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On the virtual waiting time in an M/G/1 retrial queue

Published online by Cambridge University Press:  14 July 2016

G. Falin  and
C. Fricker
G. Falin*
Affiliation:
Moscow State University
C. Fricker*
Affiliation:
INRIA
*
∗Postal address: Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow 119899, USSR.
∗∗Postal address: INRIA, Domaine de Voluceau B.P. 105, 78153 Le Chesnay Cedex, France. e-mail address: fricker@seti.inria.fr
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Abstract

This paper deals with the stationary distribution of the virtual waiting time, i.e. the time between the arrival and the beginning of service of a customer in a single-server queue that operates as follows. If the server is busy at an arrival time, the customer is rejected. This customer attempts service again after some random delay and continues to do so until the first time at which the server is idle. At this time, the customer is served and leaves the system after service completion. Interarrival times and delays are assumed to be two independent sequences of i.i.d. exponentially distributed random variables. Service times are also i.i.d., generally distributed, and independent of the previous sequences.

Keywords

REPEATED CALLSONE-SERVER QUEUELAPLACE TRANSFORMDIFFERENTIAL EQUATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 446 - 460
Copyright
Copyright © Applied Probability Trust 1991 

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References

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