Fg. 5. Functon.

7 622 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 4, NO. 6, NOVEMBER/DECEMBER 2005 other nodes n the Wreless LAN snoop on the pggybacked Scalng F actor value and adjust ther Scalng F actor accordngly so that all nodes have a unfed vew of the contenton for the channel bandwdth. We now descrbe ths scheme for dynamc adaptaton of the Scalng F actor n more detal. Every node n the network mantans a CollsonCounter (as already explaned n the earler dscusson of the DFS scheme) and a SuccessCounter. A node uses these two varables n the followng manner:. Before node s about to transmt a data packet (after recevng the CTS): Fg. 6. Illustraton of the mappng functons: For all mappngs, the Scalng F actor s assumed to be For the exponental and lnear mappngs, the Threshold s 80. For exponental mappng, K 1 ¼ 80 and K 2 ¼ 0:002. The choce of weghts for the flows and the Scalng F actor can sgnfcantly affect the performance of DFS. It should be noted that larger weghts result n DFS choosng smaller contenton wndows. Therefore, f the weghts are chosen to be too large, DFS performance can degrade due to ncreased collsons. On the other hand, smaller weghts result n DFS choosng larger contenton wndows. Therefore, f the weghts are chosen to be too small, DFS performance can degrade due to ncreased overhead. Smlarly, when the Scalng F actor s chosen to be large, t results n DFS choosng large contenton wndows, leadng to a greater overhead. On the other hand, when the Scalng F actor s chosen to be small, t results n DFS choosng small contenton wndows, thereby resultng n an ncrease n the probablty of collsons. Snce the load on the network, as well as the number of nodes n the Wreless LAN, can vary dynamcally, t s dffcult to choose an approprate value of the Scalng F actor and approprate weghts for the flows that would result n a good performance under all load condtons. In ths secton, we present a scheme to dynamcally adapt the Scalng F actor as a functon of the contenton for the channel. In prncple, although t s possble to utlze nonlnear mappngs (e.g., exponental) mappng n conjuncton wth the adaptve DFS, here we focus only on the lnear mappng. 5.1 Dynamc Adaptaton of Scalng_Factor For tme-varyng network condtons, dynamc adaptaton of the Scalng F actor s useful. In the proposed scheme, when the contenton for the channel ncreases (ndcated by collsons on the channel), the Scalng F actor s ncreased to reduce the possblty of collsons. On the other hand, when there s low contenton for the channel, the Scalng F actor s reduced to avod large backoff ntervals and long duratons of dle tme, thereby mprovng the aggregate throughput. The dynamc adaptaton of the Scalng F actor also obvates the need for any mappng scheme to compress the backoff nterval to acheve a better performance. In the dynamc adaptaton scheme, when a node gets to transmt, t pggybacks ts Scalng Factor on the data packet. All - It resets CollsonCounter to 0. - It ncrements SuccessCounter by 1. - If SuccessCounter exceeds a certan predefned threshold, say Success T hreshold, t resets SuccessCounter to 0 and decreases the Scalng F actor by a predefned multplcatve decrement factor. Success T hreshold, together wth the decrement factor, controls how gradually the Scalng F actor would be decreased. - It then pggybacks the Scalng F actor on the data packet to be transmtted.. After node suffers a collson: - It resets SuccessCounter to 0. - It ncrements CollsonCounter by 1. - It chooses a new B unformly dstrbuted n 1; 2 CollsonCounter 1 CollsonWndow, where CollsonWndow s a constant parameter. - If the CollsonCounter > 1, t ncreases the Scalng F actor by a certan predefned multplcatve ncrement factor. 7 Whenever a node transmts a data packet, t pggybacks ts Scalng F actor on the data packet. All other nodes n the Wreless LAN snoop on the pggybacked Scalng F actor value. Specfcally, f a node, say node j, fnds that the pggybacked Scalng F actor s dfferent from ts Scalng F actor, t takes the followng actons:. If CollsonCounter j ¼ 0, - If node j was backlogged, t updates ts remanng slots to be counted down (say rs j ) as follows: rs j ¼ rs j Scalng Factor =Scalng F actor j ; ð6þ - Node j sets Scalng F actor j ¼ Scalng Factor. - Node j resets SuccessCounter j to 0.. If CollsonCounter j ¼ 1, - Node j sets Scalng F actor j ¼ Scalng Factor. 7. A node ncrements the Scalng Factor only when the CollsonCounter > 1 because the frst collson for a gven packet s not necessarly an ndcaton of heavy contenton for the channel. However, when a node suffers a seres of collsons for the same packet (n whch case, ts CollsonCounter would be > 1), t s lkely that there s heavy contenton for the channel.

