The third one uses different maximum frame lengths for different stations. ...... bnD b i. (19). We note that sum of the probabilities of all the states is equal to 1.
Achieving Weighted Fairness between Uplink and Downlink in IEEE 802.11 DCFBased WLANs Jiwoong Jeong, Sunghyun Choi, and Chong-kwon Kim School of Electrical Engineering and Computer Science Seoul National University Seoul, Korea Abstract- In this paper, we first propose an analytical model of WLANs (Wireless LANs) with an arbitrary backoff distribution and AIFS (Arbitration Inter-Frame Space). From the analysis, we show that the achievable bandwidth is determined by the mean of backoff distribution regardless of the shape of the backoff distribution. We compare the effectiveness of four parameters on channel access differentiation, namely, the mean of backoff distribution, CWmin (Initial Contention Window), the number of backoff stages, and AIFS. Numerical results show that the mean of backoff distribution provides weighted fair channel access most accurately. Second, based on the proposed analytic frame work, we develop three schemes for the uplink/downlink bandwidth differentiation in order to achieve weighted fairness between uplink and downlink transmissions. Note that IEEE 802.11 is known to have unfairness between uplink and downlink accesses. Each scheme is characterized according to the corresponding channel access rule. The simulation results show that the proposed schemes achieve high system throughput while accurately differentiating bandwidth allocation.
I. INTRODUCTION
IEEE 802.11 MAC (Medium Access Control) includes the mandatory contention-based and the optional pollingbased channel access functions, namely, DCF (Distributed Coordination Function) and PCF (Point Coordination Function), respectively. Most of today’s WLANs devices employ only the DCF because of its simplicity and efficiency for the data transmission process. The DCF employs CSMA/CA (Carrier-Sense Multiple Access with Collision Avoidance) protocol with BEB (Binary Exponential Backoff). The DCF is relatively simple while it enables quick and cheap implementation, which is important for the wide penetration of a new technology. This paper deals with the weighted fair channel access support problem in WLANs based on 802.11 DCF. Previous studies explore the effects of DCF parameters as the service differentiation while analyzing the performance of DCF. We have observed that DCF performance can be expressed as a function of the mean of backoff distribution. Based on this observation, we propose to use the mean of backoff distribution as a parameter for differentiating channel access probability. To compare the effectiveness of each parameter, we develop analytic model based on the
Bianchi’s model [3] with an arbitrary backoff distribution and AIFS (Arbitration Interframe Space). We observe that the mean of backoff distribution most accurately differentiates the channel access. In order to address an unfairness problem between uplink and downlink under the DCF, we propose three schemes using the mean of backoff distribution that can improve the system throughput while providing the throughput fairness. Each scheme is characterized according to the channel access rule of the AP (Access Point). Scheme 1 uses a contention-based medium access. On the other hand, in Schemes 2 and 3, the AP employs a credit-based channel access while all the stations except the AP use the contention-based channel access. The analysis and simulation results show that the proposed schemes effectively allocate bandwidth to uplink and downlink in a fair manner, and improve the system throughput. This paper is organized as follows. In Section II, we first present the related work. Section III develops an analytic model, and the influences of various parameters are compared. In Section IV, we present the proposed three schemes. In Section V, the performances of the proposed schemes are evaluated, and then we conclude the paper in Section VI. II. BACKGROUND AND RELATED WORK
An unfair channel access between uplink and downlink are well known in IEEE 802.11 DCF-based WLANs [13]. IEEE 802.11 DCF provides an equal access opportunity to all the nodes including the AP. Due to this characteristic, as the uplink traffic amount increases, the downlink traffic from the AP to the wireless stations can be significantly starved. Consequently, the asymmetric link characteristic incurs the unfair phenomenon between uplink and downlink even if there are more downlink flows than the uplink flows. To solve the unfairness problem, the authors in [16] propose simulation-based approach using empirical EDCA access parameters. However, the parameter sets used in its approach does not provide accurate UL/DL fairness. Theoretical approach is needed to select the access parameters. Therefore, this paper proposes a solution based on analytic results. There are many studies to analytically model IEEE 802.11 WLANs. In [3], Bianchi proposes a simple and accurate analytic model for DCF under the saturation condition. Bianchi’s model motivates a significant amount of subsequent analysis work. Ziouva et al. [8] enhance Bianchi’s model to derive the saturation delay, and reduce an assumption that the backoff counter is always decremented during a busy slot. 802.11+ proposed in [4] allows each station to estimate the number of active stations, and tunes its contention window to the optimal value during the runtime in order to improve the throughput performance. In [5], a more accurate model is proposed to derive saturation throughputs, saturation delays, and frame dropping probabilities of different priority classes. Several schemes have been proposed in order to provide the differentiated service. A priority scheme proposed in [12] is divided into two parts: shorter IFS and shorter random backoff time for higher priority stations. Each class is
prioritized by combining these two parts. Aad et al. [6] present three service differentiation schemes. The first one is based on scaling the contention window according to the priority. The second one assigns different interframe spaces to different stations. The third one uses different maximum frame lengths for different stations. In [7], the main idea of P-MAC protocol is that the contention window size for each station is properly selected to reflect the relative weights among data flows so as to achieve the weighted fairness and the number of stations contending for the channel so as to maximize the aggregate throughput. The IEEE 802.11e is currently being standardized to support QoS. The IEEE 802.11e MAC defines two different channel access schemes called HCF Controlled Channel Access (HCCA) and HCF contention based channel access. The latter is also called Enhanced Distributed Coordination Access (EDCA). The EDCA provides service differentiation among different service priorities while maintaining a backward compatibility with the legacy DCF. The EDCA achieves service differentiation by assigning different MAC parameters to priority classes, where the parameters include the minimum/maximum contention window size and AIFS, which is a generalized version of DIFS in the legacy DCF [2]. In [13], the authors show unfairness between uplink and downlink flows because there are N uplink CSMA instances contending with only one downlink CSMA instance in WLANs with N stations. Saar et al. [15] identify four different regions of TCP unfairness that depend on the buffer availability at the AP. They propose a solution that different TCP flows have equal bandwidth share irrespective of the buffer availability at the base station. Casetti et al. [16] try to address the problem of unfairness between uplink and downlink with the empirical EDCA parameter set. The algorithm proposed in [14] obtains fair access to the medium to all the TCP flows by awarding longer transmission opportunities to stations that experienced short channel failures. III. ANALYTIC MODEL
In this section, we propose a discrete-time Markov chain model with an arbitrary backoff distribution and an AIFS analysis. The performance for each MAC parameter is evaluated via the numerical result, and then the most accurate parameter is selected to support weighted fair channel access.
