A two-queue model with Bernoulli service schedule and switching times

In this paper, we present a detailed analysis of a cyclic-service queueing system consisting of two parallel queues, and a single server. The server s erves the two queues with a Bernoulli service schedule described as follows . At the beginning of each visit to a queue, the server always serves a cus tomer. At each epoch of service completion in the ith queue at which the qu eue is not empty, the server makes a random decision: with probability p(i) , it serves the next customer; with probability 1 - p(i), it switches to th e other queue. The server takes switching times in its transition from one queue to the other. We derive the generating functions of the joint station ary queue-length distribution at service completion instants, by using the approach of the boundary value problem for complex variables. We also deter mine the Laplace-Stieltjes transforms of waiting time distributions for bot h queues, and obtain their mean waiting times.