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Stability of finite queue, tandem server systems

Published online by Cambridge University Press:  14 July 2016

David K. Hildebrand
David K. Hildebrand*
Affiliation:
University of Pennsylvania
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Extract

One of the troublesome problems in the extension of queueing theory to more complex systems of servers is the development of models suitable for the analysis of assembly lines and similar structures. Results in special cases are given in [2], [5], and [6]. A reasonable model would assume:

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 3 , November 1967 , pp. 571 - 583
Copyright
Copyright © Applied Probability Trust 

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References

[1] Hildebrand, D. K. (1966) On tandem server, finite queue, service systems. Ph.D. dissertation, Carnegie Institute of Technology, Pittsburgh, Pa. (unpublished).Google Scholar
[2] Hunt, G. C. (1956) Sequential arrays of waiting lines. Operat. Res. 4, 674–683.Google Scholar
[3] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
[4] Loève, M. (1963) Probability Theory. D. Van Nostrand, Princeton, N. J. Google Scholar
[5] Avi-Itzhak, B. and Yadin, M. (1965) A sequence of two servers with no intermediate queue. Management Sci. 11, 553–564.Google Scholar
[6] Avi-Itzhak, B. (1965) Sequence of service stations with arbitrary input and regular service times. Management Sci. 11, 565–571.Google Scholar
[7] Loynes, R. M. (1962) The stability of a queue with non-dependent interarrival and service times. Proc. Camb. Phil. Soc. 58, 497–520.Google Scholar