(1-pc)· Dc,0(j)
0, 0
1-pb_c
0, 1
1-pb_c
(1-pc)· Dc,0(j)
1-pb_c
pb_c
0, Wc,0- 1 pb_c
i-1, 0 pc· Dc,i(j) 1-pb_c
i, 0
pc· Dc,i+1(j)
1· Dc,0(j)
0, Wc,0- 2
pb_c
pc· Dc,1(j) pb_c
(1-pc)· Dc,0(j)
0, 2
pc· Dc,r(j) 1-pb_c r, 0
i, 1
1-pb_c
i, Wc,i- 2
pb_c
pb_c
r, 1
pc· Dc,i(j) i, 2
1-pb_c
pb_c
i, Wc,i- 1 pb_c
pc· Dc,r(j) 1-pb_c r,Wc,m- 2 r,Wc,m- 1
r, 2 pb_c
pb_c
1-pb_c
pb_c
pb_c
Fig. 1 Markov chain model with arbitrary backoff distribution
A. Model Description
Based on [3], we model the system with an arbitrary backoff distribution using two-state Markov chain, in which state {i, j} represents the state of a station with backoff counter j for the i-th transmission attempt (or backoff stage i). In Fig. 1, Dc,i(j) in the dotted circle corresponds to the probability mass function of backoff distribution. Specifically, when a frame transmission results in collision or success in state {i, 0}, the state transition from stage i to i+1 or to 0 occurs according to the backoff distribution Dc,i(j) or Dc,0(j). We use the following key notations in our model and analysis: (1) the probability pc that the transmitted frame by a station in class c collides; (2) the probability pb_c that the channel is sensed busy by a station in class c; (3) the stationary transmission probability tc for class c; (4) the total number N of classes in the system; and finally (5) the probability mass function Dc,i(j) of backoff distribution indexed by class c for next backoff stage i and backoff counter j. On the other hand, Ziouva’s model and Xiao’s model consider pb_c as follows. N
pb _ c = 1 -
Õ (1 - t q =1
1-t c
q
)
nq
, (c Î {1,..., N })
(1)
where nc is the number of class c ( c Î {1,..., N } ) stations. Therefore, the total number nTOTAL of stations is equal to n1 + n2 + … + nN. Both models are more suitable for the DCF access case. Notice that there is a little difference between the access rules of the EDCA and that of the legacy DCF. Although Bianchi’s model is for legacy DCF, it is more suitable to analyze the EDCA. The reason is that in EDCA, one slot is decremented before AIFS expiration and when the backoff counter reaches zero, the station transmits a frame after waiting for one extra idle slot. The probability pb_c for Bianchi’s model is equal to 0. Therefore, the transition probability from state j+1 to j for a stage i
becomes 1 in Fig. 1 (See [23] for the detailed discussion on this issue). We employ the model with EDCA access rule, based on Bianchi’s model. There is a more detailed derivation for the model in Appendix A. From Fig. 1, we can obtain tc as follows. r +1 ì (1 - 2 pc )(1 - pc ) ( r £ mc ) ï r +1 mc +1 ï (1 - ( 2 pc ) )(1 - pc )k cWc + (1 - 2 pc )(1 - pc )(1 - k c ) tc = í r +1 (1 - 2 pc )(1 - pc ) ï ï (1 - ( 2 p ) mc +1 )(1 - p )k W + (1 - 2 p )(1 - p r +1 )(1 - k ) + 2 mc (1 - 2 p )( p mc +1 - p r +1 ) k W c c c c c c c c c c c c î
(
)
(
(2)
)
( r > mc )
where r is the retry limit (i.e., short retry limit or long retry limit), mc is the maximum backoff stage (i.e., 2 m ×Wc = CWmax + 1 ) for class c, Wc is the initial contention window (CWmin+1) for class c, and kc is the c
normalized mean of backoff distribution for class c, respectively. The mean of backoff distribution is introduced as an additional MAC parameter. The relationship between the backoff distribution and kc is as follows. Wc ,i -1
å nD n =0
c ,i
(n) = k c (Wc ,i - 1) (0 £ k c £ 1)
(3)
where Wc,i is the contention window on backoff stage i for class c. On the other hand, in order to evaluate the effect of the AIFS differentiation, we try to derive the model with AIFS analysis. We have observed that according to the difference of the AIFS for each class, the channel access probability is differentiated.
