Optimization of IEEE Multirate Wireless LAN

Transcription

1 JOURNAL OF INFORMATION SCIENCE AND ENGINEERING (200) Optimization of IEEE 802 Multirate Wireless LAN A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN Department of Electronics and Communication Engineering National Institute of Technology Calicut Calicut India IEEE 802 standards support multiple data transmission rates with dynamic rate switching capability to improve the performance With multirate enhancement data transmission from wireless LAN (WLAN) stations can take place at various rates according to channel conditions This paper investigates the problem of optimizing aggregate saturation throughput of a multirate WLAN Analytical expressions for transmission rate specific optimal minimum Contention Window (CW min ) values that simultaneously maximize aggregate saturation throughput and provide proportional throughput differentiation among different stations are determined It is demonstrated that with these optimal CW min values the achievable aggregate throughput is much greater than that of the basic configuration in which competing stations use the same MAC parameters Further every station gets a throughput proportional to its data rate We also derive analytical expression for the maximum aggregate saturation throughput assuming very large number of active stations Keywords: IEEE 802 multirate wireless local area networks distributed coordination function maximum aggregate throughput proportional differentiation performance analysis INTRODUCTION The IEEE 802 family is an increasingly popular WLAN standard The IEEE 802 standard [] provides two medium access methods: () the Distributed Coordination Function (DCF) also known as the basic access method; (2) the Point Coordination Function (PCF) an access method similar to a polling system which uses a point coordinator to arbitrate the access right among nodes DCF is based on Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) and supports only best effort service DCF distributes the control of the channel through a set of listen and wait procedures observed by every station Today s WLANs are rate adaptive in which stations can transfer data at a number of transmission rates IEEE 802 standards [2 3] support multirate enhancement and data transmission can take place at various rates according to channel conditions Consequently with IEEE 802a [3] the set of possible data rates include and 54 Mbps; whereas for IEEE 802b [2] the set of possible data rates include 2 55 and Mbps As the multirate enhancements are physical layer protocols MAC mechanisms are required to exploit this capability The Auto Rate Fall back (ARF) protocol [4] is the commercial implementation of a MAC that utilizes this feature In this paper we consider the issue of maximizing aggregate throughput in a multirate WLAN We derive analytical solutions for transmission rate specific optimal CW min values that maximize aggregate saturation throughput and provide proportional throughput differentiation among stations in a multirate WLAN Through analysis and simulation Received August ; revised December ; accepted February Communicated by Yu-Chee Tseng 77

2 772 A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN it is demonstrated that the proposed CW min based solution achieves very large aggregate throughput compared to the basic configuration in which all stations use the same MAC parameters Rest of this paper is organized as follows: Section 2 gives a brief account of related work In section 3 expression for optimal CW min is derived Section 4 presents the results both analytical and simulation The paper is concluded in section 5 2 RELATED WORK Several papers have appeared in the literature for the performance analysis of IEEE 802 DCF with homogeneous or heterogeneous data transmission rates among competing stations [6-6] Bianchi [6] presents an analytical model to compute the saturation throughput performance of IEEE 802 DCF In [7] authors determine optimum CW min that maximizes the throughput by appropriate tuning of back off algorithm Qiao and Shin [8] propose a fair medium access control (PMAC) protocol to maximize wireless channel utilization subject to weighted fairness among multiple data traffic flows An analytical model to compute individual station throughput and delay in a multirate WLAN is proposed in [9]; but aggregate throughput maximization is not considered The performance anomaly of IEEE 802b is analyzed using a simplified model with saturated sources [0] Pong and Moors [] use the new feature of IEEE 802e draft standard transmission opportunity (TXOP) to provide temporal fairness among stations in a multirate WLAN Tinnirello and Choi [2] again consider temporal fairness provisioning in a multirate WLAN Yang et al [3] present remedies for the performance anomaly problem in multirate WLAN Sadegi et al [4] propose OAR an opportunistic media access protocol for multirate ad hoc networks Nitin et al [5] describe a distributed fair scheduling algorithm for a WLAN to achieve weighted fairness among the contending nodes Chou et al [6] propose airtime usage control of stations in multirate WLANs Banchs et al [7] propose two schemes to achieve proportional fair throughput allocation among contending stations in a multirate WLAN Ma et al [8] propose an adaptive mechanism to adjust the protocol parameters based on the number of competing stations to improve the WLAN performance In [9] authors address the selection of optimal CW min to achieve proportional fairness among stations in a multirate WLAN Finally works in [20-23] propose algorithms for rate adaptation in 802 networks In this paper differently from above a proportional throughput differentiation model [5] and aggregate throughput maximization is investigated for a WLAN with stations using distinct transmission rates 3 MAXIMIZING AGGREGATE SATURATION THROUGHPUT IN MULTIRATE WLAN Consider a WLAN with multiple transmission rates and n i stations having rate R i : i = 2 N Let Z i be the total throughput of class i station with rate R i ; z i be the per station throughput ie z i = Z i /n i ; and Z be the aggregate network throughput The proportional differentiation model [5] is defined as follows: z i /z = D i where D i is the differentiation ratio for stations with rate R i ; D = and 0 < D i < ; i = 2 N The throughput maximization problem with proportional throughput allocation is as follows: Max Z such that z i /z = D i First of all we consider maximization of aggregate system throughput in a two bit

