Realistic Modeling of IEEE 802.11 WLAN Considering ... - IEEE Xplore

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IEEE Transactions on Consumer Electronics, Vol. 57, No. 4, November 2011

Realistic Modeling of IEEE 802.11 WLAN Considering Rate Adaptation and Multi-Rate Retry Igor Kim, Young-Tak Kim, Member, IEEE Abstract — Most recent mobile multimedia devices, such as smart phones, laptops and tablet PCs, are equipped with IEEE 802.11 Wi-Fi interfaces for broadband wireless Internet access. The multimedia applications utilized by end users strongly require guaranteed QoS. Resource availability checking during initial connection establishment and seamless handover is essential under such conditions. Several analytical models of IEEE 802.11 WLAN have been proposed to estimate achievable throughput. However, they do not consider rate adaptations with multi-rate retry and individual channel conditions of each station. This paper proposes a realistic model to estimate achievable throughput considering Minstrel rate adaptation and multi-rate retry chain. The proposed model also considers each station individually, since stations may have different frame error rates in a real environment and thus, select different physical rates for frame delivery. Frame error rates are carefully read from the hardware registers of each station and applied to the model for enhanced accuracy. The correctness of the proposed model was verified through a series of experiments in a real testbed environment with up to 20 stations with MadWiFi interface cards. The proposed model shows accurate results in terms of aggregated and per-station throughput in various channel conditions.1 Index Terms — IEEE 802.11, Rate Adaptation, Minstrel, Performance Modeling, WLAN.

I. INTRODUCTION Most of the recent mobile multimedia devices are equipped with IEEE 802.11 [1] Wi-Fi interfaces for broadband wireless Internet access and strongly require guaranteed QoS for realtime multimedia applications, such as VoIP, videoconference, online gaming and IPTV. The correct information of the available resource (e.g., bandwidth) is essential to provide guaranteed QoS. For instance, resource availability information must be checked at initial connection with the wireless access network through the connection admission control (CAC) or must be used in smart handover decisionmaking algorithms for QoS-aware seamless mobility [2]. In most situations, the network bandwidth is shared among multiple users, since IEEE 802.11 access points (APs) are deployed in many public places. Thus, it is challenging to estimate the correct available resource for individual stations (STA) for intelligent AP selections, and, conversely, for APs 1 This work was supported by 2011 Yeungnam University research grant. Authors are with the Department of Information and Communication Engineering, Graduate School, Yeungnam University, Gyeongsan-Si, Korea (e-mail: [email protected], [email protected]).

Contributed Paper Manuscript received 08/30/11 Current version published 12/27/11 Electronic version published 12/27/11.

to perform CAC to guarantee QoS provisioning. Correct estimation of the available resources is the most important part of the CAC and handover decision-making algorithms [3]. More optimized decisions can be made using more accurate estimation. Thereby, realistic assumptions must be considered in the resource estimation models. There are several proposals of mathematical models for estimation of achievable throughput [10] – [19]. However, they do not fully consider realistic assumptions. Original work in [10] and the work in [11] proposed the Markov model to estimate saturation throughput. However, it assumed the frame errors occurred only due to collisions considering an ideal channel. In addition, there was no consideration of rate adaptation algorithms that are usually implemented in most commercial wireless interface cards. The work in [14] analyzed the performance of IEEE 802.11 distributed coordination function (DCF) considering different physical transmission rates. However, there was no consideration of any rate adaptation algorithm, and the rates of STAs were fixed. In addition, only ideal channel conditions were considered. A series of proposals considering rate adaptations are made in [15] – [19]. However, in those proposals each STA was assumed to have the same average frame error probability due to channel noise. This is untrue in a real environment. In addition, they assumed that frames were retransmitted at the same physical rate but this may not be applied in most existing implementations [9]. This paper proposes a Markov chain based realistic mathematical model to estimate the achievable throughput of each STA considering the Minstrel rate adaptation algorithm [9] and multi-rate retry chain (MRRC). The major contribution of this paper is the modeling of frame transmissions using different physical rates selected by the rate adaptation algorithm with a multi-rate retry. This is the first proposal that considers MRRC to the authors’ best knowledge. Moreover, the frame error probabilities are obtained by reading hardware registers from the hardware abstraction layer (HAL) and are applied to the mathematical model to achieve enhanced accuracy. The proposed model also considers each STA individually, since in practice each STA may have different link conditions with AP, thus achieving different throughput. The performance of the proposed mathematical model is analyzed by a series of experiments in a real IEEE 802.11g WLAN testbed with up to 20 STAs. Performance analysis shows the proposed model accurately estimates the aggregated and per-STA throughput in various scenarios.

