An Explicit Solution for a Series and Parallel Queue with Retrial, Losses, and Bernoulli Schedule

Abstract

This paper deals with the series and parallel queueing system in which there are two servers whose service time follow two exponential distributions. Each arriving customer either enters into the tandem service with probability or joins the service of the single server with complementary probability. We assume that the customers of arriving at the first server who find the first server is busy join an orbit and retry to enter the server after some time and of arriving at the second server who find the second server is busy are lost. For this model, we obtain the explicit expressions of the joint stationary distribution between the number of customers in the orbit and the states of the servers.