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Analysis of a two-class priority queue with Bernoulli schedules. (English) Zbl 0771.60079

Summary: A Bernoulli schedule is random service discipline for a multi-class priority queueing system which operates as follows: If queue \(i\) \((1\leq i\leq N)\) is not empty just after servicing a message in its queue, a message in queue \(i\) is served again with probability \(p_ i\), and the highest class message present in the system is served with probability \(1-p_ i\), where \(0\leq p_ i\leq 1\). This paper presents an analysis of a two-class priority queue \((M/G/1\) type queue) with Bernoulli schedules of parameter \((p_ 1=1,\;0\leq p_ 2\leq 1)\) and class-dependent set-up times. The generating functions of joint queue-length distributions and the Laplace-Stieltjes transforms of waiting time distributions are determined. A closed-form expression with infinite summations is obtained for the mean waiting times.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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