# Understanding the Performance of Networks

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2 For 82.g, the efficiency at 54 Mb/s becomes U =.69. Thus, a single station sending frames of 5 bytes over 82.b can at most obtain the throughput of 8.69 Mb/s and Mb/s over 82.g. Fact : The constant overhead lowers the throughput of the 82. DCF to about 2% or 3% of the bit rate depending on the variant. B. Random backoff and collisions TABLE II MAC-LEVEL THROUGHPUT, SIMULATION N stations b, Mb/s cumulative g, 54 Mb/s cumulative When a station senses the channel busy, it waits for a random backoff, which further lowers its useful throughput (the random backoff even applies to a single station). On the average, a station waits t cont = CW/2 SLOT, which means that for a single station efficiency decreases to U =.65 for 82.b (throughput of 7.5 Mb/s) and U =.57 for 82.g (throughput of 3.68 Mb/s). Table II presents simulated throughput values for 82.b and 82.g in function of the number of contending stations (stations are greedy, i.e. they have always a frame of 5 bytes to transmit). The cumulative throughput first increases (e.g Mb/s for N = 2 and 82.b), because the interval between transmission attempts is shorter it is the minimum of two or more uniformly distributed random variables. However, for a larger number of stations, the cumulative throughput decreases (e.g. 7. Mb/s for N = ), because of an increased collision rate. TABLE III COLLISION RATE, SIMULATION N stations b, Mb/s g, 54 Mb/s Table III shows simulated values of the collision rate that significantly increases with the number of stations. Note that it is much larger for 82.g due to smaller CW. Fact 2: Random backoff increases the overhead (35% for 82.b and 43% for 82.g) and available throughput (7.5 Mb/s and 3.68 Mb/s). Increasing contention between stations results in collisions that further decrease the available throughput. C. Influence of transmission errors The quality of received signals over a wireless channel changes in time due to multiple causes (noise, fading, interference, multipath propagation, station mobility) and may result in incorrectly received frames and decreased throughput. Under 82. DCF, the influence of frame errors is even more important, because failed transmissions are undistinguishable from collisions: stations apply the exponential backoff after a lost frame. Table IV shows simulated values of throughput for a single station under 82.b for different values of e, the frame error rate. It is lower than the throughput that could be obtained by a station without the exponential backoff after a frame loss: U ( e). TABLE IV THROUGHPUT FOR 82.B, FRAME ERRORS, N =, SIMULATION e, frame error rate % 2% 5% % throughput (Mb/s) U ( e) (Mb/s) Fact 3: Transmission errors result in a lower throughput amplified by the 82. contention control based the exponential backoff. D. Channel adaptation and rate diversity A station may lower its bit rate at some threshold frame error rate to obtain better throughput a station transmitting at a lower bit rate uses a more robust modulation scheme that decreases the frame error rate. Obviously, the transmission at the lower bit rate takes longer, but it is compensated by a lower frame error rate, which globally results in a better throughput. The main issue is to decide when it is beneficial to switch to a lower bit rate. Let us consider a single station transmitting frames of the same size at the higher bit rate (lower bit rate) r h (respectively r l ). When switching to the lower bit rate, we expect to lower the frame error rate from e h to e l. We assume that some part of the frame transmission time does not depend on the bit rate: σ h (respectively σ l ) denote the proportion of useful throughput when using the higher bit rate (respectively lower bit rate). To find the threshold value of the frame error rate for which a station needs to lower its bit rate, we need to have at least the same throughput for both bit rates: r h σ h ( e h ) = r l σ l ( e l ). (2) The threshold frame error rate is thus e h = r lσ l r h σ h ( e l ). (3) As a first approximation, we can assume that lowering the bit rate will reduce the frame error rate to and the proportions of useful throughput are equal (σ h = σ l ). In this case, we simply obtain e h = r l r h (4) This means that for 82.b, a station needs to switch from Mb/s to 5.5 Mb/s when the frame error rate exceeds 5%. If the frame error rate at the lower bit rate is not, this value should be even increased, e.g. if e l =.2, the threshold increases to 6%.