3 OPTIMIZATION OF IEEE 802 MULTIRATE WLAN 773 rate WLAN based on tuning of CW min values The analysis is then extended to WLAN with three or more transmission rates 3 Optimal CW min Values for Slow and Fast Stations in a Two Bit Rate WLAN Consider a WLAN with two different data transmission rates lower rate R S corresponding to slow station and higher rate R F corresponding to fast station Further assume that there are n S slow stations and n F fast stations A station belongs to the ith class if it transmits at a rate R i Let m and m respectively represent the retry limit and the maximum value of back off stage (equal for all the stations) such that for station with rate R i the maximum value of CW CW imax = 2 m W i0 where W i0 is the CW min It is assumed that each node always has data to transmit and transmits only one frame in each TXOP All nodes are assumed to be within the transmission range of each other and use the basic access mechanism alone (without RTS/CTS) Further frame losses on the wireless channel are caused only by collisions It is also assumed that each node executes locally an ideal link adaptation algorithm to select the best physical transmission rate among the available rates permitted by the standard Let W ij represents the CW size in the jth retry/retransmission for station with rate R i Let p ci and τ i respectively represent the frame collision probability and frame transmission probability for station with rate R i The following expressions for τ i p ci and Z i are derived in [9] The probability that a node senses the channel to be idle is: p I = ( τ S ) n S ( τf ) n F () where τ i (i = S F) can be expressed as: m+ 2( 2 pci )( ( pci ) ) τi = [ W ( (2 p ) )( p ) ( 2 p )( ( p ) ) + m + m+ i0 c i c i + c i c i m m m Wi0 ( 2 pc i)(2 pc i) pc i( ( pc i) )] (2) The collision probabilities for slow and fast stations are given by: p cs = ( τ S ) n S - ( τ F ) n F ; pcf = ( τ S ) n S ( τf ) n F - (3) Let p tr be the probability that there is at least one transmission in a given time slot; and p trs and p trf be respectively the corresponding probabilities for slow and fast stations These probabilities are calculated as follows: p tr = ( τ S ) n S ( τf ) n F ; ptrs = ( τ S ) n S ; ptrf = ( τ F ) n F (4) Let p ss denotes the probability of having a successful transmission by one of the slow stations given that at least one slow station transmits a packet and let p sf be the corresponding probability for the fast station These are given by: ns nf nf n nsτs τ S τf nfτf τf τs ss psf ptr S ptr F p S ( ) ( ) ( ) ( ) = ; = (5)

