Bulk Queueing Model With Bernoulli Vacation, Different Service And Breakdown Disciplines And State Dependent Arrival Rates

Abstract

The basic model of this article is a bulk arrival, batch service non-Markovian queue. The customers arrive in batches of variable size follows compound Poisson process. If the service is not immediate, the customer waits in a waiting line of infinite capacity, while waiting in the line, the first in first out queue discipline is applied for service. The services are given in batches of fixed size. Two types of services are given by the server for each group. The first type is of essential kind of service with two modes, based on Bernoulli schedule. The second type is of optional kind of service. The second type is based on Bernoulli schedule. After completion of each service, the server takes vacation of Bernoulli type. During the busy mode of the server, the server may breakdown, immediately send for repair. There are two types of repairs, called essential and optional. The optional repairs follows Bernoulli schedule. The service periods, vacation period and repair periods, all are random time periods follows different general distributions. The number of breakdowns follows Poisson process. In addition, the arrival rates are state dependent, based on the server state. This model is analysed in time independent domain, using supplementary variable technique by obtaining probability generating functions at various server states. Some performance measures and particular models are derived. A numerical study is also carried out.