A two-queue model with Bernoulli service schedule and switching times |
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Authors: | Feng W Kowada M Adachi K |
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Institution: | (1) Department of Systems Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan |
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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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | two parallel queues Bernoulli service schedule Riemann boundary value problem analytic continuation stationary distribution generating function waiting time |
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