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On queueing systems by retrials

Published online by Cambridge University Press:  14 July 2016

Vidyadhar G. Kulkarni
Vidyadhar G. Kulkarni*
Affiliation:
The University of North Carolina at Chapel Hill
*
∗ Postal address: Curriculum in Operations Research and Systems Analysis, The University of North Carolina at Chapel Hill, Smith Building 128A, Chapel Hill, NC 27514, U.S.A.
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Abstract

A general result for queueing systems with retrials is presented. This result relates the expected total number of retrials conducted by an arbitrary customer to the expected total number of retrials that take place during an arbitrary service time. This result is used in the analysis of a special system where two types of customer arrive in an independent Poisson fashion at a single-server service station with no waiting room. The service times of the two types of customer have independent general distributions with finite second moments. When the incoming customer finds the server busy he immediately leaves and tries his luck again after an exponential amount of time. The retrial rates are different for different types of customers. Expressions are derived for the expected number of retrial customers of each type.

Keywords

QUEUEING SYSTEMSRETRIALSREPEATED ORDER SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 380 - 389
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Aleksandrov, A. M. (1974) A queueing system with repeated orders. Engineering Cybernetics Rev. 12 (3), 1–4.Google Scholar
[2] Choo, Q. H. and Conolly, B. W. (1979) New results in the theory of repeated orders queueing systems. J. Appl. Prob. 16, 631–640.CrossRefGoogle Scholar
[3] Cohen, J. W. (1957) Basic problems of telephone traffic theory and the influence of repeated calls. Phillips Telecommun. Rev. 18 (2), 49–104.Google Scholar
[4] Falin, G. I. (1979) A single-line system with secondary orders. Engineering Cybernetics Rev. 17 (2), 76–83.Google Scholar
[5] Kulkarni, V. G. (1982) Letter to the editor. J. Appl. Prob. 19, 901–904.CrossRefGoogle Scholar
[6] Stidham, S. (1972) L = ?W: A discounted analogue and a new proof. Operat. Res. 20, 1115–1126.Google Scholar
[7] Stidham, S. (1974) A last word on L = ?W . Operat. Res. 22, 417–421.CrossRefGoogle Scholar