4 774 A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN Saturation throughputs for slow and fast stations are calculated as follows: Z S = p tr S p s S E [ L S ] tr F s F [ F ] ; Z p p E L F E[ θ] = E[ θ] (6) where E[L S ] and E[L F ] respectively denote average payload for slow and fast station E[θ] represents the average duration of a generic slot which is given by: E[ θ] = ( p ) σ + p p T + p p T + [ p ( p ) p p ] T tr trs ss ss trf sf sf trs trf trs ss cs + [ p ( p ) p p ] T + p p max( T T ) trf trs trf sf cf trs trf cs cf (7) where σ T si and T ci (i = S F) respectively represent the duration of an empty time slot the average time channel is sensed busy because of successful transmission of station with rate R i and average time the channel is sensed busy because of a transmission failure due to collision of frames belonging to station with rate R i The per station saturation throughput ratio between slow and fast station D S is given by [9]: D S zs ZS/ ns τs( τf) = = z Z / n τ ( τ ) F F F F S (8) Let Z = Z S + Z F be the aggregate system throughput The throughput maximization problem with proportional differentiation is formulated as follows Max Z with the constraint of z S /z F = D S (9) Proposition The optimal frame transmission probabilities of slow and fast stations τ i (i = S F) respectively corresponding to Eq (9) can be approximated as follows: Di /[ Ts FK + Ts SK2] τ i (+ D /[ T K + T K ]) i s F s S 2 (0) where D F = ; 0 < D S < ; K = (n F /2)(n F ); K 2 = (n S /2)(n S )D S 2 + n S n F D S ; T s S = T ss /σ; and T s F = T sf /σ Here T s S and T s F represent the successful transmission duration expressed as number of idle slot time σ for slow and fast stations respectively Proof: Let α S = τ S /( τ S ); α F = τ F /( τ F ) then from Eq (8) α S = α F D S Combining Eqs () and (4)-(6) and assuming E[L S ] = E[L F ] = E[L] the aggregate throughput is given by: pi( nsαfds + nfαf) E[ L] Z = ZS + ZF = () E[ θ ] Consider E[θ] given by Eq (7) For basic access assume T cs T ss ; T cf T sf Note that max (T cs T cf ) = T cs Define the probabilities P IS and P IF as follows: p IS = ( τ S ) n S ; pif = ( τ F ) n F (2)

5 OPTIMIZATION OF IEEE 802 MULTIRATE WLAN 775 The expression for E[θ] becomes: E[θ] = p I [σ + T ss (p I p I F ) + T sf (p I F )] (3) Combining Eqs (8) and (2) we have: ns nf nsds+ nf IS αf S IF αf I αf p = ( + D ) ; P = ( + ) ; P = ( + ) (4) Expanding p I and p I F and neglecting higher order terms the expression for Z in Eq () becomes: ae[ L] Z = {( σ / αf) + Ts S[ a nf + ( b/2) αf ( nf/2)( nf ) αf] + T [ n + ( n /2)( n ) α ]} sf F F F F (5) where a = n S D S + n F and b = a 2 (n S D S 2 + n F ) The value of α F corresponding to maximum throughput Z is obtained by solving dz/dα F = 0 and is given by: α F T K + T K sf ss 2 (6) where K = (n F /2)(n F ); K 2 = (n S /2)(n S )D S 2 + n S n F D S The corresponding optimal transmission probability τ F for fast stations is given by: τ F + T K + T K sf ss 2 (7) Combining Eqs (8) and (6) α D /[ T K + T K ] τ S ( + ) ( + /[ + ]) FDS S s F s S 2 αfds DS Ts FK Ts SK2 (8) The optimal collision probabilities p c j and optimal CW min values W i 0 (i = S F) to meet the desired objectives can be obtained by rearranging Eqs (3) and (2) as follows: p W p I ci = 2 ( τi ) ( τi )( + aαf + ( b/2)( αf) m ( 2 p ci )( ( p ) + ci )((2/ τ i) ) i0 = m + m m m pci pci + pci pci pci pci [( (2 ) )( ) ( 2 )(2 ) ( ( ) )] (9) (20) Given D S the optimal frame transmission probabilities τ F and τ S are computed using Eq (0) Then the corresponding collision probabilities p c F and p c S are computed using Eq (9) The optimal CW min values are then determined using Eq (20)