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I. Kim, Y.-T. Kim: Realistic Modeling of IEEE 802.11 WLAN Considering Rate Adaptation and Multi-Rate Retry

The remainder of this paper is organized as follows. Section II explains the Minstrel rate adaptation, MRRC, and related work on IEEE 802.11 throughput estimation. Section III proposes a realistic analytical model to estimate the achievable throughput with Minstrel and MRRC. Section IV explains the performance analysis and evaluation of the estimation accuracy of the proposed scheme. Finally, section V concludes this paper. II. RELATED WORK A. Minstrel Rate Adaptation and MRRC IEEE 802.11 wireless LAN (WLAN) [1] supports multiple rates at the physical layer for adaptive data transmission under different channel conditions. Many rate adaptation algorithms have been proposed to improve WLAN performance [4] – [8]. Several attempts have been made to study empirically the performance of rate adaptation algorithms, such as in [20] and [21]. The rate adaptation algorithms can be classified into i) frame loss based and ii) SNR based. In practice, frame loss based rate adaptation algorithms are more common. However, frame loss based algorithms may degrade performance due to slow responses to changes in channel conditions [18]. The Minstrel rate adaptation algorithm is an algorithm targeted to resolve this problem [9]. Minstrel utilizes the multi-rate retry chain (MRRC) with four rate-count pairs (r0/c0, r1/c1, r2/c2, and r3/c3). When transmitting a frame a station first tries to deliver the frame at rate r0 for c0 times. If these transmissions are unsuccessful, it keeps trying at rate r1 for c1 times, at rate r2 for c2 times, and finally at rate r3 for c3 times. If the frame is not delivered within c0 + c1 + c2 + c3 attempts, it is dropped. The determination of rates r0 – r3 is based on the statistics of achievable throughput and the probability of success updated every 50 ms. The update interval is selected to be appropriate to react rapidly to the changes in environment and at the same time minimizing the CPU load to process updates. The number of transmission attempts c at each rate r is calculated based on the desire to send it within 26 ms. Minstrel differentiates the rates into normal and look around. Look around rates are randomly selected and needed to probe the rates that may be potentially better than the current operating rates in the MRRC. By default, 10% of frames are selected as look around frames. In the case of normal frames r0 is the rate with highest throughput, r1 the rate with next highest throughput, r2 the rate with best probability of success, and r3 the lowest base rate. When the randomly selected rate is higher than the rate that has the best throughput, r0 is changed to the randomly selected rate, r1 to the rate of highest throughput, r2 to the rate of best probability of success, and r3 to the lowest base rate. When the randomly selected rate is lower than the rate that has the highest throughput, r0 is set to the rate of highest throughput, r1 is changed to the randomly selected rate, r2 to the rate of best probability of success, and r3 to the lowest base rate.

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B. Analytic Models of IEEE 802.11 WLAN Markov chain models for throughput estimation of IEEE 802.11 WLAN have been studied in many proposals, such as in [10] – [19]. The original model described in [10] has been extended in many directions, considering differentiated channel access [13], maximum retry limit [11], and rate adaptation [15] – [19]. In [14], a multi-rate environment is considered, where groups of STAs use different transmission rates depending on the location. However, each STA transmits at a fixed rate that cannot be applied to real environment. In addition, frame errors are assumed only due to collisions without consideration of channel noise. In [15] – [19], the performance of IEEE 802.11 DCF was analyzed considering rate adaptation techniques, such as auto-rate fallback (ARF), collision-aware rate adaptation (CARA), and SampleRate. However, each STA is assumed to have the same average frame error probability, which is untrue in practice. It is also assumed that the frames are retransmitted at the same rate that cannot be applied to some existing implementations with multi-rate retry [9]. III. REALISTIC MODELING OF IEEE 802.11 WLAN WITH MINSTREL RATE ADAPTATION AND MRRC This paper describes a model that consists of two levels. First, the rate selection procedure with Minstrel is analyzed and the probability distributions of rates being selected in the order of rates of the highest throughput, next highest throughput, and best probability of success are estimated. Second, the estimated probability distributions are applied to the estimation of transmission probabilities of each rate of individual STA using the Markov chain model of MRRC. Finally, the aggregated and per-STA throughputs are estimated. A. Estimation of Rate Selection Probabilities in Minstrel Careful measurement of frame error rate (FER) is essential to correctly estimate the probability distributions of rates being selected as the rates of highest throughput, next highest throughput, and best probability of success. FER for each physical rate is obtained by reading the hardware registers of the number of transmission attempts associated with each transmitted frame at the interface driver. FER is measured at 50 ms intervals, the default interval in Minstrel to evaluate the rates statistics and to build segments of MRRC. The default value of exponentially weighted moving average (EWMA) level (LEWMA) in Minstrel is 75%, which provides a smoothing effect, where the statistic from the last observation interval has reasonable influence on the rate selection. Equation (1) shows the estimation of EWMA probability of success at rate r and estimation interval l. The probability of success for a given time interval (P this S(r) ) is calculated as a ratio of the number of successful attempts to the total number of attempts. PSEWMA ( r ,l ) 

EWMA PSthis ( r ) 100  LEWMA   PS ( r ,l 1 ) LEWMA

100

(1)

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The estimated weighted average of probability of success is then used to estimate the approximated throughput achieved by each rate. Equations (2) and (3) show the estimation of the throughput and the time required to send one frame in seconds, respectively. The estimation is an approximation, because the frame size considered in the estimations is assumed 1200 bytes. In addition, it considers only ideal transmission without retransmissions and channel occupancy by other STAs. one _ fr S( r ,l )  PSEWMA (2) ( r ,l ) / Tr Trone _ fr  TDIFS  TSIFS  TACK  T fr ,r   CWmin / 2

(3)

