Abstract
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 serves 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 customer. At each epoch of service completion in the ith queue at which the queue is not empty, the server makes a random decision: with probability pi, it serves the next customer; with probability 1-pi, it switches to the other queue. The server takes switching times in its transition from one queue to the other. We derive the generating functions of the joint stationary queue-length distribution at service completion instants, by using the approach of the boundary value problem for complex variables. We also determine the Laplace-Stieltjes transforms of waiting time distributions for both queues, and obtain their mean waiting times.
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Feng, W., Kowada, M. & Adachi, K. A two-queue model with Bernoulli service schedule and switching times. Queueing Systems 30, 405–434 (1998). https://doi.org/10.1023/A:1019185509235
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DOI: https://doi.org/10.1023/A:1019185509235