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A single-server queue with server vacations and a class of non-renewal arrival processes. (English) Zbl 0709.60094
A single-server queueing system with multiple vacations is considered. Service times and vacation times have general distributions. The input process is a general Markovian arrival process. Such a process is defined, with the help of some additional Markov process with finite state space. It is assumed that after each jump of this process with some probability a new customer arrives in the system.
The authors investigate the waiting time process and queue length process at arbitrary time as well as corresponding embedded processes. With the help of matrix factorizations, formulas for stationary distributions of the above processes are obtained.
Reviewer: G.Falin

MSC:
60K15 Markov renewal processes, semi-Markov processes
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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