Transient Solution of an Batch arrival Queue with Two Types of Service, Multiple Vacation, Random breakdown and Restricted Admissibility

Abstract

In this paper we analyse a batch arrival queue with two types of service subject to random breakdowns having multiple server vacation. We assume that the server provides two types of service, type 1 with probability and type 2 with probability with the service times following general distribution and each arriving customer may choose either type of service. The server takes vacation each time the system becomes empty and the vacation period is assumed to be general. On returning from vacation if the server finds no customer waiting in the system, then the server again goes for vacation until he finds at least one customer in the system. The system may breakdown at random and repair time follows exponential distribution. In addition we assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Average queue lenth and average system size are also computed.