A Study of Short-Term Fairness. in Wireless MAC Protocols. Andrew Swan and Suchitra Raman. May 11, 1998.

Transcription

1 A Study of Short-Term Fairness in Wireless MAC Protocols Andrew Swan and Suchitra Raman May 11, 1998 Abstract In this paper, we study short-term fairness in distributed, contention-based wireless medium access control (MAC) protocols. While most MAC protocols provide fairness among contending stations in the long term, they are not fair over shorter time scales. We rst demonstrate short-term unfairness of CSMA/CA using packet-level traces collected from an in-bulding wireless LAN network. We also analyze these traces and show adverse interactions between TCP and CSMA/CA. We then model the system of contending stations as a Markov chain and dene the short-term fairness index for this model as the zeroth-order entropy rate of the underlying stochastic process. We argue that because this quantity is a good measure of uncertainty in channel accesses, it models short-term fairness well. We solve the analytical model for a CSMA/CA-based system with dierent numbers of stations and conclude that its short-term fairness is signicantly lower than ideal. 1 Introduction The recent emergence of wireless networks has enabled many exciting new applications, but also brings with it new and challenging research problems. Some of these problems include protocol and application design for networks with non-negligible bit-error rates and asymmetry [1], providing transparent connectivity and services to mobile users [7], and managing limited resources in small portable devices[11]. An area that has received comparatively little attention is media access protocols for shared wireless channels. The problem of shared media access has been studied extensively on wired networks. In the Carrier Sense Multiple Access (CSMA) family of media access control (MAC) protocols, a station listens to the channel and determines if it is being used before starting a transmission. With basic CSMA, there is no guarantee that simultaneous tranmissions from dierent stations will not \collide", or interfere with each other in such a way that neither transmission succeeds. To resolve collisions in wired networks such as Ethernet, CSMA can be augmented with Collision Detection (CSMA/CD). In CSMA/CD, a transmitting station continues to listen to the channel during its transmission and is able to detect a collision because it can hear transmissions from all other stations sharing the channel. If a collision is detected, the transmitting stations wait a randomized short period of time and transmit again. One of the challenges in designing a media access control (MAC) protocol for a wireless network is the hidden terminal problem. The hidden terminal problem is actually a class of problems, all of which result from the fact that all devices connected to a single wireless LAN may not be able to communicate directly with each other over the wireless channel. Due to the hidden terminal problem, CSMA/CD is not suitable for wireless networks. As a result, CSMA with Collision Avoidance (CSMA/CA) has been proposed for wireless networks. In CSMA/CA, a transmitting station may not be able to determine that a collision has taken place. While CSMA/CA does not have a provision for re-transmissions they must be handled by a higher level protocol it does attempt to reduce the likelihood of collisions. In order to do this, a station that has transmitted waits some period of time before attempting to transmit again. This time is called the Inter-Frame Spacing (IFS). In both CSMA/CA and CSMA/CD, a station that must wait to transmit (due to either a collision or a busy carrier sense) uses a randomized timer. In an attempt to avoid collisions, the interval from which the timer is 1