3 * ' \$(! ) %! \$ Fact 4: Under imperfect channel conditions, switching to a lower bit rate is beneficial if the frame error rate exceeds some significant threshold. E. Performance anomaly Bit rate diversity in 82. leads to performance anomaly: the rate of a slower station limits the throughput of fast ones, because it takes more time to transmit frames at a lower bit rate, which decreases the channel time available for the transmission of fast stations [2]. To understand this effect, let us consider two stations transmitting at different bit rates: one station uses the high transmission rate R = Mb/s and another one transmits at a degraded rate r = 5.5,2, or Mb/s. If both stations send frames of size s, they respectively spent T f = s/r + t R ov and T s = s/r+t r ov in transmission (t R ov and t r ov denote all overhead that does not depend on the bit rate: headers, interframe spaces, contention, and time spent in collisions). As the long-term channel access probability is equal for both stations, their mean throughput is as follows: s X f = X s = X =, T f + T s which means that both stations obtain the same throughput. We also have: X = R + r + s(tr ov + t r ov), (5) which means that throughput roughly corresponds to a geometric mean of the respective bit rates. We provide more detailed analysis and results for any number of stations elsewhere [2]. The main consequence of this relation is that the slow station degrades the throughput of fast stations they see their throughput reduced to the order of magnitude of the slow station throughput. Fact 5: Stations switching to lower bit rates to adapt to bad channel conditions may significantly lower the throughput of stations that use higher bit rates. III. FAIRNESS Fairness can be defined at different time scales: long-term fairness guarantees that the probability of successful channel access observed on a long term converges to /N for N competing stations. An access method is short-term fair if channel allocation is fair over short time intervals. In this case, each station can expect to access the channel after a short time, which in turn results in short delays. Note that shortterm fairness implies long-term fairness, but inverse does not hold. A. Short-term fairness for small number of stations Koksal et al. analyzed the short-term unfairness of an early Wavelan wireless card [3] and identified the short-term unfairness problem of its access method in which stations performed exponential backoff whenever the channel was sensed busy. Since this paper, many authors have stated that 82. suffers from short-term unfairness and referenced it as the paper that proves the short-term unfairness of 82. [4], [5]. However, they have not realized that the access method of 82. has changed with respect to that of the Wavelan cards: in the 82. DCF [], the exponential backoff is only applied after a collision. This misleading common wisdom has emerged from the confusion of two different access methods. In fact, short-term fairness of the 82. DCF in the case of two stations is fairly good [6]. We evaluated it by considering patterns of transmissions and computing their average Jain fairness index in a window of an increasing size [3]. It is defined as follows: let γ i be the fraction of transmissions performed by station i during window w; the fairness index is the following: F J (w) = ( N i= γ i) 2 N. (6) N i= γ2 i Perfect fairness is achieved for F J (w) = (as in TDMA) and perfect unfairness for F J (w) = /N. We have normalized the window size with respect to the number of stations and computed the Jain index for windows multiple of N., + ' ( ' (! &! " Fig : ; < = A B C D E F B G H I J K L L M N O P P Q R S T U V S -. / Measured Jain fairness index for two 82. DCF stations Figure 2 shows the Jain fairness index measured for two stations. It can be seen that the threshold value of.95 is quickly attained for the normalized window size of 5. The figure also presents the fairness of Slotted Aloha, a multiple access randomized protocol with good fairness properties that was used by Koksal et al. as a fairness gauge [3] 82. presents even better short-term fairness. Such a good behavior comes from the fact that 82. stations use their residual contention intervals when a station chooses a long interval, it will wait during one or several turns, but then it will eventually succeed, because its backoff gets smaller at each turn. Note also that 82. presents much better short-term fairness than the Ethernet CSMA/CD known for its capture effect [7]. Fact 6: For a small number of stations, 82. benefits from good short-term fairness. B. Short-term fairness for a larger number of stations For a larger number of stations, the fairness index gets worse, because of the exponential backoff after a collision,

