Finite Population and Finite Capacity Single Server Batch Service Queue With Single Vacation and Impatient

Two single server queues are considered in this paper. The models are (i) Finite source and (ii) Finite waiting line models. For both the models, if there are no customers at a service completion epoch, the server takes a single vacation. Also, the waiting customers may become impatient and leaves the queue without getting service called reneging behaviour of the customer. In addition the services are given in batches of fixed service. It is assumed that the inter arrival times, service times, vacation times and reneging times all follows different exponential distributions. Steady state analysis is carried out for both models. Cost and profit analyses are also provided. The two models are compared numerically.