MX/G/1 Queue with Negative Arrival and Breakdown

The author considers a batch arrival queueing system in which two types of customers (namely positive and negative) arrive. The arrival of a negative customer to a queueing system removes one positive customer who is in service if any. A cycle starts whenever the system empties and the server is turned off and stays idle in the system. The idle period ends as soon as a batch of positive customers arrives for services. The positive customer who is in the head of queue will join the service immediately. The arrival ofnegative customers causes the server to breakdown. Whenever the server fails, it is sent to repair facility. The arriving negative customers during the idle period are assumed to be lost. Immediately after the server is fixed the customer waiting in the head of the queue is taken up for service. In the present paper, the author analyzes steady state behavior of the system size distribution of MX/G/1 queue with negative customers. The probability generating function (PGF) of the stationary queue length are presented and performance measures are obtained. Numerical examples to illustrate the effect of the parameters are also provided.