Queueing analysis of network multiplexers: Loss ratio and end-to-end delay distribution.

摘要

The queue-length distribution, the loss ratio, and the delay probability are QoS (Quality of Service) metrics commonly used for network engineering. While the queue-length distribution in infinite buffer systems has been extensively studied, there has been relatively little work on the loss ratio and the delay probability. Although the queue-length distribution is quite different from these quantities, it has often been used to represent the others without justification.; We first study the relationship between the loss ratio (P _L(x)) in a finite buffer system with buffer size x, and the tail of the queue-length distribution ($P${lcub}Q > x{rcub}) in the corresponding infinite buffer system, when the capacity is constant. We provide asymptotic upper and lower bounds on the difference between log $P${lcub}Q > x{rcub} and log P_L( x) under some conditions. Based on these results, we propose an approximation for the loss ratio by a simple mapping from the queue-length distribution. We validate our approximation for a variety of well established traffic models and trace-driven simulations.; We next study the relationship between the queue-length distribution and the delay probability when the capacity is non-constant. We then model an end-to-end path as a single queue with a time-varying capacity, called the end-to-end capacity. We show that the single queue model is equivalent to the original end-to-end path in terms of the queue-length behavior, and propose an approximation for the end-to-end delay probability by a mapping from the end-to-end queue-length distribution. Our approach is the first attempt to estimate the end-to-end delay distribution itself. This approximation is also validated by numerical experiments.