An M/PH/K queue with constant impatient time

摘要

This paper is concerned with an M/PH/K queue with customer abandonment, constant impatient time, and many servers. By combining the method developed in Choi et al. (Math Oper Res 29:309-325, 2004) and Kim and Kim (Perform Eval 83-84:1-15, 2015) and the state space reduction method introduced in Ramaswami (Stoch Models 1:393-417, 1985), the paper develops an efficient algorithm for computing performance measures for the queueing system of interest. The paper shows a number of properties associated with matrices used in the development of the algorithm, which make it possible for the algorithm, under certain conditions, to handle systems with up to one hundred servers. The paper also obtains analytical properties of performance measures that are useful in gaining insight into the queueing system of interest.