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An upper bound on the performance of queues with returning customers

Published online by Cambridge University Press:  14 July 2016

Betsy S. Greenberg  and
Ronald W. Wolff
Betsy S. Greenberg*
Affiliation:
University of Texas, Austin
Ronald W. Wolff*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of General Business, University of Texas at Austin, Austin, TX 78712, USA.
∗∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
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Abstract

Multiple channel queues with Poisson arrivals, exponential service distributions, and finite capacity are studied. A customer who finds the system at capacity either leaves the system for ever or may return to try again after an exponentially distributed time. Steady state probabilities are approximated by assuming that the returning customers see time averages. The approximation is shown to result in an upper bound on system performance.

Keywords

APPROXIMATIONSRETRIALSLOSS SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 466 - 475
Copyright
Copyright © Applied Probability Trust 1987 

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References

Aleksandrov, A. M. (1974) A queueing system with repeated orders. Engineering Cybernet. 123, 1–3.Google Scholar
Cohen, J. W. (1957) Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommun. Rev. 18, 49–100.Google Scholar
Fredericks, A. A. and Reisner, G. A. (1979) Approximations to stochastic service systems, with an application to a retrial model. Bell System Tech. J. 58, 557–576.CrossRefGoogle Scholar
Greenberg, B. S. (1986) Queueing Systems with Returning Customers and the Order of Tandem Queues. , University of California, Berkeley.Google Scholar
Keilson, J., Cozzolino, J. and Young, H. (1968) A service system with unfilled requests repeated. Operat. Res. 16, 1126–1137.Google Scholar
Le Gall, P. (1969) Sur une théorie des répétitions des appels téléphoniques. Ann. Télécommun. 24, 261–281.CrossRefGoogle Scholar
Le Gall, P. (1976) Trafics généraux de télécommunications sans attente. Commut. Electron. 55, 5–24.Google Scholar
Lubacz, J. and Roberts, J. (1985) A new approach to the single server repeat attempt system with balking. Proc. 3rd Internat. Sem. Teletraffic Theory, 290–293.Google Scholar
Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.Google Scholar