2 chosen is backed o exponentially upon every collision or busy carrier sense. While this policy achieves high utilization of the channel by reducing the frequency of collisions, it leads to short-term unfairness. When multiple stations attempt to transmit simultaneously, one station will transmit successfully and the others will all back o. After the rst transmission is completed, there is a \timer race" all stations have set timers and the station whose timer expires rst will get access to the channel next. Since all other stations have backed their timers o, they are less likely to win the timer race, so they continue to back o. The interval over which the timer is chosen is typically bounded to prevent a station from getting completely starved, but it is still easy for a station to become completely backed o at which point its chance of winning the timer race is very small. Other recent research in the eld of wireless MAC protocols has proposed layering new mechanisms on top of CSMA/CA to provide fairness. Although such approaches are promising, we are not aware of any detailed study of the fairness properties of CSMA/CA alone to provide context for enhancements to it. In the rest of this paper, we carry out such a study. In the next section, we present the results of a series of experiments we carried out to observe the problem of short-term unfairness in real wireless networks. We present an analytical study of the short-term fairness properties of CSMA/CA in Section 3. In Section 4, we validate our analytical model with our experimental results. We conclude with a summary in Section 5. 2 Experiments We present experimental evidence of short-term unfairness in CSMA/CA-based systems from experiments on the Daedalus in-building wireless LAN testbed [6]. This wireless network uses Lucent's WaveLAN technology [12] that uses direct sequence spread spectrum (DSSS) modulation to meet the regulatory requirements for unlicensed usage in the 915 MHz ISM frequency band. WaveLAN has a rated data bandwidth of about 2 Mb/s and uses CSMA/CA as the channel access protocol. In this section, we analyze the short-term fairness properties from packet-level traces collected in our testbed. Traces were gathered using the tcpdump [5] packet capture tool running on a host connected to the same LAN. We perform two sets of experiments. The rst set involves multiple UDP [8] senders that always have data ready to transmit. This experiment allows us to analyze the exact channel access patterns for identical senders. In the second set of eperiments, we look at the eects of short-term unfairness on TCP [9] transfers. Our measurements show that CSMA does not eectively prevent a single host or small group of hosts from monopolizing the channel for several packet transmission times. Competing UDP transfers. Using two competing UDP transfers between distinct pairs of hosts as shown in Figure 1, we studied the channel access pattern of the two senders. Both the UDP senders were congured to transmit at 200 Kbps using 512B packets. Figure 2 shows the channel access pattern with two UDP senders. We nd that each host \captures" the channel for prolonged durations even though the other host has data ready for transmission. This causes each sender to burst out data when it does gain access to the channel. Since increased burstiness results in increased jitter in packet delays as perceived by the receiver, jitter is an approximate indication of short-term unfairness. Table 1 summarizes the packet arrival jitter at the receiving host. The jitter was computed over all correctly received packets 1 at the receiver as the mean linear deviation in packet transit time or delay. Jitter = nx i=1 j(r i+1? S i+1 )? (R i? S i )j where S i and R i are the sending and receiving times of packet i. As the number of competing UDP transfers is increased to 3 or 4, we nd that each host captures the channel for progressively smaller periods of time. However, we do still observe signicantly long intervals of time when one station does not gain access to the channel as shown in Figures 3 and 4. 1 We do not include dierences in transit delay between non-contiguous packets. 2

3 Sender Receiver Total transmitted Total received Jitter (packets) (packets) (ms) yacht-wl ajanta-wl cruiser-wl inr-daedalus Table 1: Two competing UDP transfers at 200 Kbps using 512B packets. In all these experiments, the long-range fairness over the entire duration of the transfer is close to ideal. We report the values of Jain's long-term fairness index [3] in all these cases in Table 2. S 1 Packet capture S 2 UDP transfer #1 Wireless LAN UDP transfer #2 R 1 R 2 Figure 1: Experimental setup for fairness experiments showing two identical contending UDP transfers. Yacht-wl Cruiser-wl yacht-wl cruiser-wl Elapsed time (s) Figure 2: With two competing UDP transfers in which both sources always had data to send, each source \captures" the channel for a prolonged period of time before the other station gains access. Single TCP connection. We studied the progress of a single TCP connection between two hosts connected over a single-hop Wave- LAN network. The TCP sequence plot for this transfer in Figure 6 shows that the sender is extremely bursty. The sender and receiver take turns monopolizing the wireless channel. The sender eectively transmits a full window of data, yielding the channel to the receiver. On gaining access, the receiver transmits a burst of ACKs that subsequently triggers the next window of data. This adverse interaction causes the \pipe" to remain under-utilized resulting in low TCP throughputs. In fact, the smooth ACK-clocked TCP protocol degenerates to a window-by-window stop and wait protocol. A similar eect was also reported in 3

4 Channel access cruiser-wl inr-daedalus-192 ajanta-wl Elapsed time (s) Figure 3: The channel access pattern with 3 UDP senders shows shorter capture periods. However, there are signicantly long durations in which one host does not gain access. Channel access yacht-wl cruiser-wl inr-daedalus-192 ajanta-wl Elapsed time (s) Figure 4: The channel access pattern with 4 UDP senders. CSMA/CD-based Ethernets [10]. In summary, while CSMA/CA is asymptotically fair, it is unfair over short time scales. This short-term unfairness leads to undesirable eects in feedback-based protocols such as TCP. While good metrics (e.g., minmax fairness index) exist to quantify long-term fairness, there is no quantitative metric for short-term fairness. Our goal, in the rest of this paper, is to model short-term fairness accurately. 3 Analysis of CSMA/CA In this section we present an analysis of the fairness properties of a simple CSMA/CA MAC protocol. 4

