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Steady state solution of a single-server queue with linear repeated requests

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

J. R. Artalejo  and
A. Gomez-Corral
J. R. Artalejo*
Affiliation:
Universidad Complutense de Madrid
A. Gomez-Corral*
Affiliation:
Universidad Complutense de Madrid
*
∗Postal address: Departamento de Estadistica e I.O., Facultad de Matematicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
∗Postal address: Departamento de Estadistica e I.O., Facultad de Matematicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
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Abstract

Queueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.

Keywords

QUEUES WITH REPEATED REQUESTSHYPERGEOMETRIC FUNCTIONS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 223 - 233
Copyright
Copyright © Applied Probability Trust 1997 

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References

Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Artalejo, J. R. (1993) Explicit formulae for the characteristics of the M/H2/1 retrial queue. J. Operat. Res. Soc. 44, 309–313.Google Scholar
Artalejo, J. R. and Falin, G. I. (1994) Stochastic decomposition for retrial queues. Top 2, 329–342.Google Scholar
Bailey, W. N. (1972) Generalized Hypergeometric Series. Hafner, New York.Google Scholar
Cooper, R. B. (1981) Introduction to Queueing Theory. Elsevier, Amsterdam.Google Scholar
Falin, G. I. (1980) An M/M/1 queue with repeated calls in the presence of persistence function. Paper #1606-80. All-Union Institute for Scientific and Technical Information, Moscow.Google Scholar
Falin, G. I. (1984) Double-channel queueing system with repeated calls. Paper #4221-84. All-Union Institute for Scientific and Technical Information, Moscow.Google Scholar
Falin, G. I. (1990) A survey of retrial queues. QUESTA 7, 127–168.Google Scholar
Farahmand, K. (1990) Single line queue with repeated demands. QUESTA 6, 223–228.Google Scholar
Fayolle, G. (1986) A simple telephone exchange with delayed feedbacks. In Teletraffic Analysis and Computer Performance Evaluation. ed. Boxma, O.J., Cohen, J. W. and Tijms, H. C. Elsevier, Amsterdam.Google Scholar
Fuhrmann, S. W. and Cooper, R. B. (1985) Stochastic decomposition in the M/G/1 queue with generalized vacations. Operat. Res. 33, 1117–1129.Google Scholar
Hanschke, T. (1987) Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts. J. Appl. Prob. 24, 486–494.Google Scholar
Jonin, G. L. and Sedol, J. J. (1970) Telephone systems with repeated calls. Proc. 6th Int. Teletraffic Congress 435/1–435/5.Google Scholar
Martin, M. and Artalejo, J. R. (1995) Analysis of an M/G/1 queue with two types of impatient units. Adv. Appl. Prob. 27, 840–861.CrossRefGoogle Scholar
Pearce, C. (1989) Extended continued fractions, recurrence relations and two-dimensional Markov processes. Adv. Appl. Prob. 21, 357–375.CrossRefGoogle Scholar
Sennott, L. I., Humblet, P. A. and Tweedie, R. L. (1983) Mean drifts and the non-ergodicity of Markov chains. Operat. Res. 31, 783–789.CrossRefGoogle Scholar
Yang, T. and Templeton, J. G. C. (1987) A survey on retrial queues. QUESTA 2, 201–233.Google Scholar