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Single-Server with Delay-Dependent Arrival Streams

Published online by Cambridge University Press:  27 July 2009

P. H. Brill
P. H. Brill
Affiliation:
University of Windor, Windsor, Ontario, Canada N9B 3P4
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Abstract

This paper derives the steady-state distribution of the virtual wait in GI/M1 queues in which the interarrival times depend on the virtual wait. Applications are queues in which the time it will take for the system to start servicing a new arrival (virtual wait) affects the generation of new arrivals. Such queues arise in airport or large-city freeway traffic control systems. Related state-dependent situations occur in production-inventory systems, cash flow in banking or in insurance systems, dam control systems, and in natural sciences. The method of analysis is by means of system-point level crossing theory.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 2 , April 1988 , pp. 231 - 247
Copyright
Copyright © Cambridge University Press 1988

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