After estimating the EWMA probabilities of success and the approximated throughputs for each time interval, the probability mass functions (PMF) are obtained. The PMFs of rates selected as the rates of highest throughput (Πr,i), next highest throughput (Λr,i), and best probability of success (Ωr,i) are estimated individually for each STA, since in practice the link qualities among AP and individual STAs differ. The estimated probabilities are applied further to the estimation of transmission probabilities of each rate acquired from the discrete-time Markov chain model. B. Modeling MRRC using Markov Chain The major contribution of this paper is the mathematical evaluation of the throughput achieved by the WLAN and each STA considering the Minstrel rate adaptation algorithm and MRRC. The analysis considers the saturation conditions, where each STA, after successful transmission or frame drop due to reaching the retry limit, always has a frame to be transmitted. IEEE 802.11g [1] WLAN with M=12 physical rates is assumed. The distributed coordination function (DCF) of IEEE 802.11 uses Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA), where each STA has its initial backoff window (W1=CWmin). STA has to wait DCF inter-frame space (DIFS) time interval and select random backoff value among [0, Wt-1] before any transmission. The contention window increases with each consecutive retransmission until reaching CWmax. The value of the contention window at transmission attempt t is shown in (4). The value of m' is the maximum backoff stage and defined as CWmax = 2m'W1. A list of all symbols used in the equations is shown in Table III in Appendix. 2 t 1W1 , t  1  m' (4) Wt   m' CW max  2 W1 , t  1  m' The discrete-time Markov chain is proposed, assuming the probability that a transmitted frame collides with another frame in a slot, and the probability that the channel is busy in a slot are independent of the backoff mechanism. The Markov chain model depicted in Fig. 1 also considers MRRC, where four different rates are set up in the retry chain. The state of the Markov chain is denoted as (r, t, g), where r [1, M] is the index of rate selected as the rate of highest throughput (h), next highest throughput (n), best probability of success (s), and lowest base rate (l), t [1, c] is the transmission attempt counter, and g [0, Wt - 1] is the backoff counter. The state transition probabilities are shown in (5) – (9). The backoff

counter is decremented by one, if an STA senses the channel idle during a slot. STA freezes the backoff counter if a slot is busy until the channel becomes idle again. An STA selects a new backoff counter for the next transmission attempt after unsuccessful transmission caused by frame collision or noise error. STA selects the backoff counter for the first transmission attempt t = 1, after each successful transmission or frame drop due to reaching the maximum allowed retransmissions. When an STA reaches the maximum allowed number of transmission attempts on a given rate, the next rate in MRRC is selected for transmission.  Ph ,t , g  | h ,t , g  1  1  pb ,h ,i ,t  1, mh , g  0 ,Wt  2  Pn ,t , g  | n ,t , g  1  1  p ,t  m  1, a , g  0 ,W  2  b ,n ,i h t           1 1 1 0 2        P s , t , g | s , t , g p , t a , b , g , W b ,s ,i t   Pl ,t , g  | l ,t , g  1  1  pb ,l ,i ,t  b  1, c , g  0 ,Wt  2

 Ph ,t , g  | h ,t , g   pb ,h ,i ,t  1, mh , g  1,Wt  1  Pn ,t , g  | n ,t , g   p ,t  m  1, a , g  1,W  1  b ,n ,i h t           P s , t , g | s , t , g p , t a , b , g , W      1 1 1 b ,s ,i t   Pl ,t , g  | l ,t , g   pb ,l ,i ,t  b  1, c, g  1,Wt  1

(6)

 Ph , t , g  | h , t  1,0  ph ,i / Wt , t  2, mh , g  0,Wt  1  Pn , t , g  | n , t  1,0  p / W , t  m  2, a , g  0,W  1  n ,i t h t   1 0    2  0  1          P s , t , g | s , t , p / W , t a , b , g , W s , i t t   Pl , t , g  | l , t  1,0   pl ,i / Wt , t  b  2, c , g  0 ,Wt  1  Ph ,1, g  | h ,t ,0  1  p h ,i  / W1 ,t  1,mh , g  0 ,W1  1  Ph ,1, g  | n ,t ,0  1  p  / W ,t  m  1,a , g  0 ,W  1 1 1 n ,i h   Ph ,1, g  | s ,t ,0  1  p s ,i  / W1 ,t  a  1,b, g  0,W1  1  Ph ,1, g  | l ,t ,0   1  p  / W ,t  b  1,c , g  0,W  1 1 1 l ,i   Ph ,1, g  | l ,c ,0   1 / W1 , g  0 ,W1  1





 Pn , mh  1, g  | h , mh ,0   ph ,i / Wm 1 , g  0 ,Wm 1  1   Ps , a  1, g  | n , a ,0   pn ,i / Wa 1 , g  0 ,Wa1  1  Pl ,b  1, g  | s , b ,0   p / W , g  0 ,W  1 s ,i b 1 b 1  h

h

(5)

(7)

(8)

(9)

Let br,t,g be the steady-state distribution of the Markov chain of rate r, with transmission attempt t, and backoff counter g. Equations (10) – (13) are derived from the balance equations in a steady-state. Thus, all the values br,t,g are expressed as functions of the bh,1,0 and pb,r,i the probability of busy medium for rate r of STA i. bh ,t ,g  Wt  g bh ,t ,0 / Wt 1  pb ,h ,i   t 1 bh ,t ,0  ph ,i bh ,1,0 t  1, m , g  1,W  1 h t 

