Abstract
This paper investigates a single server batch service queueing system with second optional service and reneging. The transient state probabilities of the queueing model are computed by using fourth order Runge Kutta method. Cost analysis is performed to determine the optimal values of the service rates of First Essential Service (FES) and Second Optional Service (SOS) simultaneously at the minimum total expected cost per unit time. Some important performance measures and numerical illustrations are provided in order to show the managerial intuitions of the model.
Highlights
1.IntroductionA service process is among the important characteristics of a queueing system
In queueing theory, a service process is among the important characteristics of a queueing system
The service times distribution of both First Essential Service (FES) and Second Optional Service (SOS) are exponential with mean rates μ1 and μ2, respectively and the services are given in batches of size not more than b such that if the server finds the customers less or equal to b in the waiting queue, the server takes all of them in the batch for service, but if the server finds the customers more than b waiting in the queue, the he takes a batch of size b while others remain waiting in the queue
Summary
A service process is among the important characteristics of a queueing system. Later on, [11,12] studied a finite buffer multiple working vacation queues with balking, reneging and vacation interruption under N-Policy and obtained the solution for the steady state probabilities using recursive. The study of the transient solution of the performance measures of the queue system has been analysed by [14,15,16,17,18] etc. A time dependent solution of a single server queueing system with a Poisson input process has been considered by [19,20]. The transient behaviour analysis of an M/M/1/ N queue with working breakdowns and server vacations has been studied by [22]. From the above literature study, most of the heterogeneous server queueing systems are analysed in steady state. The transient probabilities of the queueing model are obtained using fourth order Runge-Kutta method
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