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General customer impatience in the queue GI/G/1

Published online by Cambridge University Press:  14 July 2016

D. J. Daley
D. J. Daley*
Affiliation:
University of Cambridge
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Abstract

For the queueing system GI/G/1 with both waiting-line and service-line customer impatience an integral equation for the limiting waiting-time distribution function W(x) is derived and the existence of W(x) proved when the system satisfies certain conditions. Two counter examples are constructed showing that W(x) does not necessarily exist. A sufficient condition for its existence in GI/G/1 with deterministic waiting-line impatience is given. Formal solutions for M/G/l are derived for deterministic impatience and negative exponential impatience.

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 1 , June 1965 , pp. 186 - 205
Copyright
Copyright © Sheffield: Applied Probability Trust 

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