(10)

bn ,t ,g  Wt  g bn ,t ,0 / Wt 1  pb ,n ,i   t  2 m m t 1m bn ,t ,0  pn ,i bn ,m 2 ,0  ph ,i pn ,i bh ,1,0 t  m  1, a , g  1,W  1 h t 

(11)

h

h

h

h

bs ,t ,g  Wt  g bs ,t ,0 / Wt 1  pb ,s ,i   m m t  2 a t 1a bs ,t ,0  ps ,i bs ,a2 ,0  ph ,i pn ,i ps bh ,1,0 t  a  1, b, g  1,W  1 t  h

n

bl ,t ,g  Wt  g bl ,t ,0 / Wt 1  pb ,l ,i   m m m t  2 b t 1b bl ,t ,0  pl ,i bl ,b2 ,0  ph ,i pn ,i ps ,i pl bh ,1,0 t  b  1, c , g  1,W  1 t  h

n

s

(12)

(13)


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Fig. 1. Markov Chain model for the backoff window size with rate adaptation multi-rate retry mh Wt 1

1    bh ,t ,g  t 1 g 0

mh Wt 1

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 , mh  m'    W1 2 m' p hm,i'  p hm,i  , mh  m'  1  p h ,i 



 pm b  2 m W1 1  2 p n ,i m 1  p nm,i  h ,i h ,1,0   1  2 p n ,i 1  p n ,i  21  pb ,n ,i    m m  2 m W1 1  2 p n ,i  1  p nm,i  p b    h ,i h ,1,0   1  2 p n ,i  21  pb ,n ,i   m m  p b 1  p W 2 m'  1 n ,i 1  h ,i h ,1,0 , 21  pb ,n ,i 1  p n ,i    h

h

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

n

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(14)

l ,t ,g

t b 1 g 0

 b  W1 1  2 p h ,i m 1  p hm,i h ,1,0    1  2 p h ,i 1  p h ,i  21  pb ,h ,i    m m   bh ,1,0  W1 1  2 p h ,i   1  p h ,i  21  p   1  2 p h ,i b ,h ,i  

Wt 1

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a



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 ,    W1 2 m' p nm,i'  m  p nm,i 1  p n ,i



(15)



h

n

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 ,  

a  m' , mh  m' a  m' , mh  m'

(16)

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



 p m p m b  2 a W 1  2 p m 1  p sm,i s ,i 1  h ,i n ,i h ,1,0   1  2 p s ,i 1  p s ,i  21  pb ,s ,i    m m m a      p sm,i p p b W p 2 1 2 1  s ,i 1   h ,i n ,i h ,1,0    1  2 p s ,i  21  pb ,s ,i   m m  p p b 1  p m W 2 m'  1 s ,i 1  h ,i n ,i h ,1,0 , 21  pb ,s ,i 1  ps ,i    n

s





s

s



s



s











 ,    W1 2 m' psm,i'  a  psm,i 1  ps ,i

 phm,ih pnm,in p sm,is bh ,1,0  2b W1 1  2 pl ,i ml 1  plm,il    1  2 pl ,i 1  pl ,i  21  pb ,l ,i    mh mn ms ml b  2 W1 1  2 pl ,i  1  plm,il p p p b   h ,i n ,i s ,i h ,1,0    1  2 pl ,i  21  pb ,l ,i    p mh p mn p ms b 1  p ml W 2 m'  1 l ,i 1  h ,i n ,i s ,i h ,1,0 , 21  pb ,l ,i 1  pl ,i   









s











(17)

b  m' , a  m'

c  m'

 ,  

(18)

c  m' , b  m' c  m' , b  m'





 

 ,    W1 2 m' plm,i'  b  plm,il 1  pl ,i

mh mh  1  phm,ih t 1  h ,i  bh ,t ,0  bh ,1,0 ph ,i  bh ,1,0 1  ph ,i t 1 t 1  a a  1  pnm,in mh t 1 mh  phm,ih bh ,1,0 bn ,t ,0  bh ,1,0 ph ,n pn  n ,i  1  pn ,i  t  mh 1 t  mh 1  b b 1  psm,is   bs ,t ,0  bh ,1,0 phm,ih pnm,in pst ,i1a  phm,ih pnm,in bh ,1,0 s ,i  1  p s ,i t  a 1 t  a 1  c c 1  plm,il   bl ,t ,0  bh ,1,0 phm,ih pnm,in psm,is plt,i 1b  phm,ih pnm,in p sm,is bh ,1,0 l ,i  1  pl ,i t b 1 t b 1 



 ,

b  m' , a  m'

Equations (15), (16), (17), and (18) are obtained from (10), (11), (12), and (13), respectively. When deriving (15) – (18) the consideration of maximum backoff stage m' is needed, since the backoff window should not increase after reaching CWmax. The bh,1,0 is found by considering the normalization condition for stationary distribution shown in (14) and substituting summation values obtained in (15) – (18). Further, the transmission probabilities with highest throughput rate h, next highest throughout rate n, best probability of success rate s, and lowest base rate l are estimated as in (19). The transmission probabilities are obtained assuming the transmission of a frame is performed when the backoff counter decrements to zero. The frame loss probability pr,i, which takes into account both collision probability and frame errors due to channel noise, was carefully measured from the NIC driver routine, as mentioned before, and applied to the mathematical model. Measuring pr,i at every STA allows considering each STA individually and thus, makes estimations more realistic. Applying the measured data to the numerical estimation facilitates achieving the most accurate results.



