This paper analyzes the effectiveness of a class of adaptive algorithms for rate control in a data network with the following two elements: many sources with diverse characteristics (e.g., nonadaptive and adaptive sources with different feedback delays, different constraints on transmission rates) and a switch, based on ATM or cell-relay technology, with finite buffers. Several adaptive sources compete among themselves as well as with other nonadaptive sources for bandwidth at a single queue. We first model random fluctuations in the queue-length process due to the nonadaptive sources as Brownian motion, and we show, for a large class of adaptive strategies, how the amount of bandwidth wasted because of idleness and the amount of offered traffic lost because of overflowing buffers scale with the speed of the network. We then model the arrival process of nonadaptive traffic more realistically as a general stochastic fluid with bounded, positive rates. For a class of adaptive strategies with linear adaptation functions, we prove that the results obtained from the Brownian model of randomness extend to cover the more realistic model. This occurs because the adaptive sources induce heavy-traffic conditions (corresponding to the power-maximizing regime of Mitra (1990)) by accurately estimating and using the residual bandwidth not occupied by the nonadaptive traffic. Our analysis gives new insight about how performance measures scale with the variability of the nonadaptive traffic. We illustrate through simulations that queue fluctuations behave as predicted.>

Emerging technologies for high-speed data network provide users with explicit feedback about congestion. Users, however, have questioned whether feedback can help in avoiding congestion in wide-area networks that operate at speeds of multiple megabits- or gigabits-per-second. In this paper we analyze a class of adaptive schemes with delayed feedback, where adaptive sources interact with each other as well as with non-adaptive sources through a single queue. We model the network as a stochastic, delay-differential equation and the rate at which an adaptive source transmits data as a fluid. Our model accounts for different levels of traffic burstiness introduced by the non-adaptive sources and for distinct propagation delays for different adaptive sources. We show how the performance of the system scales with increasing network speeds for quite general fluctuations in the bandwidth available to the adaptive sources. Simulation results show the accuracy of the model's predictions as a function of key parameters. This paper should raise the expectations of users about the potential effectiveness of responding to congestion notification.

In this paper we analyze a class of delayed feedback schemes that achieves the dual goal of keeping buffers small and utilizations high, despite propagation delays and regardless of network rates. We analyze delayed feedback schemes as a system of delay-differential equations, in which we model the queue-length process and the rate at which a source transmits data as fluids. We assume that a stream of acknowledgements carries information about the state of a bottleneck queue back to the source, which adapts its transmission rate according to any monotone function of that state. We show stability for this class of schemes, in that their rate of transmission and queue length rapidly converge to a small neighborhood of the designed operating point. We identify the appropriate scaling of the model's parameters for the system to perform optimally.

The authors continue an investigation of the way diverse traffic from different data applications affects the performance of packet queues. This traffic often exhibits significant dependence among successive interarrival times, among successive service times, and between interarrival times and service times, which can cause a significant degradation of performance under heavy loads (and often even under moderate loads). This dependence and its effects on performance (specifically, the mean steady-state workload) are partially characterized here by the cumulative correlations in the total input process of work, which is referred to as the index of dispersion for work (IDW). The authors evaluate approximations for the mean steady-state workload based on the IDW by making comparisons with computer simulations.>

Measurements and approximations are proposed to describe the variability of offered traffic to a queue and predict the average workload in the queue. The principal traffic measurement considered is a normalized version of the variance of the total input of work as a function of time, which is called the index of dispersion for work (IDW). Given ample traffic data, the IDW can easily be estimated using sample averages. Given a mathematical model, such as a multiclass queue in which each class has GI/G/1 offered traffic, the IDW can often be calculated analytically, or approximated by using the limits as t approaches 0 and t approaches infinity . The basic premise is that the average workload is primarily determined by the offered traffic, beyond the offered load (the deterministic rate work arrives), through the IDW. Support is provided for this premise, and it is shown how the average workload can be predicted from the IDW or basic model parameters.>

The burstiness of the total arrival process has been previously characterized in packet network performance models by the dependence among successive interarrival times. It is shown that associated dependence among successive service times and between service times and interarrival times also can be important for packet queues involving variable packet lengths. These dependence effects are demonstrated analytically by considering a multiclass single-server queue with batch-Poisson arrival processes. For this model and more realistic models of packet queues, insight is gained from heavy-traffic limit theorems. This study indicates that all three kinds of dependence should be considered in the analysis and measurement of packet queues involving variables packet lengths. Specific measurements are proposed for real systems and simulations. This study also indicates how to predict expected packet delays under heavy loads. Finally, this study is important for understanding the limitations of procedures such as the queuing network analyzer (QNA) for approximately describing the performance of queuing networks using the techniques of aggregation and decomposition.>