On the virtual waiting time for an M/G/1 retrial queue with two types of calls

Choi, Bong Dae; Han, Dong Hwan; Falin, Guennadi

doi:https://doi.org/10.1155/S1048953393000024

International Journal of Stochastic Analysis

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Volume 6 |Article ID 473409 | https://doi.org/10.1155/S1048953393000024

Bong Dae Choi, Dong Hwan Han, Guennadi Falin, "On the virtual waiting time for an M/G/1 retrial queue with two types of calls", International Journal of Stochastic Analysis, vol. 6, Article ID 473409, 13 pages, 1993. https://doi.org/10.1155/S1048953393000024

On the virtual waiting time for an M/G/1 retrial queue with two types of calls

Bong Dae Choi,¹ Dong Hwan Han,¹ and Guennadi Falin²

¹Korea Advanced Institute of Science and Technology, Department of Mathematics, Yusong.gu, Korea

²Moscow State University, Department of Probability, Mechanics and Mathematics Faculty, Russia

Received01 Apr 1992

Revised01 Jan 1993

Abstract

We consider an M/G/1 retrial queueing system with two types of calls which models a telephone switching system. In the case that arriving calls are blocked due to the channel being busy, the outgoing calls are queued in priority group whereas the incoming calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the Laplace-Stieltjes transform of the distribution of the virtual waiting time for an incoming call. When the arrival rate of outgoing calls is zero, it is shown that our result is consistent with the known result for a retrial queueing system with one type of call.

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Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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