8 VAIDYA ET AL.: DISTRIBUTED FAIR SCHEDULING IN A WIRELESS LAN 623. If CollsonCounter j > 1, - If Scalng F actor j < Scalng F actor, node j sets Scalng Factor j ¼ Scalng F actor. Else Scalng F actor j remans unchanged. We study the performance of Adaptve DFS n the performance evaluaton secton. 6 OBSERVATIONS 6.1 Vrtual Clocks Recall that, wth lnear mappng, the backoff nterval s calculated usng (3) and (4). Thus, the vrtual clock value mantaned by a node s not used n the calculaton of the backoff nterval at all. Ths means that, when usng the lnear mappng, there s no need to tag the fnsh tag to the transmtted packet or to mantan a vrtual clock at the nodes. Ths s the approach used n the evaluaton of DFS. For exponental and square-root mappngs though, we need to tag current of the transmtted packet. Smlarly, n the exponental mappng scheme and the recalculaton procedure presented n the paper, the vrtual tme s not used. Thus, there s no need to mantan vrtual clocks n ths case as well. However, t should be noted that alternatve recalculaton procedures can be conceved whch make use of the vrtual tme. When such procedures are used, t s necessary to mantan vrtual clocks. 6.2 Multple Flows Per Node In our dscusson of DFS, we assumed that only one flow exsts at each node. In general, t s possble that each node may mantan multple flows locally. In ths case, we modfy the DFS protocol as descrbed below.. Whenever a packet reaches the front of ts flow at some node, start and fnsh tags for the packet are calculated as descrbed n DFS. Specfcally, the start tag s set equal to the current vrtual tme at node and the fnsh tag for the packet s set equal to the (start tag + Scalng_Factor*packet length/flow weght).. When node needs to choose the next packet that t wll attempt to transmt, t chooses the packet, say P, wth the smallest fnsh tag among packets at the front of all backlogged flows at node. The backoff nterval for packet P s calculated usng procedure descrbed n Secton 3. The rest of the steps for transmttng P are dentcal to those descrbed n DFS. An analogous procedure has been suggested n the paper on MACAW [3], although that paper does not present a mechansm for allocatng bandwdth proportonal to weghts of the flows. 6.3 Impact of Transmsson Errors In case of a wreless LAN, transmsson errors can occur, resultng n packet loss. There are two ssues that need to be addressed n ths area: 1) How to determne whch packet s lost due to transmsson errors. 2) How to mantan farness n presence of transmsson errors, assumng that the above queston can be answered satsfactorly. We have performed evaluaton of the proposed DFS scheme n the presence of errors. Our smulatons ndcate that, n the presence of errors, farness acheved by DFS degrades (as mght be expected), however, t remans farer than IEEE We now brefly present some prelmnary deas on addressng the above two questons:. For the sender of a packet on the wreless channel, t s dffcult to determne whether a packet was lost due to transmsson errors or due to collson wth transmsson by another node on the LAN. As dscussed prevously, IEEE provdes for an exchange of RTS and CTS packets that precedes the transmsson of the data packet. The heurstc we propose (to be used n conjuncton wth DFS) s to assume that any loss of RTS or CTS packets s due to collsons and any loss of data or ACK packet s due to transmsson errors. Clearly, RTS and CTS packets may be lost due to errors, too. Assume ther loss to be due to collson results n the nvocaton of the collson handlng procedure n DFS. Snce the backoff nterval chosen after the frst collson of a packet s small, the cost of msnterpretng an error loss as