6 776 A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN 32 Maximum Aggregate Saturation Throughput in Two Bit Rate WLAN An expression for maximum aggregate throughput Z is obtained by combining Eqs () and (3) and is given by Z aα F E[ L] ss I IF sf IF = σ + T ( p p ) + T ( p ) (2) Consider α F given in Eq (6) Assume n S n F >> and n S = n F = n Then K = n 2 /2 and K 2 = n 2 [(D S 2 /2) + D S ] and hence α F = /n[(t s F /2) + T s S [D S ( + (D S /2))]] /2 Since a = n( + D S ) we have α F a = [ + D S ]/[(T s F /2) + T s S [D S ( + (D S /2))]] /2 Note that α F a is independent of n and let α F a = K Further since α F << Eq (4) can be simplified as follows n a n K φ a K K IF ( α F) ; I ( α = + = + = + F) = + n( + DS ) a p e p e (22) where φ = K/( + D S ) Combining Eqs (2) and (22) the maximum aggregate throughput is given by: Z KE[ L] φ ( σ + T ( e e ) + T ( e )) K φ ss sf (23) Hence in a two bit rate WLAN with n S = n F = n and n >> Z approaches a constant value insensitive to the number of stations Under the above conditions and assuming τ S τ F << the collision probabilities p c S and p c F (for slow/fast stations) approaches a constant value and is given by: p c S = p c F p I = e K (24) 33 Extension to Wireless LAN with Three Bit Rates Consider a WLAN with three transmission rates: R S R M and R F corresponding to slow medium and fast stations Let n S n M and n F respectively be the numbers of these stations Also let W S0 /W M0 /W F0 be the CW min value for the slow/medium/fast rate stations Saturation throughput Z i of station with rate R i is calculated using Eq (6) for slow and fast stations and using a similar expression for the medium rate stations The computation of various probabilities involved is a straightforward extension of the two bit rate case E[θ] is determined as follows: E[ θ ] = ( ptr) σ + ptrs pss TsS + ptrm psm TsM + p p T + p ( p p p + p p ) T + p ( p p p + p p ) T tr F s F s F tr S s S tr M tr F tr M tr F c S tr M s M tr S tr F tr S tr F c M + ptr F ( ps F ptr S ptr M + ptr S ptrm ) TcF + ptr S ptr M ( ptr F ) max( Tc S Tc M ) + ptr S ptr F ( ptr M ) max( Tc S Tc F ) + p p ( p ) max( T T ) + p p p max( T T T ) tr M tr F tr S c M c F tr S tr M tr F c S c M c F (25)

7 OPTIMIZATION OF IEEE 802 MULTIRATE WLAN 777 Ratio of throughputs per station for any pair of rates R i and R j is given by [9]: z / ( ) i Zi n τi τ i j Di = = ; i j = S M F z Z / n τ ( τ ) j j j j i (26) The throughput maximization problem with proportional differentiation is given by: Max Z (= Z S + Z M + Z F ) such that z S /z F = D S ; z M /z F = D M (27) Proposition 2 The optimal frame transmission probabilities of slow medium and fast rate stations τ i (i = S M F) corresponding to Eq (27) can be approximated as follows: Di /[ Ts FJ + Ts MJ2 + Ts SJ3] τ i (+ D /[ T J + T J + T J ]) i s F s M 2 s S 3 (28) where D F = ; 0 < D S D M < ; T s i = T si /σ (i = S M F); J = (n F /2)(n F ); J 2 = (n M /2)(n M )D M 2 + n M n F D M ; J 3 = (n S /2)(n S )D S 2 + n S D S (n M D M + n F ) Proof: Let α M = τ M /( τ M ) then α M = α F D M Similar to Eq () the aggregate throughput is given by: pi( nsαfds + nmαfdm + nfαf) E[ L] Z = (29) E[ θ ] where p I = ( τ S ) n S ( τm ) n M ( τf ) n F Consider E[θ] given by Eq (25) For basic access assume T cs = T ss ; T cm = T sm ; T cf = T sf Note that max (T cs T cf ) = T cs ; max (T cs T cm ) = T cs ; max (T cm T cf ) = T cm and max (T cs T cm T sf ) = T cs Define the following probabilities: p ISM = ( τ S ) n S ( τm ) n M ; pisf = ( τ S ) n S ( τf ) n F ; pimf = ( τ M ) n M ( τf ) n F (30) A simplified expression for E[θ] is given by: I σ s S I I M F s M I M F I F s F I F E[ θ] = p [ + T ( p p ) + T ( p p ) + T ( p )] (3) Combining Eqs (26) and (30) we have: n n n D + n IMF= + αfdm + αf + αf M F M M F P ( ) ( ) ( ) ns n ( ) ( ) M nf nsds nmdm nf P + + = + α D + α D ( + α ) ( + α ) (32) I F S F M F F Expanding p I pi M F and p IF and neglecting higher order terms Z becomes: xe[ L] Z = {( σ / αf) + Ts S[ x c+ ( y/2) αf ( d/2) αf] + Ts M[ c nf + ( d/2) αf ( n /2)( n ) α + T [ n + ( n /2)( n ) α ]} F F F s F F F F F (33)

