Stationary analysis of a discrete-time GI/D-MSP/1 queue with multiple vacations

This paper analyzes the steady-state behavior of a discrete-time single-server queueing system with correlated service times and server vacations. The vacation times of the server are independent and geometrically distributed, and their durations are integral multiples of slot duration. The customers are served one at a time under discrete-time Markovian service process. The new service process starts with the initial phase distribution independent of the path followed by the previous service process when the server returns from a vacation and finds at least one waiting customer. The matrix-geometric method is used to obtain the probability distribution of system-length at prearrival epoch. With the help of Markov renewal theory approach, we also derive the system-length distribution at an arbitrary epoch. The analysis of actual-waiting-time distribution in the queue measured in slots has also been carried out. In addition, computational experiences with a variety of numerical results are discussed to display the effect of the system parameters on the performance measures.