b  m'

success are estimated by using (21) and (22). For the lowest base rate of index 1, the last stage of the retry chain must be also considered. Equation (23) shows the transmission probability from the last stage of MRRC. Note that in (20) – (23) n≠ r, h≠ r, and n≠ h, since the rate that is selected as the rate with highest throughput can not be considered as the rate with next highest throughput at the same time. Summing up results in (20) – (23) and multiplying it by the probability of normal frame the transmission probabilities for normal frames and rate r of STA i are obtained, as shown in (24) and (25). M M 1  prm,i (20) Prh,i,nor   r ,i   n ,i  s ,ibrn,1,s,0 1  pr ,i n 1, s 1 r

nr M

M

Prn,i,nor   r ,i   h ,i  s ,i phm,i bhr ,,1s,0 h

h 1, s 1 hr M

1  prm,i 1  pr ,i r

M

Prs,i,nor   r ,i   h ,i  n ,i phm,i pnm,i bhn,1,r,0 h

n

h 1 n 1, nh

M

M

(21)

1  prm,i 1  pr ,i r

M

P1l,i,nor    h ,i  n ,i  s ,i phm,i pnm,i psm,i bhn,1,s,0 h

(19)

Correct estimation of transmission probabilities of each rate is essential to estimate the per-STA and aggregated throughput in WLAN. The estimation of transmission probability τr,i for each rate r considers normal and look around frames. The values Πr,i, Λr,i, and Ωr,i, which are used in the estimation of τr,i, are estimated as described in previous subsection. For normal frames, the estimation of transmission probability for rate r, assuming it is selected as the rate with highest throughput, is given in (20). r2,r3 Here and further in the equations the br1,1,0 is the bh,1,0 with r1, r2, and r3 being the first, second, and third rate in the retry chain, respectively. Similarly, transmission probabilities assuming rate r is the rate with next highest throughput and best probability of

h 1 n 1, s 1 nh

n

s

(22) 1  p1m,i 1  p1,i

h ,nor  rnor  Prn,i,nor  Prs,i,nor , r  2, M  ,i  1  pla Pr ,i

1

h ,nor  1nor  P1n,i ,nor  P1s,i,nor  P1l,i,nor , r  1 ,i  1  pla P1,i

(23) (24) (25)

The estimation of look around frames is similar to the estimation of normal frames. However, the randomly selected rate can be higher than the rate currently considered as the rate with highest throughput. In this case, the randomly selected rate must be the first in the retry chain. This is considered in the estimations of transmission probabilities in (26) – (28). Summing up results in (26) – (28) and multiplying it by the probability of the look around frame the transmission probabilities for look around frames and the rate r of STA i are obtained, as shown in (29). Look around frames are never transmitted at the lowest rate. It is assumed that the lowest rate is reliable, since the initial connection with AP is established using this rate. Finally, the transmission probability of STA i at rate r, τr,i, is obtained by


1501

The multi-rate environment is considered in the estimation of collision probability in a slot, since the duration of collision M M is dominated by the longest transmission time, i.e. lowest rate,  r M 1 p 1 p  Prh,i,la   r ,i    M1  s ,ibrn,1,s,0 1 p    M1  s ,i pnm,i bnr ,,1s,0 1 p  (26) involved in the collision. A single rate r collision probability n  r 1 s 1  n 1 s 1  (P srcol,r), where the frames involved in the collision are r M 1  M M 1 p 1 p  transmitted at the same rate, and multi-rate collision     h ,i  s ,i p hm,i bhr ,,1s,0 1 p    h ,i  s ,i brh,1,s,0 1 p  (27) Prn,i,la  M  h  r 1 s 1 h 1 s 1  probability (Pmrcol,r), where the frames involved in the h M M M  m m m m s ,la n ,r 1 p h ,r 1 p  (28) collision are transmitted at different rates with the lowest rate 1 1 Pr ,i   r ,i     h ,i M p h ,i p n ,i bh ,1,0 1 p     h ,i M p h ,i p n ,i bn ,1,0 1 p  h 1 n  h 1  h 1 n 1  r, are shown in (39) and (40), respectively. The collisions la h ,la n ,la s ,la  r ,i  pla Pr ,i  Pr ,i  Pr ,i , r  2, M  (29) where the rate r is not the lowest rate are included in collisions where the rates from 1 to r-1 are the lowest. Thus, only la  r ,i   rnor (30) consideration of collisions where rate r is the lowest is needed. ,i   r ,i A collision occurs when at least one STA, other than the The multi-rate collision probability for the lowest rate is given considered transmitting STA, also transmits. Conversely, the in (41). Finally, the probability Pcol,r of the single rate r medium is sensed busy when at least one STA, other than the collision and multi-rate collision with r being the lowest is considered STA, transmits. Equations (31) and (32) look the given in (42). same; however, in (31) the considered STA transmits, while in   N  N   N M N (32) it does not.      Psrcol ,r  1    1   r ,i    r , j  1   r ,k   1   m ,l  (39)

summing up the probabilities of transmission for normal and look around frames, as shown in (30). mr r ,i

mr r ,i

n

r ,i

r ,i

h

h

mr r ,i

mr r ,i

r ,i

r ,i

mr r ,i

n

h

r ,i



mr r ,i

r ,i



  pc ,r ,i  1  1   

pb ,r ,i

n

M

 

t 1, t r

 u 1,   u i



N

M



v 1



 t ,i  1   v ,u 

  N M M      1  1   t ,i  1   v ,u    t 1,  u 1,  v 1  t r  u i







(32)

