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Assembly-like queues

Published online by Cambridge University Press:  14 July 2016

J. Michael Harrison
J. Michael Harrison*
Affiliation:
Stanford University
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Abstract

A queueing theoretic model of an assembly operation is introduced. The model, consisting of K ≧ 2 renewal input processes and a single server, is a multiple input generalization of the GI/G/1 queue. The server requires one input item of each type k = 1,…, K for each of his services. It is shown that the model is inherently unstable in the following sense. The associated vector waiting time process Wn cannot converge in distribution to a non-defective limit, regardless of how well balanced the input and service processes may be. Limit theorems are developed for appropriately normalized versions of Wn under the various possible load conditions. Another waiting time process, equivalent to that in a single-server queue whose input is the minimum of K renewal processes, is also identified. It is shown to converge in distribution to a particular limit under certain load conditions.

Keywords

ASSEMBLY PROCESSGI/G/1 QUEUEUNSTABLE QUEUESDONSKER'S THEOREMWAITING TIME PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 354 - 367
Copyright
Copyright © Applied Probability Trust 1973 

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References

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