Stochastic Processing Networks
R. J. Williams
Abstract
Stochastic processing networks arise as models in manufacturing,
telecommunications, transportation, computer systems, the customer service industry and biochemical reaction
networks. Common
characteristics of these networks are that they have entities, such
as
jobs, packets, vehicles, customers or molecules, that move along routes, wait in buffers,
receive processing from various resources, and are subject to the
effects of stochastic variability through such quantities as arrival
times, processing times and routing protocols.
Understanding, analyzing and controlling congestion in stochastic processing networks
is the aim of the mathematical theory of queueing.
In this article, we begin by summarizing some of the highlights in the development of the theory of queueing
prior to 1990; this includes some exact analysis and development of
approximate models for certain queueing networks.
We then describe some surprises of the early 1990s and ensuing developments of the last 25
years related to the use of
approximate models for analyzing the stability and performance of multi-class queueing
networks. We conclude with a description of recent developments for more general stochastic processing networks, and point to some open problems.
Published in the Annual Review of Statistics and Its Application,
Vol. 3: 323-345 (Volume publication date June 2016).
DOI: 10.1146/annurev-statistics-010814-020141
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