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Multi-server assembly queues

Published online by Cambridge University Press:  14 July 2016

Michael A. Crane
Michael A. Crane*
Affiliation:
Control Analysis Corporation, Palo Alto, California
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Abstract

A model is studied in which each of several servers assembles finished products consisting of N different input items. Items of each type arrive independently at the assembly station and are grouped into N-tuples consisting of one item of each type. N-tuples are assembled into finished products by the servers on a first come-first-served basis. The model is analyzed by means of the theory of weak convergence, and functional limit theorems are obtained for appropriately normalized random functions induced by the queue size processes. The limits are expressed as functionals of multi-dimensional Wiener processes, with ordinary central limit theorems obtained as corollaries.

Keywords

ASSEMBLY QUEUESWEAK CONVERGENCEUNSTABLE QUEUESFUNCTIONAL CENTRAL LIMIT THEOREMSNORMAL APPROXIMATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 629 - 632
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Billingsley, P. (1968) Convergence of Probability Measures. John Wiley, New York.Google Scholar
[2] Crane, M. (1971) Limit theorems for queues in transportation systems. Technical Report No. 16, Department of Operations Research, Stanford University, Stanford, California, (Ph.D. Dissertation).Google Scholar
[3] Harrison, J. M. (1973) Assembly-like queues. J. Appl. Prob. 10, 354–367.Google Scholar