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Teaching M/G/1 theory with extension to priority queues

Peter G. Harrison

Journal Article
IEE Proceedings - Computers and Digital Techniques
Volume 147
Issue 1
January, 2000
DOI 10.1049/ip-cdt:20000154

The derivation of sojourn time distribution is easily understood in M/M/1 queues in terms of numbers of service completions, using the random observer property. The same approach does not generalise directly to the M/G/1 queue because of a subtle dependence between the random variables involved, and an entirely different approach is usually taught in most courses on queueing theory. The M/M/1 approach to the M/G/1 case is applied by accounting for the dependence explicitly. The method then extends simply to M/G/1 queues with priority classes. Although the results themselves are not new, it is believed that the approach used is illuminating, constructive to consistent teaching of the subject and facilitates a concise treatment of priority queues.

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