Katayama, Tsuyoshi; Takahashi, Yoshitaka Analysis of a two-class priority queue with Bernoulli schedules. (English) Zbl 0771.60079 J. Oper. Res. Soc. Japan 35, No. 3, 236-249 (1992). 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. Cited in 2 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:Bernoulli schedule; multi-class priority queueing system; generating functions; mean waiting times × Cite Format Result Cite Review PDF Full Text: DOI