Chitkara University Publications

A Single Server Retrial Queue with Impatient Customers


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.


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



Retrial, arrivals, departures, impatient


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

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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.



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