Loss and Delay Multi Server State Dependent Queue with Discouragement, Additional Server and No-Passing

International Journal of Research and Scientific Innovation (IJRSI) | Volume V, Issue VIII, August 2018 | ISSN 2321–2705

Loss and Delay Multi Server State Dependent Queue with Discouragement, Additional Server and No-Passing

 Pankaj Sharma

 Department of Mathematics, School of Science, Noida International University, G. B. Nagar, G. Noida, India

Abstract: – This study deals with loss and delay multi-server no passing queueing system with discouragement. To reduce the balking behaviour of the customers in case of long queue, we incorporate additional removable servers. The customers arrive according to Poisson process and departs from the system in the same chronological order in which they join the system, due to nopassing restriction. The service facility consists of s permanent and r additional removable heterogeneous servers. The service times of the customers are exponentially distributed. The departing constraint categorizes customers in two types (i) the customers having zero service time and (ii) the customers having exponentially distributed service time. By stating the state dependent rates, the product type solution for queue size distribution at equilibrium. The analytical formulae for the expected waiting time and the difference between the expected waiting times of both type of customers are also derived. To examine the effect of variation of parameters, the sensitivity analysis is carried out. Numerical results are tabulated and displayed graphically so as to explore the advantage of additional removable servers on the performance metrics.

Keywords: Multi-server Queue, No-passing, Removable additional servers, Discouragement, Queue size distribution, Expected waiting time.

I. INTRODUCTION

The performance analysis of multi-server queues with discouragement has significant impetus on the optimal control of various service systems such as computer, manufacturing, distribution and production systems, etc. In order to discourage the balking and reneging behaviour of the customers, it is advisable to improve the service facility subject to cost constraint. The concept of nopassing in multi-server queue was introduced by Washburn (1974). Nopassing restriction implies that the customers depart from the system in the same chronological order in which they join the queue. Some other researchers have also done valuable works in this direction. Jain (1998) extended the work of infinite capacity to finite capacity and finite population models for loss and delay queueing system subject to nopassing constraint. M/M/m/K queue with nopassing and additional servers was also studied by Jain and Ghimire (1999). Finite population loss and delay queue under no passing restriction and discouragement was analysed by Sharma (2017).

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