M/M/1 multiple vacation queueing systems with differentiated vacations and vacation interruptions

Abstract

We consider an M/M/1 multiple vacation queueing system with two types of server vacations. Type 1 vacation is taken after the server has exhaustively served all the customers in the system, where the number of customers served is at least one. Type 2 vacation is taken when the server returns from a vacation and finds no customer waiting. Each type of vacation can be interrupted when the number of customers in the system reaches two predefined thresholds, where each vacation type has a different threshold. It is assumed that service times and vacation durations are exponentially distributed with different means. We present a steady-state solution of the system under two vacation interruption policies.