Markovian Multi-server Queue with Reneging and Provision of Additional Removable Servers

Abstract

Many queuing situations with discouragement are encountered in real life in which the customers do not wait for a longer time and may renege from the system after waiting for some time. To avoid this reneging behavior of the customers, the provision of additional removable servers may be helpful. From economic viewpoint, the additional servers may be installed or removed from the system according to a threshold policy on the basis of number of clients present in the system. In this paper, a steady state solution of a finite M/M/R+r Markov model with discouragement and operating under threshold policy for inducting the additional removable $r$ servers along with $R$ permanent servers is presented. The first-come first-served discipline is followed in providing services to the customers. The queue size distribution at the equilibrium is obtained using a recursive approach. The formulations of various performance measures, namely expected number of customers in the system, throughput, have been done in terms of system state probabilities. By taking numerical illustration, the system behavior via sensitivity analysis and cost optimization has been examined.