The Effects of Fairness in Buffer Sizing

Buffer sizing in Internet routers is a fundamental problem that has major consequences in the design, implementation, and economy of the routers, as well as on the performance observed by the end users. Recently, there have been some seemingly contradictory results on buffer sizing. On the one hand, Appenzeller et al. show that as a direct consequence of desynchronization of flows in the core of the Internet, buffer sizes in core routers can be significantly reduced without any major degradation in network performance. On the other hand, Raina and Wischik show that such reduction in buffer sizing comes at the cost of synchronization and thus instability in the network. This work unifies these results by studying the effects of fairness in buffer sizing. We show that the main difference arises from the implicit assumption of fairness in packet dropping in the latter result. We demonstrate that desynchronization among flows observed by Appenzeller et al. is caused by unfair packet dropping when a combination of TCP-Reno and the drop-tail queue management is used. We also show that bringing fairness in packet dropping will introduce synchronization among flows, and will make the system unstable as predicted by Raina and Wischik. Our analysis suggests that there is an intrinsic trade-off between fairness in packet drops and desynchronization among TCP-Reno flows when routers use the drop-tail queue management. Achieving fairness, desynchronization, small buffer size, and 100% link utilization at the same time is desirable and feasible yet challenging. The studies in this paper provide insights for further explorations in reaching this goal. 1 Motivation and Introduction There have been increasing amount of interests on buffer sizing due to the important role that buffer plays in routers and the performance of the Internet. The goal of buffer sizing is to find out how small we can make Internet router buffers without any degradation in network performance. A plethora of recent work emerged to reduce buffer sizes [1–5] and to understand the relationships between buffer sizing and other parameters of the network [8–14], such as, throughput, delay, loss, stability [6, 7], and the impacts of various traffic conditions [8, 15]. Recently, there have been some seemingly contradictory results on buffer sizing in Internet core routers. Appenzeller et al. show that buffer sizes in core routers can be reduced significantly, without any major degradation in network performance [1], whereas, Raina and Wischik show that such reduction in buffer sizing can cause instabilities in the network [7]. Instability, here, is defined as the periodic variations in the aggregate congestion window size of the flows. Which result is correct? To answer this question, we studied the dynamics of the system in terms of buffer sizing through mean-field theory [16, 22] analysis and ns2 [17] simulations. We demonstrated that there is an intrinsic trade-off between fairness among TCP-Reno flows and desynchronization among them using the drop-tail queue management scheme: fairness in packet drops can create synchronization among flows; conversely, unfair packet drops can lead to reduced synchronization. Fairness has always been considered to be a desirable property in the network. The network is expected to treat individual flows in a fair manner when resources are limited. Synchronization among TCP flows, on the other hand, has always been considered to be an undesirable effect. Synchronized flows need much larger buffer sizes in core routers and cause local/global instabilities in the system, as well as degradation in the performance observed by individual flows. To see the origins of the trade-off between fairness and desynchronization, let us consider a congested link in a network carrying a large number of flows. An Active Queue Management (AQM) scheme that fairly drops packets at times of congestion will impact a large percentage of flows since it will distribute packets dropped among the flows. On the other hand, an unfair AQM scheme can drop a lot of packets from a few flows, thus reducing the number of flows which see one or more packet drops. TCP-Reno flows react dramatically to packet drops by halving their congestion window sizes for each dropped packet [18]. Therefore, when a large number of flows see packet drops around the same time they will synchronously react by reducing their congestion window sizes. This may lead to a significant reduction in instantaneous throughput of the system. In an unfair AQM scheme, however, only a few flows will take the hit, and thus only a small fraction of flows will react to packet drops. Therefore, the aggregate congestion window will change less significantly. Our results unify the seemingly contradictory conclusions mentioned above. Appenzeller et al. have shown that due to the desynchronization of flows in the core of the Internet, one can reduce buffer sizes in core routers by a factor of √ N from the original value of bandwidth-delay product [1]. Here N is the total number of flows going through the core router. Our analysis shows that this desynchronization is a direct result of the unfair nature of packet drops in TCPReno combined with the drop-tail queue management scheme (Section 2.1). Also, in Section 2.2 we show that introducing fairness in packet dropping using the drop-tail scheme creates global synchronization. This is consistent with Raina and Wischik’s results. Our study shows that the results from both groups are correct, and the main difference can be well explained by understanding the effects of fairness in buffer sizing. Fairness also explains the recent observation by Dhamdhere et al. that the majority of flows have dropped packets in a congestion cycle [8]. The same results are obtained in our work when there is fair packet dropping among flows. We demonstrate this through both the mean-field analysis[22] and ns2 simulations (Section 2). Achieving fairness, desynchronization, small buffer size, and 100% link utilization at the same time is desirable yet very challenging. The studies on the dynamics in this paper show insights and feasibility for further explorations in reaching this goal. 2 Fairness-Desynchronization Trade-off In this section we study the relationship between synchronization and fairness in a network using TCP-Reno as the congestion control mechanism. We show that, when the congested routers use the drop-tail queue management scheme, there is an inherent trade-off between fairness in packet dropping and desynchronization amongst TCP-Reno flows. We investigate this trade-off through two different scenarios. First, we consider a scenario using the standard droptail queue management scheme in which TCP-Reno flows are desynchronized, and show that desynchronization comes at the cost of losing fairness in dropping packets. Second, we show that a slightly modified drop-tail queue management scheme in intermediate routers which is fair in dropping packets can lead to synchronization among TCP-Reno flows.