The frame error probability considering the collision and noise error is given in (33). With known pr,i and pc,r,i, the pno,r,i is estimated, as shown in (34). pr ,i  1  1  pc ,r ,i 1  pno ,r ,i  (33) pno ,r ,i  1 

1  pr ,i

(34)

1  pc ,r ,i

The probability that an STA i successfully transmits with rate r in a slot is given by N M   p s ,r ,i   r ,i 1  p no ,r ,i  1   v ,u  (35) v 1 u 1,   u i

C. Deriving Throughput The average duration of time slot is required to estimate the average throughput achieved by each STA. The slot may be idle or may contain successful transmission, collision, or erroneous transmission due to channel noise. A slot is idle when no STAs transmit, as shown in (36). The probabilities a slot contains successful transmission or erroneous transmission due to channel noise with rate r are given in (37) and (38), respectively. M   1   v ,u   v 1 u 1   N

Pidle





(36)

N N M   Psuc ,r   r ,i 1  p no ,r ,i  1   v ,u  i 1 v 1 u 1,  

N

N

i 1

u 1, u i



M





v 1



 r ,i pno ,r ,i  1   v ,u 

 

 Pmrcol ,r  1   

j 1

i 1

N



M

 1  

 Pmrcol ,1  1   

i 1



N

 i 1

j  r 1

 1   

M

j ,i

  l 1   

k 1, k j

   1     

N

N

k 1

    

(38)

l 1

N



k 1



Pcol ,M  Psrcol ,M , rM Pcol ,r  Psrcol ,r  Pmrcol ,r , 1  r  M

 

r 1

r ,k

 j ,i  1   1   1,k  j 2

m 1, m r

   1    1   m 1

m ,l

  (40) 

(41)

(42)

The normalized saturation throughput achieved by STA i with rate r is given by (43), where Tp,r is the time required to transmit a packet without UDP/IP/MAC overhead. The saturation throughput achieved by STA i is given by (44), where Rr is the physical transmission rate of rate with index r. Finally, the aggregated throughput of the WLAN is given by (45). p s ,r ,iT p ,r S r ,i  (43) Tidle  Tsuc  Tcol  Tnoise Si 

M

S

r ,i

(44)

Rr

r 1

S

N

S

(45)

i

i 1

The denominator in (43) corresponds to the average time slot duration, as found in (46) and (47). M  Tnoise  Pnoise ,rT fail ,r Tidle  Pidle ,  r 1  M M Tsuc  Psuc ,rTsuc ,r , Tcol  Pcol ,rT fail ,r  r 1 r 1

(46)

Tsuc ,r  TPHY  TMPDU ,r  TSIFS  TACK  TDIFS  T fail ,r  TPHY  TMPDU ,r  TEIFS

(47)



(37)

u i

Pnoise ,r 

 

(31)





1502


IV. PERFORMANCE EVALUATION

A. Testbed Configuration and Measurements A series of experiments were performed in the laboratory to evaluate the accuracy of the proposed analytical model. The testbed is configured with 21 PCs equipped with IEEE 802.11a/b/g based wireless NICs supporting the open source MadWiFi driver [9]. All PCs operating in “STA” mode are uniformly distributed 5 – 6 meters around the AP operating in “AP” mode. The traffic generation tool is configured on each STA to send data traffic to AP configured as the traffic sink. The generated traffic rate is configured to maintain the transmit queue so it always has a frame available for transmission. The application packet size is configured appropriately to get the total MPDU size of 1000 bytes with UDP/IP/MAC headers overhead of IEEE 802.11g WLAN with 12 physical bit rates. One PC with installed packet sniffer software is configured to operate in “monitor” mode, to carefully analyze the captured traffic and the timing information. The rate information for ACK frames cannot be acquired from the driver, since control frames are handled in HAL hidden from the user. It is possible to retrieve the bit rate information from ACK control frames and acquire mapping information between data frame rates and corresponding ACK frame rates by capturing transmitted data frames and corresponding ACKs. In addition, the ath_hal_computetxtime() function is used in the numerical estimations to achieve the most accurate results. This function estimates the frame transmission times at each physical rate (TMPDU,r). It is applied to the numerical estimations, as it is implemented in the driver to get the most accurate results. Several scenarios are considered in evaluating the accuracy of the proposed model. The aggregated and per-STA application throughputs are measured during the experiments and then compared to numerical data. Table I shows the scenarios considered in the experiments. Each experiment lasts at least 10 minutes.

