Study of customers' impatience in a GI/M/1/N queue with working vacations

This paper presents a renewal input finite buffer queueing system with balking, reneging and multiple working vacations. Arriving customers decide either to enter the system or to balk, and renege (leave the queue after entering) without being served, based on their desire for service, or their unwillingness for waiting. The inter-arrival times of customers are assumed to be arbitrarily distributed. Service times during a service period, vacation times and service times during vacation are assumed to be exponentially distributed. Employing the supplementary variable technique, we provide a recursive algorithm to compute the stationary system length distributions during vacations and regular busy periods. Based on the various system length distributions, various performance measures of the model and some special cases have been investigated. Numerical results illustrating the effect of the parameters on several performance characteristics are also presented.