Control of G/M-X/1 Queueing System with N-Policy and Customer Impatience

Abstract

We introduce a queueing system with general arrival stream and exponential service time under the N-policy, where customers may renege during idle period and arrival rates may vary according to the server's status. Probability distributions of the lengths of idle period and busy period are derived using absorbing Markov chain approach and a method to obtain the optimal control policy that minimizes long-run expected operating cost per unit time is provided. Numerical analysis is done to illustrate and characterize the method.