Analysis of Queueing System with Non-Preemptive Time Limited Service and Impatient Customers

We consider a single-server queueing system with server vacations as the important component of the polling queueing model of a real-world system. Period of continuous operation of the server (the maximum server attendance time) is restricted, but the service of a customer cannot be interrupted when this period expires. Such features are inherent for many real-world systems with resource sharing. We assume that the customers arrival is described by the Markovian Arrival Process and service, vacation and maximum server attendance times have a phase-type distribution. We derive the stationary distributions of the system states and waiting time. Taking in mind the necessity of further application of the results to modeling the polling queueing systems, the distribution of the server visiting time is derived. Extensive numerical results are presented. They highlight that an account of the coefficient of variation of vacation and maximum attendance time is very important for exact evaluation of the key performance measures of the system, while only the results for the coefficient of variation equal to zero or one are known in the literature. Impact of the possible customers impatience, which is intuitively important because the time-limited service is considered, is confirmed by the results of the numerical experiments. Optimization problem of matching the durations of vacation and maximum attendance time is considered.