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Single-Server Queues with Impatient Customers

F. Baccelli, P. Boyer and G. Hebuterne
Advances in Applied Probability
Vol. 16, No. 4 (Dec., 1984), pp. 887-905
DOI: 10.2307/1427345
Stable URL: http://www.jstor.org/stable/1427345
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Single-Server Queues with Impatient Customers
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Abstract

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

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