a collson loss s not hgh.. Compensaton of flows: Many centralzed approaches have been developed for mprovng farness n the presence of locaton-dependent errors [15], [18], [19], [21]. Among these proposals, the schemes presented n [5] and [21] lend themselves well to a dstrbuted mplementaton. An addtonal compensatng flow at each node, smlar to the Long-Term Farness Server (LTFS) defned n [21] can be mantaned n DFS. An LTFS s used to temporarly allocate addtonal bandwdth to compensate flows that suffer transmsson errors. In the dstrbuted case, one or more LTFS can be mantaned at each node on the LAN, whereas, n the centralzed algorthm n [21], only the base staton mantans LTFSs. Reference [5] proposes a dfferent mechansm, consstng of dynamc adaptaton of weghts by erroneous flows to ncrease effort n order to reclam lost bandwdth. It shows that flows experencng low error-rates can acheve long-term farness. In [5], the amount of compensaton can be lmted admnstratvely by means of a power factor. The dea of dynamc adaptaton of weghts has been mplemented n DFS n [10] to acheve long-term farness n the presence of errors. 6.4 Comparson of DFS and SCFQ Note that we began wth the goal of mtatng SCFQ. As seen from the descrpton of DFS, the DFS algorthm may appear to mtate SCFQ. However, there s a sgnfcant dfference between the behavors of SCFQ and DFS. Specfcally, DFS can yeld packet transmssons n an order that cannot possbly be obtaned n the centralzed mplementaton of SCFQ. In general, we beleve that such

9 624 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 4, NO. 6, NOVEMBER/DECEMBER 2005 a devaton s lkely to occur when any centralzed workconservng scheme 8 s appled to a dstrbuted envronment. To llustrate the dfference between SCFQ and DFS, consder a system consstng of two flows (n the dstrbuted case, the two flows resde on two dfferent nodes). Let the weght of flow 1 be 0.1 and the weght of flow 2 be 0.5. Assume that, ntally, both flows are empty. Also assume that a packet arrves on flow 1 at tme 0 and a packet of the same sze arrves on flow 2 at tme second. Now, n the centralzed mplementaton, snce only flow 1 s backlogged at tme 0 when usng a work-conservng scheduler, the packet from flow 1 s transmtted at tme 0, followed by the packet from flow 2. In the dstrbuted case, let us assume that the two flows resde on two dfferent nodes. Wth the dstrbuted mplementaton n DFS, a backoff nterval of, say, 100 slots may be chosen for flow 1. Let us assume that a slot s of duraton second. Also, assume that the lnear mappng s beng used. Now, the packet on flow 2 arrves at tme second. By ths tme, flow 1 s backoff nterval would have counted down from 100 to 80 (because each slot s of duraton second). Snce, weght of flow 2 s fve tmes the weght of flow 1, the backoff nterval chosen for the packet on flow 2 may be 20 slots. Thus, the backoff nterval of flow 2 wll count down from 20 to 0 before flow 1 s backoff nterval counts down to 0. Therefore, flow 2 wll transmt a packet before flow 1 can transmt. Clearly, the centralzed and dstrbuted mplementatons result n dfferent orderng of packet transmssons. Essentally, ths s because the dstrbuted mplementaton s not work-conservng. Some of the work s spent on performng medum access control (MAC), not transmttng packets from the flows. As seen above, the overhead ncurred by MAC may allow transmsson of packets whch could not have been consdered for transmsson n the centralzed case. 7 PERFORMANCE EVALUATION In ths secton, we present performance evaluaton results for the proposed DFS protocol. Performance evaluaton s performed usng a modfed verson of the ns-2 smulator [6]. The ns-2 smulator