8 778 A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN Here x = n S D S + n M D M + n F ; y = x 2 (n S D S 2 + n M D M 2 + n F ); a = n S D S + n F ; b = a 2 (n S D S 2 + n F ); c = n M D M + n F ; and d = c 2 (n M D M 2 + n F ) The value of α F corresponding to maximum throughput Z is obtained by solving dz/dα F = 0 and is given as follows: α F T J + T J + T J sf sm 2 ss 3 (34) Here D F = ; 0 < D S D M < ; T s i = T si /σ (i = S M F); J = (n F /2)(n F ); J 2 = (n M /2)(n M )D M 2 + n M n F D M ; J 3 = (n S /2)(n S )D S 2 + n S D S (n M D M + n F ) T s i (i = S M F) represents the successful transmission duration for slow medium and fast rate stations expressed in terms of idle slot time σ The corresponding optimal transmission probability for fast stations τ F is given by: τ F + T J + T J + T J sf sm 2 ss 3 (35) Combining Eqs (26) and (35) we get the optimal transmission probabilities τ i (i = S M): Di /[ Ts FJ + Ts MJ2 + Ts SJ3] τ i (+ D /[ T J + T J + T J ]) i s F s M 2 s S 3 (36) Similar to Eqs (9) and (20) the optimal collision probabilities p c i and optimal CW min values W i 0 (i = S M F) are obtained as: p W ci y 2 ( τi ) + xαf + ( αf ) 2 m+ ( 2 pci )( ( pci ) )((2/ τi) ) i0 = m + m m m pci pci + pci pci pci pci [( (2 ) )( ) ( 2 )(2 ) ( ( ) )] (37) (38) Given D S D M and 802b parameters the optimal values of frame transmission probabilities collision probabilities and hence CW min can be determined 34 Maximum Aggregate Saturation Throughput in a Three Bit Rate WLAN The maximum aggregate throughput Z is obtained by combining Eqs (29) and (3) and is given by: Z xα F E[ L] ss I IM F sm IM F IF sf IF = σ + T ( p p ) + T ( p p ) + T ( p ) (39) Consider α F in Eq (34) Let n S = n M = n F = n and n >> Then x n( + D S + D M ); J =

9 OPTIMIZATION OF IEEE 802 MULTIRATE WLAN 779 n 2 /2; J 2 = n 2 ((D M 2 /2) + D M ); J 3 = n 2 ((D S 2 /2) + D S D M + D S ); and hence α F x = ( + D S + D M )/ [(T s F /2) + T s M ((D M 2 /2) + D M ) + T s S [(D S 2 /2) + D S (D M + )]] /2 Since α F x is independent of n let α F x = J Further since α F << the various optimal probabilities in Eq (39) can be simplified as follows: n J β p IF = ( + αf) + e n( + DS + DM) x n( + DS+ DM ) J J p I = ( + αf) + e x n( + D ) J( + D ) M M δ p IMF = ( + αf) + e n( + DS + DM) n n (40) (4) (42) J( + DM ) where β = J/( + D S + D M ) and δ = Combining Eqs (39)-(42) Z is given by: ( + DS + DM) Z JE[ L] ( σ + T ( e e ) + T ( e e ) + T ( e )) J δ δ β β ss sm sf Hence in a three bit rate WLAN with n S = n M = n F = n and n >> Z approaches a constant value insensitive to the number of stations Under the above conditions and assuming τ S τ M τ F << the collision probability experienced by slow/medium rate/fast stations approaches a constant value and is given by: (43) J pcs = pcm = pcf pi = e (44) 35 Wireless LAN with More than Three Bit Rates For a WLAN with multiple transmission rates and n i stations with rate R i ; (i = 2 N) the throughput maximization problem with proportional throughput allocation is as follows: Max Z such that z j /z = D j ; j = 2 3 N The optimal transmission probabilities of τ i of stations with rate R i can be approximated as: N N τ i Di / TS ij i + Di / TS iji i= i= (45) where J = (n /2)(n ); J i = (n i /2)(n i )D 2 i + nd i i( njdj) i = 2 3 N; D = j= i j i ; 0 < D i < (i = 2 3 N); and T s k = T sk /σ (k = 2 N) 4 NUMERICAL AND SIMULATION RESULTS In this section we present the numerical and simulation results The simulation

