Alternative Approach for Analyzing Discrete-time Finite-buffer Queues with Server Vacations

In this paper, we present a discrete-time single-server finite-buffer queue in which the server takes single/multiple vacations whenever the system becomes empty. The interarrival times are geometrically distributed and service, vacation times are independently identically distributed random variables and their durations are integral multiples of a slot duration. We obtain the state probabilities at service completion, vacation termination and arbitrary epochs using supplementary variable and imbedded Markov chain techniques. The analysis of actual waiting time under the first-come-first-served (FCFS) queueing discipline is also carried out.