Performance analysis of a GI/M/1 queue with single working vacation
A GI/M/1 queue with a single working vacation is considered. This queue in which during the vacation period the server works at a lower rate rather than stopping completely, can be used in production management with multiple working vacations during the repair of the machines, etc. The model formulation of the GI/M/1 queue was based on an embedded Markov chain. The steady-state queue length distributions at arrival and arbitrary epochs for this model were obtained by means of the Neuts' matrix-geometric approach. Some technical foundations, such as the closeness property of the conditional probability of \(\Gamma\)-distributions, and results for the waiting time of arbitrary customers are obtained. The effect of the critical model parameters on the performance measures in the D/M/1 and \(E_{2}/M/1\) with single working vacation queues were studied by means of solving numerical examples. It was demonstrated that the working vacation policy can decrease the number of the waiting customers in these systems and enhance the system efficiency. To summarize, the obtained results will be very useful for the modelling of computer networks, communication systems and production management.
scientific article; zbMATH DE number 5853791
scientific article