10 780 A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN model is developed using ns-226 [25] based on IEEE 802b standard [2] The wireless nodes are randomly deployed in a square area of 00meters 00meters and one Access Point (AP) is installed in the center of the area The nodes with possibly different data rates are trying to send saturated UDP constant bit rate (CBR) traffic towards AP A single hop network is assumed and the nodes are kept static during the whole simulation procedure The data rate of AP is assumed to be equal to that of the fastest node The available data rates for the nodes are set to 2 and Mbps as per IEEE 802b The values for the received power threshold for different data rates are chosen based on distance ranges specified in the Orinoco 802b data sheet All reported results are averages over multiple 300-seconds simulation The numerical results from the analytical model are obtained using MATLAB First consider a multirate WLAN with two different data rates: fast stations with data rate R F and slow station with data rate R S For slow station the target throughput differentiation ratio is D S = R S /R F Both slow and fast stations are configured with same AIFS values and let n S = n F = n Further we select the various parameters as follows: R S = Mbps/2Mpbs R F = Mbps m = 5 m = 8 E[L S ] = E[L S ] = 500 bytes The optimal CW min values for slow and fast stations to achieve the desired objectives are tabulated in Table for -Mbp/-Mbps WLAN as well as 2-Mbps/-Mbps WLAN We use these optimal values of CW min to investigate the performance The achieved aggregate throughput and throughput ratio between the slow and fast stations for various values of n are determined We also determine the individual station throughputs and total throughput for the case where all stations use the same MAC parameters and frame size (we refer this case as basic configuration) Table 2 shows the individual station throughputs and the aggregate throughput for the 2-Mbps/-Mbps case Fig shows the variation of aggregate throughput against n for -Mbps/-Mbps WLAN The aggregate throughputs obtained with optimal CW min values are much greater than those achieved for basic configuration In the case of a 2-Mbps/-Mbps WLAN with n S = n F = the Table Optimal W F 0 and W S 0 for -Mbps/-Mbps and 2-Mbps/-Mbps WLANs Number of nodes -Mbps/-Mbps 2-Mbps/-Mbps W F 0 W S 0 W F 0 W S 0 n S = n F = n S = n F = n S = n F = Table 2 Throughput achieved by stations in a two bit rate WLAN (2-Mbps/-Mbps WLAN) CW min setting Basic configuration Proposed CW min Z F Mbps analytic/ simulation Throughput Z S Mbps analytic/ simulation Z F /Z S analytic/ simulation Total (Z Mbps) analytic/ simulation n S = n F = 23/24 23/24 0/0 246/248 n S = n F = 0 02/06 02/06 0/0 204/22 n S = n F = 398/404 07/073 56/ /477 n S = n F = 0 39/ / / /467

11 OPTIMIZATION OF IEEE 802 MULTIRATE WLAN 78 Fig Aggregate saturation throughput vs n Fig 2 Aggregate saturation throughput vs n F Fig 3 Collision probability vs n aggregate throughput improves by as much as 92% compared to basic configuration while for -Mbps/-Mbps case the total throughput improves by as much as 200% With n S = n F = 5 the proposed method achieves about 3% increase in aggregate throughput over basic configuration while for n S = n F = 0 the total throughput is greater than basic configuration by 20% It may be noted that the improvement in aggregate throughput is greater than that reported in [9] With optimal CW min values the ratio of throughput per station is almost equal to the ratio of their data rates while for basic configuration this ratio is unity Fig 2 shows the aggregate throughput for increasing number of fast stations n F with n S = for a 2-Mbps/-Mbps WLAN Fig 3 shows the probability of collision for the slow as well as fast stations against n for basic configuration and optimal CW min method It may be noted that the probability of collision in the former case increases drastically as the network size grow while for the latter case the collision probability is almost a constant for large n With optimal CW min for n S = n F = 5 the collision probability reduces by about 60% and for n S = n F = 20 it reduces by 93% compared to basic configuration We have extended the evaluation to 802g WLAN and the throughput results are shown in Table 3 Next the performance evaluation is extended to the case of a WLAN with three bit rates: slow medium and fast stations with rates R S = Mbps R M = 2Mpbs and R F = Mbps respectively As in the previous case D F = and we select D S = R S /R F and D M = R M /R F For basic configuration the CW min values are W S0 = W M0 = W F0 = 32 Table 4 shows the throughput achieved by each station and also the aggregate throughput for different values of n In the case of a -Mbps/2-Mbps/-Mbps WLAN with n S = n M = n F