ncludes a module to smulate the DCF functon n IEEE We modfed ths module to smulate the proposed DFS protocol as well. The channel bandwdth s assumed to be 2 Mbps. The vrtual clock s not used n the mplementaton, as dscussed n Secton 6.1. In the smulaton envronment, the number of nodes on the LAN s n, where we have consdered n 128. On a LAN wth n nodes, we set up n=2 flows (n s always chosen to be an even number). Flow s set up from node 2 to node 2 þ 1 (the nodes are numbered 0 through n 1). The choce of the destnaton nodes for the flows s somewhat arbtrary, and any destnaton could have been chosen for each flow wthout affectng the results. In our smulatons, each flow s assgned a fxed weght. We assume that, n a practcal mplementaton, the weghts wll be assgned by an upper layer of the protocol stack, 8. When usng a work-conservng server, the output channel s not kept dle f any flow s backlogged. wth the job of the MAC protocol beng to schedule packet transmssons such that weghted farness s acheved. When the MAC protocol fals n ts task (for nstance, perhaps due to transmsson errors), the upper layers may potentally adapt the weghts to acheve desred bandwdth dstrbuton [10]. Such an adaptaton of weghts s beyond the scope of ths paper. 7.1 DFS wth Statc Parameters Here, we present the performance evaluaton results for the proposed DFS protocol wth statc Scalng F actor. Unless otherwse specfed, the followng assumptons are made: 9 1. Each flow s backlogged throughout the duraton of the smulaton. 2. All packets on all flows contan 584 bytes Scalng F actor s CollsonWndow s four slots. 5. For the exponental and square-root mappng schemes, Threshold = 80. For the exponental mappng, K 1 ¼ 80 and K 2 ¼ 0: The duraton of smulatons s 6 seconds. Fg. 7 consders the case when the n=2 flows (n the case of a LAN wth n nodes) have dentcal weght. The chosen weght for each flow s 2=n (ths choce s arbtrary, and the results hold for other choces too, except when the chosen weghts are very large). Ths fgure plots the rato (throughput of a flow/flow weght) for all flows. The number of nodes n s dfferent n Fgs. 7a, 7b, and 7c. Note that the horzontal axes n Fg. 7 denote the destnaton node for the flow whose (throughput/weght) rato s plotted n the fgure. Results are plotted for IEEE , and the DFS scheme usng the lnear, exponental, and square-root mappngs. The curve labeled Lnear, EXP, and SQRT corresponds to the DFS scheme usng the respectve mappng schemes. Ideally, the (throughput/weght) curve should be flat snce all flows are always backlogged. Observe that the three DFS schemes do acheve a nearly flat curve. On the other hand, observe that IEEE results n unfar performance. For envronments where all flows are always backlogged, we evaluate a farness ndex [11] as follows, where T f denotes throughput of flow f, and f denotes weght of flow f: P 2 f T f= f farness ndex ¼ number of flows P f ðt f= f Þ 2 : Fg. 8 studes the varaton n farness ndex (as defned above) and aggregate throughput wth the number of flows. Aggregate throughput s obtaned by addng the throughput of all flows. Each flow s assgned a weght of 2=n (wth n=2 flows). Average throughput and averaged farness ndex over 10 runs are consdered here. Observe that DFS 9. The evaluaton presented here dffers somewhat from [8]. There are some dfferences n ther mplementatons, such as the vrtual clock feld s elmnated from the DFS header n ths work bytes s comprsed of 512 data bytes and 72 bytes of UDP, IP, and MAC headers. The exponental and square-root mappngs have an extra 4 bytes n the MAC header for the current feld. These 4 bytes are not counted n the throughput calculaton for unformty.