lower due to the increased noise errors. Further, increasing the number of STAs in WLAN increases the number of collisions, resulting in reduction of physical transmission rate by Minstrel. In the case of scenario A2, the throughput degrades rapidly, because frame errors occur more often when transmission power is low. When the number of STAs is more than 13 in scenario A2, most of the STAs use rates of 11 Mb/s or 5.5 Mb/s as r0 in the retry chain. It was validated that the rate 11 Mb/s is more robust than 6 Mb/s, as noted in [20]. In the case of scenario A1, where the frames are mostly lost due to collisions, almost all of the STA use 54 Mb/s, 48 Mb/s, or 36 Mb/s as r0 in the retry chain, resulting in much higher throughput compared to scenario A2. Fig. 2 also shows that the proposed model estimates accurately the achievable throughput for both scenarios. Fig. 3 shows the throughput of STA1 in scenarios A1 and A2. Obviously, the application throughput of STA1 decreases rapidly when sending with 6 dBm of transmission power. Also, from Fig. 2 and Fig. 3 note that the aggregated throughput is almost equally divided among STAs.

Fig. 2. Aggregated application throughput at scenarios A1 and A2

TABLE I TESTED SCENARIOS Scenario A1 A2 B1 B2 B3 B4 B5

Number of STA (N) 1 – 20 1 – 20 2 3 3 3 4

Tx power of each STA 18 dBm 6 dBm 18 dBm, 1 dBm 18 dBm, 18 dBm, 1 dBm 18 dBm, 1 dBm, 1 dBm 18 dBm, 3 dBm, 1 dBm 18 dBm, 18 dBm, 1 dBm, 1 dBm

B. Aggregated Throughput Analysis Fig. 2 shows the experimental and numerical results for the scenarios A1 and A2. Interestingly, with only one STA the throughput is lower than the case when two STAs are used due to the underutilization caused by backoff delay. Reducing the CWmin value (15 in the experiments) may solve the problem. However, setting too small CWmin value may have a negative effect when the number of STA increases. Compared to scenario A1 the aggregated throughput in scenario A2 is

Fig. 3. Application throughput of STA1 at scenarios A1 and A2

It is crucial to estimate correctly the probabilities of rate r being selected as r0 (Πr,i), r1 (Λr,i), and r3 (Ωr,i) in the retry chain in the estimations of achievable throughput by each STA. This estimation is done for each STA, because the rate


selection may differ at different STA, even with the same transmission power. Table II shows the measured experimental data compared to the numerical results of the rate selection probabilities of STA1 for scenario A2 with 10 STAs. The numerical results show quite accurate results, because the frames error probabilities are obtained from reading the HAL hardware registers. TABLE II RATE SELECTION PMF OF STA1 AT SCENARIO A2 WITH 10 STA Rate 1 Mb/s 2 Mb/s 5.5 Mb/s 6 Mb/s 9 Mb/s 11 Mb/s 12 Mb/s 18 Mb/s 24 Mb/s 36 Mb/s 48 Mb/s 54 Mb/s

Π R,I Exp 0 0 0.0015 0 0 0.6135 0 0.0075 0.0043 0.0276 0.0663 0.2791

Λ R,I Num 0 0 0.0018 0 0 0.61 0 0.0075 0.0043 0.0217 0.0738 0.2808

Exp 0.0287 0.0666 0.1116 0 0.0072 0.2285 0 0.0283 0.0776 0.121 0.0865 0.2439

Ω R,I Num 0.0313 0.064 0.1143 0 0.0072 0.2288 0 0.0258 0.0428 0.1436 0.0925 0.2496

Exp 0.991 0.007 0.002 0 0 0 0 0 0 0 0 0

Num 0.99 0.005 0.002 0 0 0 0 0 0 0 0 0.002

C. Per-STA Throughput Analysis In real situations, the location of STAs may differ, resulting in different signal levels received by AP, even though the emitted power by each STA is the same. Scenarios B1, B2, B3, B4, and B5 are tested to evaluate these conditions. Fig. 5 shows the results of these scenarios. Scenario B1 shows a dramatic decrease in throughput compared to the scenario A1 with two STAs. The throughput is reduced to almost half, because the STA with low transmission power mostly utilizes 11 Mb/s or 5.5 Mb/s rates for frames transmission, which increases the channel occupancy time, and thus, reduces the throughput of the STA with high transmission power, even though it mostly uses the 54 Mb/s rate. In scenario B2, the throughput is also much lower compared to scenario A1 with three STAs for the same reason. Adding more STAs with low transmission power leads to significant reduction of throughput, as shown in scenarios B3 and B5. In scenario B4, the throughput is lower compared to scenario B2, since the STA with 18 dBm is replaced with STA sending at 3 dBm transmission power. The numerical results of per-STA throughput validate the accuracy of the proposed model. STA1 (18dBm)

STA2 (18dBm)

STA3 (3dBm)

STA4 (1dBm)

Exp Num (B3) (B3)

Exp Num (B4) (B4)

STA5 (1dBm)

14000

Throughput, [kbps]

12000 10000 8000 6000 4000 2000 0 Exp Num (B1) (B1)

Exp Num (B2) (B2)

Exp Num (B5) (B5)