Fig. 2 The state transition diagram for idle slot
Fig. 2 shows Markov Chain model for the AIFS analysis where the number of classes is equal to 2 and the difference of AIFS (i.e., AIFS[low]-AIFS[high]) = d. The state 0 is described as the beginning idle slot after the AIFS expiration. A state x means that the number of idle slots x have passed after the channel is busy. If the channel becomes busy again, the state comes back to 0. During the states from 0 to d-1, the only stations belonging to high weight class can access the channel. If the state is larger than d, all the stations can access the channel. The state transition probability is determined according as the system becomes idle or busy. In Fig. 2, Pidle1 and Pidle2 are the probability that the only high-weight class stations remain idle and the probability that all the stations remain idle, respectively. Pidle1 and Pidle2 are obtained as follows: 1 Pidle = (1 - t h ) nh 2 Pidle = (1 - t h ) nh × (1 - t l ) nl
(4)
where nh and nl denote the numbers of stations for high and low weight classes, respectively. Likewise, th and tl are the stationary transmission probabilities for high and low weight classes, respectively. Let p 1 and p 2 be the stationary probability that the slot states stay from 0 to d-1 and from d to infinity, respectively.
p 1 and p 2 are given as follows: p1 =
1 2 (1 - ( Pidle ) d ) × (1 - Pidle ) 2 2 1 1 1 - Pidle + ( Pidle - Pidle ) × ( Pidle )d
(5)
p 2 = 1 - p1
Therefore, (2) rewrites the stationary transmission probabilities for high and low weight classes as follows. t h = (p 1 + p 2 ) × tl = p2 ×
r +1
(1 - ph ) × bh _ 0, 0 (1 - ph )
(6)
r +1
(1 - pl ) × bl _ 0,0 (1 - pl )
where bh_0,0 and bl_0,0 are the stationary probabilities, which stay at state {0,0} in Fig. 1. Then, the stationary collision probabilities ph and pl for high and low weight classes are rewritten as follows. p h = p 1 × (1 - (1 - t h ) nh -1 ) + p 2 × (1 - (1 - t h ) nh -1 × (1 - t l ) nl ) pl = (1 - (1 - t h ) nh × (1 - t l ) nl -1 )
(7)
In Fig. 3, the analytic model with the AIFS is validated in comparison with the simulation result. Fig. 3 plots the normalized per class throughput as the total number of stations increases, and nh=nl is retained. Each simulation is executed with d=1 and d=3. Validation for AIFS Analysis (payload = 1024 byte)
1
Anal., high(d=1) Sim., high(d=1) Anal., low(d=1) Sim., low(d=1) Anal., high(d=3) Sim., high(d=3) Anal., low(d=3) Sim., low(d=3)
0.9
Normalized per class throughput
0.8 0.7 0.6
0.5 0.4 0.3 0.2 0.1 0
5
10
15 20 The number of stations (nSTA )
25
30
Fig. 3 Validation for AIFS Analysis
In this AIFS analysis, we do not consider the cases with more than two classes because such cases are not of our interest in this work, and the general AIFS analysis is out of scope. However, the case of more than two classes can be analyzed via a slight modification of the state diagram in Fig. 2.
B. Channel Access Ratio
We derive an equation to obtain our intended service differentiation. Let us assume that the weight for class h is higher than that for class l. We also assume that 1 = f1 < f2 < ... < f N where f1 is the lowest weight. From (24), the channel access ratio (R) of the high weight class h to low weight class l is defined as follows. Channel Access Ratio( R) =
v s_h v' s_l
P
P
1 -t l f t (1 - t h ) (1 - t l ) tl = h = h = , ("h, l Î {1,L, N }, "v Î h, "v'Î l ) fl t l (1 - t h ) nh (1 - t l ) nl -1 1 - t h th nh -1
nl
(8)
where fc and Ps_cv represent the weight associated with class c (i.e., c Î {1,L, N } ) and the probability (i.e., Ps_cv=Ps_c/nc) that a MAC frame transmission is successful from any station v belonging to class c, respectively. If all the frames have the same size, R becomes the throughput ratio. To rewrite (8) for general applicability, tc for each cÎ {2,…,N} is expressed as a function of t1. As a result, we obtain tc =
t1 1 -t1 +t1 fc
(9)
We use the well-known numerical tool, MATLAB, to obtain the solution of non-linear system from (2) and (23). C. Evaluation of Each Parameter
With different MAC parameters, we attempt to solve the main problem, i.e., the weighted fair channel access, considered in this paper. Then, the most desirable parameter is chosen among different MAC parameters in order to support weighted fairness. Each parameter is evaluated theoretically. The channel access ratio is a function of both the number nc of stations for each class and the MAC parameters shown in (2). Therefore, when nc is given, the MAC parameters for the low weight stations are also fixed to a given value. The parameters for the low weight class, mlow, Wlow, and klow, are set to 6, 31, and 1/2 (i.e., uniform distribution), respectively. On the other hand, the high weight station adjusts one of its MAC parameters, Whigh, mhigh, and khigh, to obtain the desired channel access ratio. Likewise, the AIFS difference d between high and low classes is also adjusted. Note that Wc, mc, and d can be only integer values while parameter kc is a real number between 0 and 1 and a raw value obtained from the analysis. Using the general numerical technique, we obtain each parameter for adjustment from (2), (23), and (9). After such computation, the obtained parameters are refined as follows. The three parameters (i.e., Wc, mc, and d) except kc should be rounded off to the closest integer, and then, each refined parameter is substituted as an input parameter in (2).