10 VAIDYA ET AL.: DISTRIBUTED FAIR SCHEDULING IN A WIRELESS LAN 625 Fg. 7. Comparson of IEEE and DFS. (a) Eght nodes. (b) 32 nodes. (c) 64 nodes. Fg. 8 Average aggregate throughput and farness ndex versus number of flows. (a) Aggregate throughput. (b) Farness ndex. Fg. 9 Impact of scalng factor. (a) Farness ndex. (b) Aggregate throughput. acheves very hgh farness, whle farness acheved by IEEE s often poor. However, the aggregate throughput acheved by may be hgher. IEEE results n a greater throughput because the DFS scheme tends to choose greater backoff ntervals than , resultng n hgher overhead for DFS. Now, when the three mappngs for the DFS scheme are consdered, as seen n Fg. 8, the three mappngs yeld comparable throughput and comparable farness. As seen later, the exponental and square-root mappngs provde a beneft when the backlogged flows have relatvely small weghts partcularly when the weghts of backlogged flows add up to much less than 1. Fg. 9 plots farness ndex and aggregate throughput as a functon of the Scalng F actor. An average of throughput and farness ndex over four runs s consdered here. Here, we only consder the lnear mappng results for other mappng are analogous. In ths case, sx flows are smulated wth weghts beng 1/2, 1/4, 1/8, 1/16, 1/32, and 1/32. Observe that, as the Scalng F actor s ncreased, farness ncreases. The throughput ntally mproves when the Scalng F actor s ncreased, but then degrades after the Scalng F actor s ncreased further. A larger Scalng F actor results n large backoff ntervals, leadng to a greater overhead. When the Scalng F actor s very small, there are too many collsons, resultng n low throughput; when the Scalng F actor s

11 626 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 4, NO. 6, NOVEMBER/DECEMBER 2005 Fg. 10 Farness results. (a) Farness wth varable packet szes. (b) Farness wth varable weght. ncreased, collsons reduce and throughput mproves. However, when Scalng F actor s ncreased further, throughput degradaton due to large backoff ntervals starts to domnate, and the aggregate throughput decreases. Fg. 9 renforces the observaton that a trade-off exsts between aggregate throughput and farness. Now, we consder the mpact of dfferng packet szes among flows. In Fg. 10a, we evaluate three flows, each wth weght 1/3, but ther packet szes are 584, 328, and 200 bytes, respectvely. The fgure plots (throughput/weght) for the three flows. Observe that the curve s horzontal for DFS schemes. The DFS scheme can handle packets of dfferng szes wthout affectng farness. We also smulated envronments where packet szes vary wthn each flow. The results are smlar to those n Fg. 10a and are omtted for brevty. Now, consder the case of four flows: flow 0! 1 wth weght 0.02 and flow 2! 3 wth a weght of 0.03, flow 4! 5 wth a weght 0.05, and flow 6! 7 wth a weght of 0.9. Frst, assume that all four flows are always backlogged. Results for ths case are shown n Fg. 10b. Ths fgure plots throughput/weght for the four flows. Observe that all three DFS mappngs are far, although lnear mappng gves slghtly hgher throughput. Next, assume that flow 6! 7 wth weght 0.9 s an on-off source, wth on-off perods of 0.3 and 5.4 seconds, respectvely. Ths flow coexsts wth the other three lower weght flows lsted above such that, for a smulaton of 6 seconds, flow 6! 7 s on for 10 percent of the tme. The aggregate throughput acheved by the three lower weght flows by the three mappng schemes s approxmately: 1) Lnear: 79 Kbps, 2) Exponental: 95 Kbps, and 3) Squareroot: 90 Kbps. The exponental and square-root schemes yeld 20 and 14 percent mprovement over Lnear. The farness acheved by the exponental and square-root schemes remans hgh, n addton to the hgher throughput. We calculated the farness ndex for each mappng, over the dfferent subntervals durng whch the set of backlogged flows remaned constant; the farness ndces for all three mappngs were over n all cases. The above example llustrates that the square-root and exponental mappngs can yeld better throughput than the lnear mappng (along wth good farness) when the aggregate weght of backlogged flows s small. On the other hand, when some backlogged flows have large weghts, ther backoff ntervals are small and the dle tme whle countng down the backoff nterval s bounded by the smallest backoff nterval. Therefore, when at least one flow wth a large weght s backlogged, the gan due to exponental and square-root mappngs s not sgnfcant. The results reported so far essentally evaluate the longterm farness of the proposed algorthm. A varaton of , referred to as _Scaled, s also consdered here _Scaled chooses contenton wndow values n the nterval [0, cw], where cw s the maxmum backoff nterval pcked by DFS after randomzaton. Ths allows us to study the mpact of proportonally large wndows on farness n Fg. 11 llustrates the short-term behavor of the DFS protocol n comparson to We count the number of packets (all packets are the same sze n ths case) servced from each flow over a wndow of sze 0.04 second, where the wndow tself sldes every 0.02 second. Fg. 11 plots the frequency dstrbuton of the number of packets receved by 8 flows, each wth a weght of 1/8. Observe that DFS always receves ether one or two packets n all ntervals receves zero packets n some ntervals, showng that some flows were put nto backoff unfarly durng those ntervals _Scaled performs better than by achevng a smaller spread than We obtaned a smlar plot for hgher number of flows as shown n [10]. Fg. 11. Number of packets receved per sldng wndow of 0.04 second.

