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On the waiting-time process in a single-line queue with repeated calls

Published online by Cambridge University Press:  14 July 2016

G. I. Falin
G. I. Falin*
Affiliation:
Moscow State University
*
∗Postal address: Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119899, USSR.
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Abstract

Waiting time in a queueing system is usually measured by a period from the epoch when a subscriber enters the system until the service starting epoch. For repeated orders queueing systems it is natural to measure the waiting time by the number of repeated attempts, R, which have to be made by a blocked primary call customer before the call enters service. We study this problem for the M/M/1/1 retrial queue and derive expressions for mean, variance and generating function of R. Limit theorems are stated for heavy- and light-traffic cases.

Keywords

NUMBER OF RETRIALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 185 - 192
Copyright
Copyright © Applied Probability Trust 1986 

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References

Choo, Q. H. and Conolly, B. W. (1979) New results in the theory of repeated orders queueing systems. J. Appl. Prob. 16, 631–640.Google Scholar
Conolly, B. W. (1982) Letter to the editor. J. Appl. Prob. 19, 904–905.Google Scholar
Falin, G. I. (1976) Aggregate arrival of customers in a one-line system with repeated calls. Ukrain. Math. J. 28, 561–565.Google Scholar
Falin, G. I. (1977) Waiting time in a single-channel queueing system with repeated calls. Vestnik Moscow Univ. Ser. 15. Comput. Math. Cybernet. 4, 83–87.Google Scholar
Falin, G. I. (1980) An M/G/1 system with repeated calls in heavy traffic. Vestnik Moscow Univ. Ser. 1 Math. Mech. 6, 48–50.Google Scholar
Keilson, J., Cozzolino, J. and Young, H. (1968) A service system with unfilled requests repeated. Operat Res. 6, 1126–1137.CrossRefGoogle Scholar
Kulkarni, V. G. (1982) Letter to the editor. J. Appl. Prob. 19, 901–904.Google Scholar