5 # Hosts Jain's fairness index Table 2: Min-max fairness is close to ideal (1.00) in all cases. S 1 Packet capture TCP transfer Wireless LAN R 1 Figure 5: A Single TCP connection across a wireless link ACK Data Sequence Number Elapsed time (s) Figure 6: The TCP sequence plot for a transfer between two hosts shows that there is no ne-grained sharing of the channel by the sender and receiver. The sender transmits a window of data in a single burst and waits for the receiver transmit a burst of ACKs that in turn trigger the sender, and so on. The result is long idle periods and low TCP throughput. 3.1 A Model for CSMA/CA We use a model for CSMA/CA based on the the Lucent WaveLAN wireless LAN system [12]. The model is as follows. Time is divided in to discrete slots. A transmission can begin only at the start of a new slot. The actual MAC protocol may not actually use a slotted time structure, but a slotted system is much easier to analyze while producing similar results. When a station wishes to transmit a packet, it rst performs a carrier sense. That is, it listens to the channel to determine if another station is currently transmitting. If it nds the channel idle, it proceeds 5

6 with the transmission at the beginning of the next time slot. If the channel is busy, the station waits until the transmission ends and then sets a timer, called the backo timer. When this timer expires, it conducts another carrier sense and repeats the procedure described above. The backo timer is randomized so that if two stations are attempting to transmit simultaneously, they will not remain synchronized in a state where neither can send. The length of the timer is initially chosen from a uniform distribution over the range [1; 32] slots. Every time a station senses a busy channel and has to wait for a transmission to complete, the range from which the timer is chosen is doubled. That is, after sensing a busy channel, the next timer is chosen uniformly from the range [1; 64], then [1; 128], and so on. To avoid starvation, the range never grows beyond [1; 256]. If a station concludes a sucessful transmission and has more packets to transmit, it waits for 16 slots before performing a carrier sense. This interval is called the Inter-Frame Spacing (IFS). We consider only the basic contention resolution protocol and not mechanisms such as RTS/CTS exchange or control protocols implemented in a base station [2]. While such mechanisms are often considered part of a MAC protocol, they are orthogonal to the study of fairness. We also don't consider the hidden-terminal problem since it is also orthogonal to fairness. 3.2 Analysis In our analysis, we consider a wireless LAN in which N stations attempt to transmit simultaneously. We assume that each station always has a packet to transmit. Since the basic CSMA contention algorithm is symmetric (i.e., each host executes the same algorithm) and there are mechanisms to prevent starvation, it provides fairness over suciently long time scales. That is, over a suciently long time scale, all hosts will receive roughly equal access to the channel (this claim is conrmed by the experimental results presented in Section 2). However, we are concerned with fairness over shorter time scales. A MAC protocol that provides long-term fairness but does not provide short-term fairness will interact poorly with higher level protocols. An example of such an interaction is illustrated for TCP in Figure 6. An application that transmits isochronous audio packets would also work very poorly if run over a MAC protocol with poor short-term fairness. Without short-term fairness, the receiver would see very high jitter (or variance in delay) of the incoming audio stream. While this problem can be mitigated by buering the incoming stream, buering makes it dicult to use such an application interactively. To evaluate the fairness properties of CSMA/CA over short time scales, we consider the random process fx i g where the index i refers to the ith successful transmission over the channel. Specically, we consider the entropy rate of this process, H(fX i g). The entropy rate of a random process measures the entropy per symbol and is dened as follows [4]. 1 H(fX i g) = lim n!1 n H(X 1; X 2 ; : : : ; X n ) Entropy quanties the uncertainty in a random variable. In a MAC protocol that relies only on randomization to provide fairness, the entropy rate of the process described above provides a reasonable measure of the protocol fairness. If there is a lot of uncertainty about which station will access the channel, that implies that all stations are competing fairly for the channel. Similarly, if there is little or no uncertainty about which station will access the channel, some station or stations do not get to compete fairly for the channel. For a random process in which each element is drawn from a discrete set of size N, the maximal entropy rate is attained by a process in which each value is independent and chosen uniformly. This process has an entropy rate of log N 2. Note that the entropy maximizing process described above correponds to an ideal fair MAC protocol. We can thus evaluate the fairness of a completely randomized MAC protocol by calculating H(fX i g) and comparing it 2 All logarithms in this paper are taken with a base of 2 6