Fig. 4 shows the evaluation for each parameter when there are only two classes without RTS/CTS exchange. We do not investigate the aggregate throughput of Fig. 4 because it is determined according to how each parameter is set. The desired ratio is equal to 2 (i.e., fhigh = 2 and flow = 1). As illustrated in Fig. 4, the approach adjusting mc widely fluctuates around the ratio 2. Since mc is the exponential parameter as in (2), the slight change of the value has a great influence on the parameter adjustment for weighted fair access. For example, let’s assume that under the different network conditions (i.e., nTOTAL is different), mlow1 and mlow2 ( low1, low2 Î {1,L, N } ) for each low weight class are fixed to 6 and mhigh1 and mhigh2 ( high1, high2 Î {1, L , N } ) obtained by numerical analysis are 3.55 and 4.341, respectively. By refining both values to the integer, mhigh1 (= 4) is equal to mhigh2 in spite of the significant difference between two values. Consequently, the fluctuation of ratio occurs. Similarly, the ratio of AIFS differentiation widely fluctuates because d is the exponential parameter in (5). On the other hand, the method adjusting Wc lightly fluctuates in comparison with mc and d while the one adjusting kc accurately maintains the ratio of 2. The reason is why Wc must be an integer while a raw kc obtained from the numerical analysis is used for parameter adjustment without rounding off to an integer As explained thus far, we can see that an approach using kc is more accurate than other parameters in term of supporting the weighted fair channel access. Likewise, in the case where the desired ratio is not equal to 2, we have obtained the results similar to Fig. 4. Consequently, from now on, we will consider kc as the only MAC parameter for the weighted fair channel access because it is theoretically more accurate and is orthogonal with EDCA parameters. Payload Size=1024 byte adjusting k high
adjusting rounded W high adjusting rounded mhigh adjusting rounded d
Ratio
2.5
2
1.5
5
10
15 20 25 The total number of stations (n)
30
35
Fig. 4 Comparison among the parameters
D. Various Distributions with the Same Mean
The effect of different distributions with the same mean value is examined by comparing the simulation with the theoretical result. Fig. 5 illustrates the possible distributions with the same mean. The probability mass function for
the distribution differs from each other while the mean values of all the distributions are the same. Distribution 1 linearly decreases from 0 to Wi-1. Distribution 2 and Distribution 3 uniformly select a backoff counter from 0 to 2·kc·(Wc,i-1) and from 1/2·kc·(Wc,i-1) to 3/2·kc·(Wc,i-1), respectively. Note that Distribution 2 and 3 are similar to the uniform distribution in only specific domain not equal to the one. Distribution 4 is equal to a normal distribution which the mean and the standard deviation are kc·(Wc,i-1) and 1/2.57·kc·(Wc,i-1), respectively. Therefore, the probability that a backoff counter is chosen from 0 to 2·kc·(Wc,i-1) is equal to 0.99. Fig. 6 shows the simulation and the theoretical results using each distribution in Fig. 5. The normalized mean of the distributions kc employs 1/3. From Fig. 6, we observe that the simulations and analytic result coincide mostly. Consequently, we are confirmed that under a saturated network condition, the system performance is only influenced by the mean of distribution irrespective of the shape of it.
Fig. 5 The backoff distributions with the same mean
Aggregate Throughput (k = 1/3, payload = 1024 byte) Theoretical Value Simulation, Distribution 1 Simulation, Distribution 2 Simulation, Distribution 3 Simulation, Distribution 4(normal)
1
Normalized Throughput
0.8
0.6
0.4
0.2
5
10
15
20 25 The total number of stations
30
35
40
Fig. 6 The effect on the system throughput by the different probability mass functions
IV. UPLINK/DOWNLINK FAIRNESS
In this section, we derive the achievable maximum throughput while providing the uplink/downlink fairness as discussed above and apply weighted fairness among the stations to achieve the uplink/downlink fairness. We also propose three different schemes for an application. A. Maximum Throughput
From (24), the aggregate throughput S is maximized when the following equation S’ is minimized: N
S' =
1 - Pbusy + ( Pbusy - Ps )T
* col
Ps
=
N nc ö * æ ) nc + Tcol çç1 - Õ (1 - t c ) ÷÷ c =1 è ø -T* col N N n t q q nc (1 - t c ) å Õ q =1 1 - t q c =1
Õ (1 - t c =1
c
(10)
where Pbusy, s, Ps, and Tcol* denote the probability that there is at least one transmission in a given slot, the duration of an empty slot time, the probability that a transmission occurring in the system is successful, and Tcol/s, respectively. Tcol represents the average time that the channel is sensed busy due to a collision. If tc for class c in (10) is substituted with (9), S’ is expressed as function of t1. If the derivative of S’ is taken with respect to t1, we can obtain an optimal t1 that the system throughput is maximized. After that, by replacing t1 in (10) with the optimal t1, the optimal tc for each class is determined easily. To apply (10) to a single BSS (Basic Service Set), tc and nc for each class are substituted to the following: the number nAP of AP (=1), the number nSTA of stations, the stationary transmission probability tAP for the AP in a given slot, and the stationary transmission probability tSTA for the station. nAP is equal to 1 due to a single BSS. After the aforementioned substitution, the derivative of S’ is taken with respect to tSTA, and then, as the solution of the equality, the optimal tSTA can be obtained as follows: t STA _ opt =
* 2 * * (6Tcol - 1)nSTA + (Tcol - 1) 2 - (Tcol + nSTA + 1) * 2 Tcol (3nSTA - nSTA - 2) - nSTA (nSTA + 1)
(11)
From (9), the optimal tAP is obtained as follows: t AP _ opt =
t STA _ opt
1 - t STA _ opt
f AP
(12)
+ t STA _ opt
where fAP is the weight assigned to the AP or downlink. By manipulating (2) with r ® ¥ and mc ® 0 , the following equation for kc_opt is obtained. kc _ opt =