12 VAIDYA ET AL.: DISTRIBUTED FAIR SCHEDULING IN A WIRELESS LAN 627 Fg. 12. Convergence of the farness ndex over the short-term. Fg. 12 shows the convergence of farness ndex over the short-term. Ths plot s for 24 flows, each wth a weght of 1/24. Note that DFS converges to the unt farness ndex value very soon. The convergence of _Scaled s faster as compared to Ths shows that the performance of can be mproved sgnfcantly by the choce of proportonally large ntal contenton wndows. Yet DFS acheves a hgher farness ndex than and _Scaled. Hence, the key to farness n DFS s the choce of proportonally large ntal backoff ntervals and the choce of a small wndow after collson. 7.2 Adaptve DFS Here, we present the performance evaluaton results for the case when the DFS protocol dynamcally adjusts the Scalng F actor accordng to the contenton for the channel. We also compare these results wth the results for the DFS protocol (lnear mappng), whch uses a statc Scalng F actor. Unless otherwse specfed, the followng assumptons are made: 1. All packets on all flows contan 500 data bytes. 2. Success_Threshold s three packets. 3. Whenever the Scalng F actor has to be ncreased, t s ncreased by 25 percent of the prevous value. Fg. 13. Dynamc adaptaton of the Scalng F actor. Whenever the Scalng Factor has to be decreased, t s decreased by 10 percent of the prevous value. 4. CollsonWndow (used n calculatng the backoff nterval after sufferng a collson) s four slots. 5. The duraton of smulatons s 10 seconds. Fg. 13 plots the pggybacked Scalng F actor as a functon of tme. Here, we consder the case when there are 10 flows, each wth a weght 0.2. Each of these flows has an on-off traffc source. The ntal Scalng F actor s As can be observed from Fg. 13, the Scalng F actor dynamcally adapts tself accordng to the contenton for the channel. When there s lttle contenton for the channel, the Scalng F actor drops down n order to reduce the overhead and long duratons of dle tme. However, f the contenton ncreases on the channel, the Scalng F actor ncreases to reduce the probablty of collsons. As we had dscussed earler, t s dffcult to choose an approprate value of the Scalng F actor and approprate weghts for the flows that would result n a good performance under all load condtons. The traffc load on a Wreless LAN can vary dynamcally. A gven Scalng F actor whch s approprate for a certan load condton may not work as well for other load condtons. Fg. 14 studes how the choce of the Scalng F actor affects the performance of DFS (wth statc Scalng F actor) and Adaptve DFS for a statc assgnment of weghts to Fg. 14. Comparson of DFS and Adaptve DFS. (a) Farness ndex. (b) Aggregate throughput.

13 628 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 4, NO. 6, NOVEMBER/DECEMBER 2005 the flows. Fg. 14a plots the varaton n farness ndex and Fg. 14b plots the varaton n aggregate throughput as a functon of the chosen Scalng F actor. Here, we consder the case when there are 10 flows, each wth a weght Each of these flows has a CBR traffc source whch s generatng traffc at the rate of 0.2Mbps. Both DFS and Adaptve DFS start wth the same ntal Scalng F actor. In DFS, the Scalng F actor remans constant throughout the entre duraton of smulaton, whereas n Adaptve DFS, the Scalng F actor dynamcally adapts as per the contenton for the channel. Here, we plot the aggregate throughput and the farness ndex acheved by DFS and Adaptve DFS as a functon of the Scalng F actor. As can be observed from Fg. 14, when the Scalng F actor s chosen to be very small, the farness ndex degrades n case of DFS. In DFS, when the Scalng Factor s very small, there s an ncreased lkelhood of collsons whch can potentally result n access prorty reversals and unfarness toward colldng nodes. When the Scalng F actor s chosen to be large, the farness ndex acheved by DFS mproves, but, at the same tme, the aggregate throughput degrades. In DFS, large Scalng F actor results n large backoff ntervals, leadng to a greater overhead. Adaptve DFS, on the other hand, dynamcally adapts the Scalng F actor and operates around the optmum Scalng F actor under the present load condtons. Hence, rrespectve of the choce of weghts for the flows or the choce of the ntal Scalng F actor, Adaptve DFS quckly converges to yeld a good performance (both n terms of farness and aggregate throughput). 