Analysis of a bulk arrival N-policy queue with two-service genre, breakdown, delayed repair under bernoulli vacation and repeated service policy.

This article deals with an unreliable bulk arrival single server queue rendering two-heterogeneous optional repeated service (THORS) with delayed repair, under Bernoulli Vacation Schedule (BVS) and N-policy. For this model, the joint distribution of the server's state and queue length are derived under both elapsed and remaining times. Further, probability generating function (PGF) of the queue size distribution along with the mean system size of the model are determined for any arbitrary time point and service completion epoch, besides various pivotal system characteristics. A suitable linear cost structure of the underlying model is developed, and with the help of a difference operator, a locally optimal N-policy at a lower cost is obtained. Finally, numerical experiments have been carried out in support of the theory.

A study on Non-Markovian Bulk Arrival And Bulk Service with Multiple Vacations

A queue or a waiting line, involves arriving customers who is waiting to be served at one or more service stations, by one or more servers. The term ‘customer’ may refer, for example, to a machine arriving at an inspection center or to a person arriving at a booking counter in a railway station. Customers are selected for service by certain rule known as queue discipline. The basic characteristics of a queuing system follows systematically (1) The arrival pattern of customer (2) The service pattern of servers (3) The queue discipline (4) The system capacity (5) Number of servers. If more than one arrival enters the system simultaneously, the input is said to Bulk Arrival. Customer may be served individually or in batches, in case of batch service the service system is called bulk service system.