A Single Server Retrial Queue with Impatient Customers

P. C. Garg; Sanjeev Kumar

doi:10.15415/mjis.2012.11006

A Single Server Retrial Queue with Impatient Customers

Authors

P. C. Garg Department of Statistics, Punjabi University, Patiala-147002
Sanjeev Kumar Department of Statistics, Punjabi University, Patiala-147002

DOI:

https://doi.org/10.15415/mjis.2012.11006

Keywords:

Retrial, arrivals, departures, impatient

Abstract

In the present paper, a single server retrial queue with impatient customers is studied. The primary arrivals and repeating calls follow the Poisson distribution. The service time is exponentially distributed. Explicit time-dependent probabilities of an exact number of arrivals and departures from the orbit are obtained by solving the differential-difference equations recursively. Steady state solution of the number of busy servers is obtained. The numerical results are graphically displayed to illustrate the effect of arrival rate, retrial rate and service rate on different probabilities against time. Some special cases of interest are also deduced.

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References

Bateman, H. (1954). Tables of integral transforms, Vol.1, Mcgraw-Hill Book Company, New York.

Bunday, B.D. (1986). Basic Queueing Theory, Edward Arnold (Publishers) Ltd., London.

Falin, G.I. and Templeton, J.G.C. (1997). Retrial queues, Chapman and Hall, London. http://dx.doi.org/10.1007/978-1-4899-2977-8

Garg, P. C., Srivastava, S.K. & Bansal, S.K. (2009). Explicit time-dependent solution of a two-state retrial queueing system, Pure and Applied Mathematika Sciences, LXIX (1-2), 33–50.

Pegden, C. D. & Rosenshine, M. (1982). Some new results for the M/M/1 queues, Management Science, 28(7), 821–828. http://dx.doi.org/10.1287/mnsc.28.7.821

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Published

2012-07-02

How to Cite

P. C. Garg, and Sanjeev Kumar. 2012. “A Single Server Retrial Queue With Impatient Customers”. Mathematical Journal of Interdisciplinary Sciences 1 (1):67-82. https://doi.org/10.15415/mjis.2012.11006.

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Issue

Vol. 1 No. 1 (2012)

Section

Articles

License

Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.

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