12 782 A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN Table 3 Throughput achieved by stations in 802g WLAN (6-Mbps/54-Mbps case) CW min setting Throughput Total throughput Z F Mbps Z S Mbps (Z Mbps) Basic configuration n S = n F = Proposed CW min n S = n F = Table 4 Throughput in a three bit rate WLAN (-Mbps/2-Mbps/ Mbps) CW min setting Throughput (Mbps) Ratio Total Z F Z M Z S Z F /Z M Z M /Z S (Z Mbps) Basic configuration n S = n M = n F = n S = n M = n F = Proposed CW min n S = n M = n F = n S = n M = n F = Fig 4 Aggregate saturation throughput vs simulation time (on-off traffic) Fig 5 Aggregate saturation throughput vs simulation time (variable on-off period) = the aggregate throughput improves by as much as 38% compared to basic configuration while for n S = n M = n F = 0 the aggregate throughput is greater than basic configuration by 88% Simulation with exponential on-off traffic: There are 6 nodes in the network with 8 slow and fast nodes and one AP Each node generates exponential on-off traffic towards the AP The duration of the on and off periods are both exponentially distributed with mean equal to 500 ms The frame size is 000 bytes and the total simulation duration is 60 sec The aggregate network throughput for 2-Mbp/-Mbps WLAN is shown in Fig 4 The simulation is repeated for variable on-off periods among the stations For the slow nodes the duration of the on and off periods are both exponentially distributed with mean 30 sec and 0 sec respectively and for the fast nodes on and off periods have mean equal to 40sec and 0 sec respectively The aggregate throughput shown in Fig 5 is obtained as average of ten simulation runs 5 CONCLUSION In this paper the problem of maximizing aggregate throughput in IEEE 802 mul-

13 OPTIMIZATION OF IEEE 802 MULTIRATE WLAN 783 tirate WLAN was investigated Optimal CW min values for stations with different bit rates to achieve both maximum aggregate throughput and proportional throughput differentiation were computed The analytical and simulation results revealed that with optimal CW min values the aggregate throughput is much greater than the basic configuration advocated by the DCF protocol Further with the proposed optimal CW min values ratio of throughputs achieved by two stations with heterogeneous transmission rate is equal to the ratio of their bit rates Hence the proposed scheme alleviates the inefficient and unfair throughput allocation of the basic configuration REFERENCES IEEE 802 WG IEEE Standard for Telecommunications and information exchange between systems Part II: WLAN MAC and PHY Layer specifications Aug IEEE 802b WG IEEE Standard for Telecommunications and information exchange between systems Part II: WLAN MAC and PHY Specifications: High-speed physical layer extension in the 24 GHz band Sep IEEE 802a WG IEEE Standard for Telecommunications and information exchange between systems Part II: WLAN MAC and PHY Specifications: High-speed physical layer extension in the 5 GHz band Sep A Kamerman and L Monteban Wave LAN II: A high-performance wireless LAN for the unlicensed band Bell Labs Technical Journal Vol pp A Dovrolis and P Ramanathan A case for relative differentiated services and the proportional differentiation model IEEE Networks Vol pp G Bianchi Performance analysis of the IEEE 802 distributed coordination function IEEE Journal on Selected Areas in Communications Vol pp F Cali M Conti and E Gregori Dynamic tuning of the IEEE 802 protocol to achieve a theoretical throughput limit IEEE/ACM Transactions on Networking Vol pp D Qiao and K G Shin Achieving efficient channel utilization and weighted fairness for data communications in IEEE 802 WLAN under the DCF in Proceedings of International Workshop on QoS 2002 pp A V Babu and L Jacob Fairness analysis of IEEE 802 multirate wireless LAN IEEE Transactions on Vehicular Technology Vol pp M Heusse F Rousseu G Berger-Sabbatel and A Duda Performance anomaly of IEEE 802b in Proceedings of the 22nd Annual Joint Conference of the IEEE Computer and Communications Societies Vol pp D Pong and T Moors Fairness and capacity trade-off in IEEE 802 WLANs in Proceedings of IEEE Conference on Local Computer Networks 2004 pp I Tinnirello and S Choi Temporal fairness provisioning in multirate contentionbased 802e WLANs in Proceedings of IEEE Symposium on World of Wireless and Mobile Multimedia Networks 2005 pp D Yang T Lee K Jang J Chang and S Choi Performance enhancement of multirate IEEE 802 WLANs with geographically scattered stations IEEE Transactions on Mobile Computing Vol pp