1 - t c _ opt
t c _ opt (CW - 1)
(13)
where CW ³ 1/tc_opt. We are able to get each optimal kc_opt value for the AP and the stations by substituting (11) to (13) and (12) to (13), respectively. In our proposed schemes, the AP periodically announces the calculated parameter, kSTA_opt, to the stations via beacon frames as if the EDCA parameter set is broadcasted by the QAP (QoS AP) in the 802.11e WLANs. During each beacon interval, the AP calculates the optimal parameter, and then transmits it via the next beacon frame. Each station receiving a beacon frame adjusts its own parameter, and then obtains the backoff counter based on the adjusted parameter value. After such an operation, the station attempts to access the channel. Note that under our proposed schemes, the operation of selecting the backoff counter value is basically similar to the backoff selection mechanism of IEEE 802.11 DCF except the contention window size/distribution. B. Estimating the Number of Stations
In this paper, we do not consider the algorithm to accurately estimate the number nSTA of active stations because the study for such an algorithm is another research issue (e.g., refer to [17]). Therefore, we take into account two simple modes for the estimation of nSTA. As a primitive approach, the number of unique MAC addresses observed from incoming frames at the AP is regarded as the number nSTA of active stations. Optionally, the state information of the wireless medium (i.e., busy or idle) measured during a beacon period can be used to estimate the number nSTA of stations. Based on [4] and [7], E[idle] and E[succ] are obtained as follows: ¥
1 - Pbusy
x =1
Pbusy
E[idle] = Pbusy × å x × (1 - Pbusy ) x = E[ succ] =
(14)
1 - Ps _ STA Ps _ STA
where E[succ] and E[idle] denote an average length between two successful transmissions for all the stations and an average length of the idle period, respectively. E[idle] and E[succ] are estimated during the simulation execution time. From (24), we can derive nSTA = k STA (WSTA - 1) ×
Ps _ STA 1 - Pbusy
= k STA (WSTA - 1) ×
E[idle] + 1 1 × E[idle] E[ succ] + 1
(15)
Scheme 1 does not use the optional mode for nSTA estimation in the simulations. However, in Schemes 2 and 3, the optional mode is used to estimate the uplink traffic amount. If the downlink is starved due to aggressive uplink transmissions or the downlink frames are intensively generated, the condition where the queue length is over Threshqueue occurs. As a result, our proposed schemes are activated. Depending on how the AP accesses the channel, we consider three different schemes as follows.
Fig. 7 Pseudo code operating in AP
Fig. 8 Data frame exchange
C. Scheme 1
In Scheme 1, the AP operates using a contention-based mechanism like DCF. Fig. 7 shows the pseudo-coded mechanism conducted by AP with Scheme 1. From (12) and (13), the AP adjusts its kAP_opt value, and gets the backoff counter. By substituting fAP with C·nSTA, the weighted fairness between uplink and downlink can be achieved. C is a downlink traffic control parameter. Therefore, the bandwidth of downlink can be C times all the station’s uplink bandwidth. D. Scheme 2
Basically, AP uses the medium access mechanism based on the credit in Scheme 2. If the AP has the credits, then the SIFS (Short Inter-frame Space) access is performed immediately after the ACK transmission for a preceding incoming uplink frame. The credit is increased for each incoming uplink frame, and decreased by each downlink transmission. The unit of credit can be defined with either the number of incoming uplink frames or the LENGTH field at PLCP (PHY Layer Convergence Procedure) header of the incoming uplink frame. The counted credits are accumulated in the credit pool. Credit_Pool + = C × T × num_of_incoming_fram e or C × T × Length
(16)
By adjusting the constant C in (16), the weighted fairness between uplink and downlink is accomplished. If C = 1 and the network traffic is overloaded (i.e., a saturation condition), the structure of data frame exchange between uplink and downlink is shown in Fig. 8 (a). In such a condition, the credit is consumed as soon as created. T is a parameter which indicates the uplink traffic amount. If the uplink traffic amount is reduced, the credit is not accumulated either. As a result, even though there are many downlink frames, they are not transmitted. This phenomenon is protected by parameter T (See line 10 of Fig. 7). Moreover, the AP manipulates kSTA_opt for the stations and periodically announces it to wireless stations as in Scheme 1. E. Scheme 3
Scheme 3 uses an ACK piggybacking mechanism using subtype field in frame control of MAC header. In addition, channel access method based on credit is again employed. When the AP receives a data frame via uplink, an ACK frame is transmitted via downlink. Before sending the ACK frame, AP examines whether the credit exists or not in the credit pool. If there is no credit, the normal ACK frame is transmitted. Otherwise, AP transmits the ACKpiggybacked DATA frame. This frame is received by the station waiting the ACK frame for the previously transmitted uplink data frame as well as the destination station for the DATA payload. When the station waiting an ACK receives the piggybacked frame, it investigates the subtype field of the frame header to determine if the ACK is received or not. Fig. 8 (b) illustrates the transmission structure of the piggybacked data frame. V. SIMULATION AND NUMERICAL RESULTS
Fig. 9 Simulation topology
A. Simulation Scenario
We carry out computer simulations in order to evaluate the performance between the conventional 802.11 DCF and the proposed schemes using the ns-2 simulation. The network topology is shown in Fig. 9. Each wireless station transmits the data traffic to each corresponding node CN via AP (i.e., WS1, WS2, …, and WS M send to CN1, CN2,…, and CN M, respectively), vice versa. Data traffic is generated using constant bit rate (CBR) over UDP.
