Queueing theory

• Authors: Robert B. Cooper
• Venue: ACM '81 Proceedings of the ACM '81 conference
• Year: 1981

Queueing theory has become an important subject to computer scientists because it forms the mathematical basis for research in computer system performance evaluation. (See, for example, the Special Issue, September 1978, of Computer Surveys on “Queueing Network Models of Computer System Performance,” and the recent conference on “Applied Probability - Computer Science: The Interface,” which was held in Boca Raton, Florida, in January 1981.) This tutorial will attempt to explain the elements of queueing theory so that the audience will understand (1) the kind of assumptions usually made in the construction of queueing models, (2) the kind of mathematical tools ordinarily used in queueing theory, and (3) the strengths and limitations of queueing theory in the design and analysis of computer systems. In particular, we will cover (1a) the properties of the Poisson process and the reasons for its use to describe the arrival process, (1b) the properties of the exponential distribution and the reasons for its use to describe service times, and (1c) the degree to which the solutions of queueing models are sensitive to these assumptions; (2a) the notation of standard queueing models, such as M/M/s and M/G/l, (2b) how to write and solve the birth-and-death equations that describe many queueing models, such as queueing networks, (2c) the reason for the introduction of such analytical tools as generating functions and Laplace-Stieltjes transforms, and (2d) the use of numerical analysis and simulation; (3a) examples of the successful application of queueing theory, such as telecommunications engineering and CPU scheduling algorithms and (3b) problems that are too hard for mathematical analysis.