14 784 A V BABU LILLYKUTTY JACOB AND S ABDUL SUBHAN 4 B Sadeghi V Kanodia A Sabharwal and E Knightly Opportunistic media access for multirate ad hoc networks in Proceedings of ACM International Conference on Mobile Computing and Networking 2002 pp N Vaidya P Bahl and S Gupta Distributed fair scheduling in a wireless LAN in Proceedings of ACM International Conference on Mobile Computing and Networking 2000 pp C Chou K G Shin and S Shankar Contention-basee airtime usage control in multirate IEEE 802 wireless LANs IEEE/ACM Transactions on Networking Vol pp A Banchs P Serrano and H Oliver Proportional fair throughput allocation in multirate IEEE 802e wireless LANs Wireless Networks Vol pp H Ma X Li H Li P Zhang S Luo and C Yuan Dynamic optimization of IEEE 802 CSMA/CA based on the number of competing stations in Proceedings of IEEE International Conference on Communications Vol 2004 pp V A Siris and G Stamatakis Optimal CW min selection for achieving proportional fairness in multi-rate 802e WLANs: test-bed implementation and evaluation in Proceedings of International Conference on Mobile Computing and Networking 2006 pp G Holland N Vaidya and P Bahl A rate-adaptive MAC protocol for multi-hop wireless networks in Proceedings of ACM International Conference on Mobile Computing and Networking 200 pp S Khan S A Mahmud K K Loo and H S Al-Raweshidy A cross layer rate adaptation solution for IEEE 802 networks Computer Communications Vol pp D Qiao and S Choi Fast-responsive link adaptation for IEEE 802 WLANs in Proceedings of IEEE International Conference on Communications Vol pp S HY Wong H Yang S Lu and V Bharghavan Robust rate adaptation for 802 wireless networks in Proceedings of ACM International Conference on Mobile Computing and Networking 2006 pp S Ivanov A Herms and G Lukas Experimental validation of the ns-2 wireless model using simulation emulation and real network in Proceedings of Workshop on Mobile Ad Hoc Networks 2007 pp The NS2 Simulator A V Babu received the ME degree in Telecommunication from the Electrical Communication Engineering department Indian Institute of Science Bangalore India in 2002 and PhD degree from Electronics and Communications Engineering department National Institute of Technology Calicut India in 2008 where he is currently employed as an Assistant Professor His primary research focus is on wireless networks

15 OPTIMIZATION OF IEEE 802 MULTIRATE WLAN 785 Lillykutty Jacob received the MTech degree in Electrical Engineering (Communication) from the Indian Institute of Technology Madras India in 985 and the PhD degree in Electrical Communication Engineering from the Indian Institute of Science Bangalore India in 993 During she was with the Department of Computer Science Korea Advanced Institute of Science and Technology Daejeon Korea for postdoctoral research and with the Department of Computer Science National University of Singapore during as a visiting faculty Since 985 she has been with the National Institute of Technology Calicut India where she is currently a Professor She has written or presented more than 75 international journal and conference papers Her research interests include wireless networks quality-of-service issues and performance analysis S Abdul Subhan received the MTech degree in Communication from Electronics and Communication Engineering department National Institute of Technology Calicut India in 2008 He is currently employed in Central Research Laboratory Bharat Electronics Limited Bangalore India