Sample-Path Analysis of Queues

Abstract

In this paper we provide a survey of sample-path methods in queueing theory, particularly in connection with “distribution-free” analysis such as (i) relations between customer averages and time averages, such as L = λW (Little’s formula); (ii) relations between the stationary distribution of a process and an imbedded process; and (iii) the phenomenon of insensitivity. We compare these results to those obtained in the computer-science literature by operational analysis, in which behavior of processes over finite time intervals is emphasized. We study probabilistic assumptions under which relations between ensemble averages can be inferred from such finite-time behavior. (Without some probabilistic assumptions, operational analysis is limited to describing past behavior, rather than predicting future behavior.) The theory of random (marked) point processes provides a natural set of weak probabilistic assumptions. We discuss the relationship between the sample-path approach and the point-process approach. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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