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.
Highlights
Queueing systems with vacations have been developed for a wide range applications in production, communication systems, computer networks and etc
Vacation queues have been studied by numerous researchers including Doshi [7], Keilson and Servi [9], Chae et al [4], Madan et al [13], Madan and Anabosi [14], Madan and Abu-dayyeh [11] and Badamchi Zadeh and Shankar [2]
In some queueing systems with batch arrival there is a restriction such that not all batches are allowed to join the system at all time
Summary
Queueing systems with vacations have been developed for a wide range applications in production, communication systems, computer networks and etc. Choudhury et al [6] have studied M/G/1 queue with two phases of service and Bernoulli vacation schedule under multiple vacation policy. Maraghi et al [16] have studied batch arrival queueing system with random breakdowns and Bernoulli schedule server vacations having general vacation time. For the first time Madan and Abu-Dayyeh [12], Madan and Choudhury [15] and Choudhury and Madan [5] proposed an M [x]/G/1 queueing system with restricted admissibilty of arriving batches and Bernoulli schedule server vacation. In this paper we consider a batch arrival queue with two types of service where breakdowns may occur at random, and once the system breaks down, it enters a repair process.
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