Transient analysis of various vacation interruption policies in a Markovian queue with differentiated multiple vacations

Two different types of interruptions (partial and complete) of server's vacation are discussed in this research work along with two different types of vacations (types 1 and 2). The transient analysis of an M / M / 1 queueing model with differentiated multiple vacations, partial and complete interruption of vacations is carried out. Two types of vacations are studied in this research work. Type 1 vacation is taken after serving all the customers in the system exhaustively. Type 2 vacation is resumed after returning from type 1 vacation and finding the empty system. Partial interruption is the one in which the interruption happens only in type 2 vacation whereas complete interruption can occur in both types 1 and 2 vacations. The system size distributions are derived using generating function and Laplace transforms under transient case. The average and variance are also obtained. Further, numerical simulations are presented.