4 Jain fairness index Fig hosts 4 hosts.2 3 hosts 2 hosts Normalized window size Measured Jain fairness index of 82. for several stations the stations that collided have more probability of choosing long backoffs, which gives other stations an increased transmission opportunity. Figure 3 shows the measured normalized Jain fairness index for several stations. To improve fairness and maximize throughput, we have proposed the Idle Sense access method [8]. In Idle Sense, contending stations make their contention windows dynamically converge in a fully distributed way to similar values solely by tracking the number of idle slots between consecutive transmissions. Each station measures n i, the number of consecutive idle slots between two transmission attempts. Every maxtrans transmissions, it estimates ˆn i, the average of the observed values of n i. Then, it uses ˆn i to adjust its contention window to the target value n target i computed numerically for a given variant of IEEE 82. PHY and MAC parameters its value is 5.68 for IEEE 82.b and 3.9 for IEEE 82.g [8]. When stations adjust their CW so that n i converges to n target i, their throughput is optimal. Stations make n i converge to n target i by applying AIMD (Additive Increase Multiplicative Decrease) [9] to contention window CW []. Figure 5 compares the measured Jain index of DCF and Idle Sense for five contending stations []. We can see that Idle Sense reaches the threshold value of.95 for a much smaller window size than the 82. DCF. Normalized Jain index DCF.5 CW = 5 CW = CW = Normalized window size Jain Index IdleSense Firmware.6 DCF Firmware Threshold Normalized window size Fig. 4. Jain fairness index of 82. DCF with equal contention windows CW, five stations, simulation. To evaluate the effect of the exponential backoff, Figure 4 compares the Jain fairness index for the 82. DCF with the case in which CW is kept equal for all stations. We can observe that equal CW results in significant improvement of short-term fairness. Fact 7: The short-term fairness of 82. becomes worse for an increasing number of stations due to the exponential backoff. C. Towards an optimal short-term fair access method The previous example suggests that an access method needs to use the equal values of the contention window for all contending stations. For given traffic conditions (number of contending stations and their frame sizes), there is an optimal value of CW for which the stations benefit from short-term fairness and high throughput: if CW is too small, collisions are more frequent and if CW is too large, stations spend too much time waiting for transmission. Thus, an optimal access method should adapt the value of CW to the current traffic conditions. Fig. 5. Measured Jain index for 82. DCF and Idle Sense firmware, five contending stations. Fact 8: To improve short-term fairness, an optimal DCF-like access method needs to use the equal sizes of contention windows for all contending stations. D. Long-term fairness When observed on a large time scale, the probability of channel access under 82. is equal for all stations, because most of the time they choose their random backoff from the same contention interval and when occasionally stations use larger backoffs after collisions, all stations have the same probability of colliding and deferring access attempts. If stations use the same data frame size, the equal channel access probability results in the equal throughput shares. Usually, such fairness is a desired property, however it is also the source of an important performance problem related to TCP. In a 82. cell, an access point acts as a bridge for wireless stations: either it forwards frames between stations or interconnects the wired and the wireless parts of the network by forwarding data flows in two directions (upload or download) on behalf of wireless stations. As most of the

