Journal of Applied Mathematics and Stochastic Analysis 
Volume 6 (1993), Issue 1, Pages 11-23
doi: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, Taejon 305- 701, Korea
2Moscow State University, Department of Probability, Mechanics and Mathematics Faculty, Moscow 119899, Russia
Received 1 April 1992; Revised 1 January 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.