Fig. 5. Per-STA and aggregated throughput for scenarios B1, B2, B3, B4, and B5

1503

V. CONCLUSION

This paper proposed a realistic mathematical model to estimate the achievable throughput considering Minstrel rate adaptation and MRRC. The proposed model also considers each STA individually, since in practice each STA may have different link conditions with AP. The frame error probabilities are carefully obtained by reading hardware registers in HAL and applied to the mathematical model to achieve the highest accuracy. The performance of the proposed model has been analyzed by a series of experiments in a real testbed. Performance analysis showed the proposed realistic model accurately estimates the aggregated and perSTA throughput in various scenarios. Even though Minstrel is considered in this paper, any multi-rate retry rate adaptation algorithm can be applied to the MRRC model. APPENDIX TABLE III LIST OF SYMBOLS Symbol h n s l mr a b c pr,i pb,r,i Wt τr,i τnor r,i la τ r,i Πr,i Λr,i Ωr,i M N pc,r,i pno,r,i ps,r,i Psuc,r Pnoise,r Pidle Psrcol,r Pmrcol,r Sr,i Si S Tidle Tsuc Tnoise Tcol Tsuc,r Tfail,r TPHY TMPDU,r TDIFS TSIFS TACK

Description Index of rate with highest throughput Index of rate with next highest throughout Index of rate with best probability of success Index of lowest base rate Try limit for rate r mh + mn mh + mn + ms mh + mn + ms + ml Frame error probability for STA i and rate r Probability of busy medium for STA i and rate r Contention window (CW) size at transmission attempt t Transmission probability of STA i at rate r Trans. prob. of STA i at rate r for normal frames Trans. prob. of STA i at rate r for look around frames Prob. rate r of STA i is selected as r0 in MRRC Prob. rate r of STA i is selected as r1 in MRRC Prob. rate r of STA i is selected as r2 in MRRC Number of bit rates Number of STAs Collision prob. for rate r of STA i Noise error probability for rate r of STA i Prob. of successful trans. for rate r of STA i Prob. slot contains successful trans. at rate r Prob. slot contains noise error at rate r Prob. of idle slot Prob. slot contains single rate r collision Prob. slot contains collision with slowest rate r Average throughput of STA i at rate r Average throughput of STA i Average system throughput Idle slot time Successful slot time Noisy slot time Collided slot time Successful frame transmission time at rate r Failed frame transmission time at rate r Physical header transmission time MAC Protocol Data Unit (MPDU) trans. time at rate r DCF inter-frame space (DIFS) interval Short inter-frame space (SIFS) interval ACK transmission time

1504


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[18] J. He, W. Guan, L. Bai, K. Chen, “Theoretic Analysis of IEEE 802.11 Rate Adaptation Algorithm SampleRate,” IEEE Communications Letters, vol. 15, no. 5, May 2011, pp. 524-526. [19] D. Senthilkumar, A. Krishnan, “Throughput Analysis of IEEE 802.11 Multirate WLANs with Collision Aware Rate Adaptation Algorithm,” International Journal of Automation and Computing, vol. 7, no. 4, Nov. 2010, pp. 571-577. [20] E. Ancillotti, R. Bruno, and M. Conti, “Experimentation and performance evaluation of rate adaptation algorithms in wireless mesh networks,” In Proceedings of the 5th ACM symposium on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks, Vancouver, Canada, 2008, pp. 7-14. [21] W. Yin, K. Bialkowski, J. Indulska, P. Hu, “Evaluations of MadWifi MAC layer rate control mechanisms,” In Proceedings of 18th International Workshop on Quality of Service (IWQoS), Beijing, China, June 2010, pp. 1. [22] K. D. Huang, D. Malone, K. R. Duffy, “The 802.11g 11 Mb/s Rate is More Robust than 6 Mb/s,” IEEE Transactions on Wireless Communications, vol. 10, no. 4, 2011, pp. 1016-1020. BIOGRAPHIES Igor Kim received his B.S degree in computer science and information technology from Tashkent University of Information Technologies (Uzbekistan) in 2005. In 2007, he received M.S degree from Yeungnam University (Korea). Since 2007, he has been pursuing his Ph. D. degree in the Department of Information and Communication Engineering, Graduate School of Yeungnam University. His research interests include mobility management, QoS provisioning in wireless networks, seamless vertical handover, and network simulation study. Young-Tak Kim received Ph.D. degree from KAIST in February 1990. He joined Korea Telecom (KT) in 1990, where he researched and developed the ATM MAN Switching System (ATM-MSS) and related network operations and management technologies for broadband networking. He participated in the standardization activities of ITU-T Study Group 13, as a representative of KT. He is currently a professor of the Department of Information and Communication Engineering, College of Engineering in Yeungnam Univ., Korea. In 2001 and 2008, he worked as a guest researcher at NIST (National Institute of Standards and Technology), USA, where he joined in the development of NIST GMPLS simulator (GLASS) and Next Generation Routing Architecture (NGRA). His research interests include QoS-guaranteed traffic engineering in next generation Internet, QoS-aware seamless secure mobility, and related cognitive network operations and management. He is a member of IEEE Communication Society, KICS, KISS, KIPS, and Korea Multimedia Society. He was the Technical Program Chair of IEEE ComSoc CNOM in the period 2007-2008, TPC Co-chair of IM2009, and the general chair of APNOMS2009.