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A single-server queue with batch arrivals and semi-Markov services

We investigate the transient and stationary queue length distributions of a class of service systems with correlated service times. The classical \(M^X/G/1\) queue with semi-Markov service times is the most prominent example in this class and serves as a vehicle to display our results. The sequence of service times is governed by a modulating process J(t). The state of \(J(\cdot...

Queue-length balance equations in multiclass multiserver queues and their generalizations

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: The distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. The constraint for this result to be valid is that arrivals, and also service completions, with probability one occur...

A Two-Queue Polling Model with Two Priority Levels in the First Queue

Marko A. A. Boon Ivo J. B. F. Adan Onno J. Boxma In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is ... License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. Marko A. A. Boon received his M.Sc. degree in Industrial