Simulations are executed in a saturated condition. Such a condition is meaningful on the evaluation for service differentiation. As shown in Fig. 9, each CN and the AP are connected to the router R through wired link of 100 Mbps, respectively. Each WS is connected to the AP on the 802.11b wireless link with 11 Mbps data rate and 1Mbps control rate. In this situation, since the 802.11 WLAN is the bottleneck link, we observe only the data frames which pass over the wireless link. We assume that there is no hidden terminal and all the wireless stations are stationary. B. Aggregate Throughput and Fairness
Figs. 10 and 11 are obtained from the simulations with CBR traffic over UDP, where the payload size is 1024 bytes. All the wireless stations are within the radio transmission range for each other and there are no channel errors. The constant C for proposed schemes is set to 1. Fig. 10 presents the aggregate throughput of the conventional DCF, Scheme 1, Scheme 2, and Scheme 3 as the number of stations increases from 5 to 40. We can validate the accuracy of our analytical model in comparison with the simulation results. Both results mostly well match. In Fig. 10, we observe that the proposed schemes are superior to the conventional DCF. The performance of Scheme 3 is the best among three proposed schemes. The throughput of Scheme 1 is better than DCF because of using the optimal parameter. In Scheme 2, since AP does not contend to access the channel, Scheme 2 outperforms Scheme 1. The performance of Scheme 3 is even further improved since the ACK transmission time is reduced by using the ACK piggyback mechanism. Fig. 11 presents the throughput ratio between uplink and downlink (i.e., the long term fairness) for each mechanism. The ratio of DCF is linearly increased according to the number of stations since all the nodes including AP and wireless stations get the equal channel access probability in DCF. Accordingly, the downlink from the AP to stations becomes the bottleneck in the conventional DCF. As shown in Fig. 11, the ratios of Schemes 1, 2, and 3 are all 1. These results imply that the fairness between uplink and downlink is achieved in the long term for all three schemes. Aggregate Throughput (payload = 1024 byte) Analysis, DCF Simulation, DCF Analysis, scheme1 Simulation, scheme1 Analysis, scheme2 Simulation, scheme2 Analysis, scheme3 Simulation, scheme3
8
Throughput (Mbps)
7
6
5
4
5
10
15
20 25 The number of stations (nSTA)
30
35
40
Fig. 10 Comparison of aggregate throughput (payload size = 1024 bytes) Throughput Ratio of UP/DOWN (payload = 1024 byte) Analysis, DCF Simulation, DCF Analysis, scheme1 Simulation, scheme1 Analysis, scheme2 Simulation, scheme2 Analysis, scheme3 Simulation, scheme3
2
Ratio (log scale)
10
1
10
0
10
5
10
15
20 25 The number of stations (nSTA )
30
35
40
Fig. 11 The throughput ratio between uplink and downlink
C. Varying the Number of Stations
In Fig. 12, the simulation is conducted for 100 seconds, and the number of active stations varies over time. The simulation run starts at time 0 when the number of active stations is 5. At time 30, the number of active stations is increased to 20. At time 60, the number of active stations is reduced to 10. In DCF, the uplink/downlink ratio oscillates severely. This phenomenon presents the instability of DCF in terms of uplink/downlink bandwidth fairness. On the other hand, Scheme 1 shows some light fluctuations because the fundamental channel access method of Scheme 1 is based on the contention as DCF. However, the ratio from Schemes 2 and 3 maintains the value of 1 over the simulation period. This results shows that Schemes 2 and 3 provides the good fairness between uplink and downlink even in the short term irrespective of the number of stations. Varying the number of active stations (payload = 1024 byte) Conventional DCF Scheme1 Scheme2 Scheme3
Throughput Ratio of UP/DOWN (log scale)
2
10
1
10
0
10
-1
10
0
30
60 Time (second)
Fig. 12 The uplink/downlink ratio variation over time
100
D. Varying Uplink Traffic Amount
Fig. 13 is simulated under the condition where the uplink traffic amount varies over time. At time 0, all the wireless stations and AP aggressively transmit data frames (i.e., all the nodes always have backlogged data frames). At time 30, all the wireless stations decrease the transmission rate to CBR traffic with 1024-byte data size and 66.67 msec packet generation interval. After time 60, the transmission rate is further reduced to the CBR of 1024-byte data size and 80 msec packet generation interval. At time 90, the CBR over UDP traffic rate becomes aggressive again. The parameter C for each proposed scheme is set to 1, and the total number of stations is set to 20. In Fig. 13, the shortterm throughput variation for the conventional DCF and Scheme 1 is not observed severely. Because of the contention-based channel access, the throughput variation becomes relatively stable regardless of the uplink traffic amount. On the other hand, in Schemes 2 and 3, the short-term throughput changes according to the uplink traffic amount. However, thanks to parameter T, the aggregate throughput of both schemes is not decreased. As the uplink traffic amount is reduced, T is increased, and then more credits are generated. Varying the offered load (payload = 1024 byte, # of station = 20)
