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

Han Seok Kim, Purdue University

Abstract

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 ([special characters omitted]{Q > x}) in the corresponding infinite buffer system, when the capacity is constant. We provide asymptotic upper and lower bounds on the difference between log [special characters omitted]{Q > x} and log PL( 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.

Degree

Ph.D.

Advisors

Shroff, Purdue University.

Subject Area

Electrical engineering

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