8 CONCLUSIONS Ths paper consders the ssue of far schedulng n a wreless LAN. The objectve here s to develop a fully dstrbuted algorthm for schedulng packet transmssons such that dfferent flows are allocated bandwdth n proporton of ther weghts. The paper proposes a Dstrbuted Far Schedulng (DFS) approach obtaned by modfyng the Dstrbuted Coordnaton Functon (DCF) n IEEE standard. The smlartes between DFS and DCF would make t easer to ncorporate DFS n a modfed verson of Performance results show that the proposed protocol can allocate bandwdth n proporton to the weghts of the flows sharng the channel. We propose varous mappngs that can be used to choose the approprate backoff nterval for a packet. We also propose a scheme for dynamc adaptaton of the Scalng F actor whch allows us to acheve good performance rrespectve of the choce of the ntal Scalng F actor or the assgnment of weghts to the flows. ACKNOWLEDGMENTS Ths work s supported n part by the US Natonal Scence Foundaton and Mcrosoft Research. Ths paper was presented n part at Mobcom REFERENCES [1] I. Aad and C. 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14 VAIDYA ET AL.: DISTRIBUTED FAIR SCHEDULING IN A WIRELESS LAN 629 Ntn Vadya receved the PhD degree from the Unversty of Massachusetts at Amherst. He s presently an assocate professor of electrcal and computer engneerng at the Unversty of Illnos at Urbana-Champagn (UIUC). He has held vstng postons at Mcrosoft Research, Sun Mcrosystems, and the Indan Insttute of Technology-Bombay. He s a recpent of a CAREER award from the US Natonal Scence Foundaton. He served as program cochar for 2003 ACM MobCom and general char for 2001 ACM MobHoc. He presently serves as edtor-n-chef the IEEE Transactons on Moble Computng. He s a senor member of the IEEE and a member of the IEEE Computer Socety. Anurag Dugar graduated from the Natonal Insttute of Technology Karnataka, Inda, n electroncs and communcaton engneerng. He receved the MS degree n computer engneerng from Texas A&M Unversty n He was a research assstant n the Moble Computng and Networkng Group n the Department of Computer Scence at Texas A&M Unversty. He s currently workng as a senor software engneer n the Modelng Research and Development Dvson at OPNET Technologes, Bethesda, Maryland. At OPNET Technologes, he has been engaged n developng features n OPNET s sute of Intellgent Network Management Solutons. Seema Gupta graduated from the Indan Insttute of Technology, New Delh, n mathematcs and computer applcatons n She receved the MS degree n computer scence from Texas A&M Unversty n Snce the summer of 2000, she had worked as a software engneer wth Csco Systems, San Jose, Calforna. She worked on several projects n the areas of network securty, AAA (Authentcaton Authorzaton Accountng), and ntellgent edge subscrber servces. Paramvr Bahl receved the PhD degree n computer systems engneerng from the Unversty of Massachusetts Amherst. He s a senor researcher and manager of the Networkng Research Group at Mcrosoft Research. Some of hs semnal research ncludes: WLIB, a general purpose programmng nterface for wreless network cards; RADAR, a sgnalstrength based ndoor user-locaton determnaton system; CHOICE, an edge-server based publc area wreless network; and UCOM, a multrado wreless system. Currently, he leads MESH, a communty networkng and resdental broadband access network project, and NetHealth, an enterprse and home network self-managng dagnostc system. Several of hs deas are ncorporated nto Mcrosoft s core Wndows Operatng System product. In addton to buldng systems, he has authored more than 65 scentfc papers, 45 ssued and pendng patent applcatons, and a book chapter. He s the founder and charman of ACM SIGMOBILE, the founder and past edtor-n-chef of ACM Moble Computng and Communcatons Revew ( ), and the founder of ACM/USENIX MobSys. Hesa fellow of the ACM, an IEEE senor member, and past presdent of the electrcal engneerng honor socety Eta Kappa Nu-Zeta P.. For more nformaton on ths or any other computng topc, please vst our Dgtal Lbrary at