9
Conventional DCF Scheme1 Scheme2 Scheme3
8
7
Throughput (Mbps)
6
5
4
3
2
1
0
0
30
60 Time (second)
90
120
Fig. 13 The effect of the traffic reduction on uplink
E. Varying downlink frame size
Fig. 14 shows the effect of the various frame sizes on the downlink in the different schemes. In previous simulations, the unit of credit for Schemes 2 and 3 could be either the number of incoming frames via uplink or the LENGTH field of PLCP header because of using the same frame size between uplink and downlink. However, in this simulation, we should consider which unit is used. Fig. 14 is simulated using the LENGTH field of PLCP header as the credit for Schemes 2 and 3. There are 20 flows that the number of uplink flows (i.e., WSàCN) and downlink flows (i.e., CNàWS) are 10 and 10, respectively. The number of downlink flows transmitting 512-byte frames varies from 0 to 10 while all the uplink flows transmit 1024–byte frames. In the x-axis of Fig. 14, 3:7 means that the
number of flows transmitting 512-byte frames and those transmitting 1024-byte frames on the downlink are 3 and 7, respectively. Schemes 2 and 3 are always fair irrespective of the frame size thanks to the usage of the credit based on the LENGTH field. On the other hand, the throughput ratio of Scheme 1 varies according to the frame size. The reason is that Scheme 1 achieves only the channel access fairness. However, Scheme 1 still maintains the channel access fairness between uplink and downlink over the simulations. Varying the frame size of the downlink traffic (payload = 512 or 1024 byte)
Throughput Ratio of UP/DOWN
Scheme1 Scheme2 Scheme3
2
1
0:10
1:9
2:8
3:7 4:6 5:5 6:4 7:3 512 byte frame size vs. 1024 byte frame size
8:2
9:1
10:0
Fig. 14 The effect of the uneven frame size on the downlink
VI. CONCLUSION
In this paper, we propose an analytical model of WLANs with an arbitrary backoff distributions and AIFS. The normalized mean kc of a backoff distribution is considered the most effective MAC parameter for channel access differentiation. To support weighted fair channel access among stations in WLANs, each parameter (i.e., Wc, mc, d, and kc) is theoretically evaluated. We have proposed three different schemes in order to support the weighted fairness between uplink and downlink while providing the maximum throughput. We have examined the characteristics of three proposed schemes via the simulation and numerical studies. Schemes 1, 2, and 3 outperform DCF regardless of considered scenarios. Schemes 2 and 3 provide good fairness between uplink and downlink. In the ideal condition, Scheme 3 achieves the best performance.
REFERENCES [1] Std. 802.11-1999, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications, ANSI/IEEE Std. 802.11, 1999. [2] IEEE 802.11e/D8.0, Draft Supplement to Part 11: Wireless Medium Access Control (MAC) and Physical Layer (PHY) specifications: Medium Access Control (MAC) Enhancements for Quality of Service (QoS), Feb. 2004. [3] G. Bianchi, “Performance Analysis of the IEEE 802.11 Distributed Coordination Function,” IEEE Journal on Selected Areas in Communications, vol. 18, no. 3, Mar. 2000. [4] F. Cali, M. Conti, and E. Gregori, “Dynamic Tuning of the IEEE 802.11 Protocol to Achieve a Theoretical Throughput Limit,” IEEE/ACM Transactions on Networking, vol. 8, no. 6, Dec. 2000. [5] Y. Xiao, “An Analysis for Differentiated Services in IEEE 802.11 and IEEE 802.11e Wireless LANs,” in Proc. IEEE ICDCS’04, 2004. [6] Imad Aad and Claude Castelluccia, “Differentiation Mechanisms for IEEE 802.11,” in Proc. IEEE INFOCOM’01, 2001. [7] Daji Qiao and Kang G. Shin, “Achieving Efficient Channel Utilization and Weighted Fairness for Data Communications in IEEE 802.11 WLAN under the DCF,” in Proc. IEEE IWQoS’2002, May 2002. [8] E. Ziouva and T. Antonakopoulos, “CSMA/CA performance under high traffic conditions: throughput and delay analysis,” Computer Communications, vol. 25, no. 3, 2002, pp.313-321. [9] Y. Kwon, Y. Fang, and H. Latchman, “A Novel MAC Protocol with Fast Collision Resolution for Wireless LANs,” in Proc. IEEE INFOCOM’03, 2003. [10] H. Wu, Y. Peng, K. Long, S. Cheng, and J. Ma, “Performance of Reliable Transport Protocol over IEEE 802.11 Wireless LAN: Analysis and Enhancement,” in Proc. IEEE INFOCOM’02, 2002. [11] J. Weinmiller, H. Woesner, J. P. Ebert, and A. Wolisz, “Analyzing and Tuning the Distributed Coordination Function in the IEEE 802.11 DFWMAC Draft Standard,” in Proc. MASCOT’96, 1996. [12] J. Deng and R. S. Chang, “A Priority Scheme for IEEE 802.11 DCF Access Method,” IEICE Trans. Commun., vol. E82-B, no.1, Jan. 1999. [13] A. Grillo and M. Nunes, “Performance evaluation of IEEE 802.11e,” in Proc. IEEE PIMRC’02, Lisboa, Portugal, Sep. 2002. [14] M. Bottigliengo, C. Casetti, C.-F. Chiasserini, and M. Meo, “Short-term Fairness for TCP Flows in 802.11b WLANs,” in Proc. IEEE INFOCOM'04, 2004. [15] S. Pilosof, R. Ramjee, D. Raz, Y. Shavitt, and P. Sinha, “Understanding TCP Fairness over Wireless LAN,” in Proc. IEEE INFOCOM’03, San Francisco, CA, USA, 2003. [16] C. Casetti and C.-F. Chiasserini, “Improving fairness and throughput for voice traffic in 802.11e EDCA,” in Proc. IEEE PIMRC’04, 2004.