7 to log N. This technique has limits: it is eective only for a MAC protocol that relies only on randomization for fairness. For example, applying this analysis to a MAC protocol based purely on Time Division Multiple Access (TDMA) would yield an entropy rate of 0; the channel access pattern is completely deterministic so there is no uncertainty. We begin by analyzing the case where N = 2 and then continue to the general case The N = 2 Case After every successful transmission, a station may be in one of ve states: It is the station that conducted the last transmission. We label this state T. It did not transmit the last packet. It thus chooses a timer uniformly from some interval. There are four of these states and we label them based on the size of the interval from which the timer is chosen: 32; 64; 128; 256. The state of the whole system includes the states of both stations. As illustrated in Figure 7, only 8 of the possible 25 combinations of states for the two stations are possible. These states form a Markov chain since the probability of a transition from one state to another depends only on what the current state is. {T,256} {256,T} {T,128} {128,T} {T, 64} {64, T} {T, 32} {32, T} Figure 7: State transition diagram for N = 2. Transitions on the right side are not shown but are equivalent to those on the left side. From a state ft; xg, there are two possible transitions, to states ft; next(x)g and f32; Tg, where next(x) = min(2x; 256). Note that states fx; Tg are equivalent to corresponding states ft; xg, with identical transitions and transition probabilities. The transition probabilities are straightforward to compute: ft; xg! ft; next(x)g This transition corresponds to the station that just transmitted transmitting again. This occurs when the randomized timer, which is drawn from a uniform distribution on [1; x], happens to be longer than 16 slots. This event has probability P ft;xg;ft;next(x)g = 1? 16 x ft; xg! f32; Tg This transition corresponds to the host that did not just transmit transmitting. This occurs when the 7

8 randomized timer is shorter than 16 slots, which happens with probability P ft;xg;f32;tg = 16 x State Probability ft;32g ft;64g ft;128g ft;256g f32;tg f64;tg f128;tg f256;tg Table 3: Steady-state probabilties of the Markov Chain for CSMA with N = 2. From these transition probabilities, it is straightforward to calculate the stationary distribution of the Markov chain. The steady-state probabilities are shown in Table 3. Even before calculating the entropy rate, we can see evidence of unfairness. The system spends nearly 75% of the time in a state in which one station is fully backed o (there are two such states, labeled ft;256g and f256;tg in Table 3). We can now calculate the entropy rate of the random process fx i g. For the case with only two stations, each state has only two out transitions, one of which correponds to the same station transmitting again, while the other corresponds to a change in the transmitting station. X As a result, the entropy rate is easily calculated: H(fX i g) = s h(p s ) statess where P s is the probability of the same station transmitting again from state s and h(p) is the entropy of a Bernoulli random variable with parameter p: h(p) =?p log p? (1? p) log(1? p) Combining the steady-state probabilities from Table 3 and the transition probabilities calculated above, we calculate that for N = 2, H(fX i g) = 0:474 Recall that a fair protocol for two stations would have H(fX i g) = The General Case As in the N = 2 case, each station may be in one of ve states after a transmission. These states are, as before, labeled T; 32; 64; 128; 256. The state of the system as a whole consists of an N-tuple of such states. Again, only a small fraction of the 5 N possible states are actually attainable (e.g., the state ft; T; : : :; Tg is invalid). From any state, there are N transitions, one for each station that might successfully transmit (including the station that just transmitted). The transition probabilities are calculated as follows. Note that we only consider transitions in which the rst station transmits. Permuting the ordering of stations does not aect the transition probabilities so we cover all transitions. (For example, if N = 3, the transitions ft; 32; 256g! f32; 64; Tg and f256; T; 32g! ft; 32; 64g have the same probabilties). There are two types of transitions with the following transition probabilities: ft; x 2 ; : : : ; x N g! ft; next(x 2 ); : : : ; next(x N )g This transition corresponds to another transmission by the station that just transmitted. This occurs when 8