6 limiting rate Fig EF size 64 bytes EF size 28 bytes EF size 256 bytes EF size 52 bytes AF packet size Limiting packet rate for two stations and different packet sizes. its traffic below this limit, even if AF stations try to gain as much throughput as possible, the EF station will experience short delays [4]. Figure 8 presents the limiting rate for two stations in function of different packet sizes. RTT EF [ms] AF size 64 AF size 28 AF size 256 AF size 52 AF size 768 AF size 24 AF size kbit/s, 64 byte packets Offered Load [kbit/s] Fig. 9. Measured RTT of the EF class for increasing offered load, constant 28 Kb/s EF traffic. Figure 9 presents the measured RTT of the EF class transmitting at 28 Kb/s (64 byte packets, 25 packet/s) when competing with the AF class. We can see that when the EF packet rate is under the limiting packet rate, the RTT of the EF class remains small (under 6 ms) even if the cell is already saturated (offered load increased to Mbit/s). As the limiting rate is 383 p/s for 472 byte AF packets and more for shorter packets, the EF class of 25 p/s packet rate always benefits from short delays. Fact : For a small number of stations, a station contending with greedy ones can benefit from short delays provided its traffic stays under a limiting rate. V. CONCLUSION The 82. DCF is a simple random access method with an important protocol overhead that works fairly well for a small number of contending stations. In this case, it benefits from good short-term fairness and short delays mainly because of remaining backoff times used in channel contention. For an increasing number of stations, DCF suffers from much worse short-term unfairness, which results in longer delays. This effect comes from the exponential backoff that is not the best way of adapting contention to the number of stations. DCF allocates the channel in a fair manner, which is a suitable property for stations in the ad hoc mode, but it leads to the TCP unfairness problem in the infrastructure mode, because the access point suffers from insufficient share of channel capacity. ACKNOWLEDGMENTS Most of the results reported in this paper come from common work with my colleagues: Franck Rousseau, Martin Heusse, Paul Starzetz, Elena Lopez-Aguilera, Yan Grunenberger, Gilles Berger- Sabbatel, Romaric Guillier, and Olivier Gaudoin. This work was partially supported by the European Commission project WIP under contract 2742 and the French Ministry of Research project AIRNET under contract ANR-5-RNRT-2-. REFERENCES [] IEEE, IEEE 82.: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, 999. [2] M. Heusse, F. Rousseau, G. Berger-Sabbatel, and A. Duda, Performance Anomaly of 82.b, in Proc. of INFOCOM, 23. [3] C. Koksal, H. Kassab, and H. Balakrishnan, An Analysis of Short- Term Fairness in Wireless Media Access Protocols, in Proc. of ACM SIGMETRICS, 2. [4] C. L. Barrett, M. V. Marathe, D. C. Engelhart, and A. Sivasubramaniam, Analyzing the Short-Term Fairness of IEEE 82. in Wireless Multi- Hop Radio Networks, in Proc. th IEEE MASCOTS 2, October 22. [5] Y. Kwon, Y. Fang, and H. Latchman, A Novel MAC Protocol with Fast Collision Resolution for Wireless LANs, in Proc. of INFOCOM, 23. [6] G. Berger-Sabbatel, A. Duda, O. Gaudoin, M. Heusse, and F. Rousseau, Fairness and its Impact on Delay in 82. Networks, in Proc. of GLOBECOM 24, 24. [7] K. Ramakrishnan and H. Yang, The Ethernet Capture Effect: Analysis and Solution, in IEEE 9th Conference on Local Computer Networks, 994. [8] M. Heusse, F. Rousseau, R. Guillier, and A. Duda, Idle Sense: An Optimal Access Method for High Throughput and Fairness in Rate Diverse Wireless LANs, in Proc. of ACM SIGCOMM 25, vol. 35, no. 4, August 25, pp [9] D. Chiu and R. Jain, Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks, Journal of Computer Networks and ISDN, vol. 7, no., June 989. [] Y. Grunenberger, M. Heusse, F. Rousseau, and A. Duda, Experience with an Implementation of the Idle Sense Wireless Access Method, in Proc. of ACM CoNEXT 27, 27. [] S. Pilosof, R. Ramjee, D. Raz, Y. Shavitt, and P. Sinha, Understanding TCP Fairness over Wireless LAN, in Proc. of IEEE INFOCOM 23, vol. 2, March-April 23, pp [2] E. Lopez-Aguilera, M. Heusse, Y. Grunenberger, F. Rousseau, A. Duda, and J. Casademont, An Asymmetric Access Point for Solving the Unfairness Problem in WLANs, IEEE Transactions on Mobile Computing, 28. [3] M. Heusse, P. Starzetz, F. Rousseau, G. Berger-Sabbatel, and A. Duda, Bandwidth Allocation for DiffServ Based Quality of Service over 82.b, in Proc. of GLOBECOM 23, vol. 2, December 23, pp [4], Scheduling Time-Sensitive Traffic on 82. Wireless LANs, in Proc. of QoFIS 23, LNCS 2856, Stockholm, Sweden, 23.

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