[17] G. Bianchi and Ilenia Tinnirello, “Kalman Filter Estimation of the Number of Competing Terminals in an IEEE 802.11 Network,” in Proc. IEEE INFOCOM’03, San Francisco, U.S.A., 2003. [18] H. Kim and J. C. Hou, “Improving Protocol Capacity with Model-based Frame Scheduling in IEEE 802.11-operated WLANs,” in Proc. ACM MOBICOM’03, San Diego, U.S.A., 2003. [19] S. Mangold, S. Choi, G. R. Hiertz, O. Klein, and B. Walke, “Analysis of IEEE 802.11e for QoS Support in Wireless LANs,” IEEE Wireless Communications, Dec. 2003, pp. 40–50. [20] S. Choi, J. del Prado, S. Shankar N, and S. Mangold, “IEEE 802.11e Contention-Based Channel Access (EDCF) Performance Evaluation,” in Proc. IEEE ICC’03, May 2003. [21] N. H. Vaidya, P. Bahl, and S. Gupta, “Distributed fair scheduling in a wireless LAN,” in Proc. ACM MOBICOM’00, Boston, MA, USA, Aug. 2000. [22] J. Kim and C. Kim, “Performance Analysis and Evaluation of IEEE 802.11e EDCF,” Wireless Communications and Mobile Computing, vol. 4, issue 1, Feb. 2004. [23] I. Tinnirello and S. Choi, "Temporal Fairness Provisioning in Multi-Rate Contention-Based 802.11e WLANs," to appear in Proc. IEEE WoWMoM’05, Taormina, Italy, June 2005. APPENDIX A
We first define Wc ,i = 2i Wc ,
i £ mc
Wc ,i = 2 Wc ,
i > mc
mc
(17)
where Wc=(CWmin+1), 2mWc=(CWmax+1), and mc denotes the maximum backoff stage for class c. We here use symbol r to represent the maximum retry count (i.e., short retry limit or long retry limit). Let bc_i,j be the stationary probability of state {i, j} for backoff distribution c. Then, we can derive the following relationship: bc _ i -1,0 × pc = bc _ i ,0 ® bc _ i ,0 = pci bc _ 0,0 , (0 £ i £ r )
(18)
From the chain regularities, we can obtain, Wi -1
bc _ i , j = å Dc ,i (n) × bc _ i ,0 , (0 £ i £ r ), (0 £ j £ Wc ,i - 1).
(19)
n= j
We note that sum of the probabilities of all the states is equal to 1. Therefore, the following relationship can be derived. r Wc ,i -1
1= å i =0
åb j =0
c _ i, j
r
= å bc _ i , 0 i =0
Wc ,i -1 Wc ,i -1
å åD j =0
n= j
c ,i
r æ Wc ,i -1 ö (n) = å bc _ i ,0 çç å nDc ,i ( n) + 1÷÷. i =0 è n =0 ø
(20)
The term
å
Wc ,i -1 n =0
nDc ,i (n) is equal to the mean of the backoff distribution Dc ,i (n) . The mean of the backoff
distribution can define as (3) with the parameter kc. Therefore, from (17), (18), and replacing
Wc ,i -1
å (n + 1) × D
c ,i
n =0
\ bc _ 0, 0 =
(n) by k cWc ,i + (1 - k c ) in (20), we can derive
1 r
å p × (k W i =0
i c
c
c ,i
(21)
+ (1 - k c ))
Now, from the definition of tc and using (18), the transmission probability tc is given by r
r
i =0
i =0
t c = å bc _ i ,0 = å pc bc _ 0, 0 = i
r +1
1 - pc bc _ 0, 0 , 1 - pc
(22)
where bc_0,0 is given in (21). At the stationary state, each station carrying class c transmits a packet with probability tc, which also depends on the collision probability pc. Now, because a collision occurs when there are at least two stations to transmit simultaneously, pc can be given by N
pc = 1 -
Õ (1 - t
q
q =1
1-t c
)
nq
.
(23)
The probabilities pc and tc can be solved by numerical methods and the solution of tc is unique. The method solving the normalized system throughput S is referred to [3]. For the service differentiation, the probability Pbusy that the channel is busy, the probability Ps_c that a successful transmission occurs from a class-c station, and the normalized system throughput Sc of class c (i.e., per-class throughput) are as follows. N
Pbusy = 1 - Õ (1 - t c ) nc c =1
N
Ps _ c = nct c ×
Õ (1 - t
q
)
nq
q =1
1-tc
N
Ps = å Ps _ c
(24)
c =1
Sc =
Ps _ c E[ P ] (1 - Pbusy )s + PsTsuc + ( Pbusy - Ps )Tcol N
\ S = å Sc c =1
where E[P] and Tsuc represent the mean packet payload size and the mean time that the channel is sensed busy because of a successful transmission, respectively.