9 the randomized timers of stations 2 through N are all longer than 16 slots. Let T i be the length of the timer at station i (i.e., T i is a realization of a random variable drawn from a uniform distribution ver the interval [1; x i ]). Since the randomization at a station is independent of all other stations: P(fT; x 2 ; : : :; x N g! ft; next(x + 2); : : :; next(x N )g) = P(T 2 > 16; T 3 > 16; ; T N > 16) = = Y Y 2iN 2iN P(T i > 16) (1? 16 ) x i fx 1 ; x 2 ; : : : ; x N?1; Tg! ft; next(x 2 ); : : : ; next(x N?1); 32g This transition occurs when station 1 transmits a packet after station N transmitted the previous packet. Station 1's randomized timer must be less than 16 slots (so that it transmits before station N) and also shorter than the randomized timers of stations 2 through N? 1. The transition probability is calculated as follows: P(fx 1 ; x 2 ; : : : ; x N?1; Tg! ft; next(x 2 ); : : : ; next(x N?1); 32g) = P(T 1 < 16; T 1 < T 2 ; T 1 < T 3 ; ; T 1 < T N?1) = P(T 1 < 16) = 16 x 1 Y 2iN?1 Y 2iN?1 (1? 8 x i ) P(T 1 < T i jt 1 < 16) From these transition probabilities, it is straightforward to generate the full state diagram with all transitions. However, as N grows, the number of states grows rapidly. We wrote a script to generate the linear equations that must be solved to calculate the stationary distribution and calculated the stationary distributions for values of N up to 6. We then use the same technique as above to calculate the entropy rate of the random process fx i g: X H(fX i g) = s H(P s ) statess Note that in this case, P s is a probability distribution dened over a discrete set of size N, rather than simply a Bernoulli random variable as before. The entropy for a probability distribution P over a discrete set of size N is dened as: The complete results are shown in Table 4. H(P ) =? NX i=1 P (i) log P (i) N H(fX i g) log N Table 4: Entropy rate for the random process fx i g. For a completely fair MAC protocol, H(fX i g) = log N. 9

10 4 Discussion To validate our theoretical model for CSMA and the analysis carried out in Section 3, we calculated the empirical entropy rate of the actual sequences of transmission observed on a real wireless LAN. The traces we examined are those illustraed in Section 2. The results are summarized in Table 5. Entropy Rate N Theoretical Empirical N/A Table 5: Predicted and measured entropy rates. For reasons we do not yet understand, we were unable to calculate the stationary distribution for the N = 4 case. We used Mathematica for the step that involves solving a system of linear equations but although it could solve the more complex systems correponding to N = 5 and N = 6, it could not solve the system for N = 4. We plan to investigate this problem more thoroughly. We rst examined the trace illustrated in Figure 2. In this trace, two stations transmitted UDP ows across a shared channel for a period of 13 seconds. Over the full 13 seconds, the MAC protocol provided reasonable fairness one host successfully transmitted 984 packets while the other transmitted 992 packets. However, there is ample evidence of short-term unfairness in Figure 2. To quantify this unfairness, we calculated the empirical entropy rate to compare it to the theoretical rate calculated previously. As shown in Table 5, the theoretical prediction matched the empirically observed entropy very well. For traces with more hosts, we observed a trend that the empirical fairness is smaller than the entropy rate predicted by our theoretical model. We did not have time to study this eect in detail but we conjecture that it is due to a bug in the MAC protocol implementation in the WaveLAN adapters used in our experiments. For all our experiments, we used older ISA based WaveLAN cards; we plan to repeat the experiments with newer PCMCIA based WaveLAN cards to see if the bug has been identied and xed. 5 Summary In this paper we have presented a detailed study of the short-term fairness properties of CSMA/CA. Our study includes both experimental results that demonstrate that a popular CSMA/CA based wireless LAN system exhibits short-term unfairness and an analytical framework for evaluating CSMA/CA. Our results indicate that short-term fairness is poor in CSMA/CA and provides a context for other MAC protocol research that addresses fairness. 6 Acknowledgements We would like to thank Hari Balakrishnan for suggesting this very interesting topic to us and advising us on this project. References [1] Balakrishnan, H., Padmanabhan, V., Seshan, S., and Katz, R. H. A Comparison of Mechanisms for Improving TCP Performance over Wireless Links. IEEE/ACM Transactions on Networking (December 1997). [2] Bharghavan, V. A New Protocol for Medium Access in Wireless Packet Networks. In University of Illinois, Urbana-Champaign Tech. Report. (1998). [3] Chiu, D.-M., and Jain, R. Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks. Computer Networks and ISDN Systems 17 (1989), 1{14. 10

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