On two priority multi-server queues with impatient customers

Abstract

This study considers a system of multi-server queues with two classes of impatient customers: high-priority and low-priority. Customers join the system according to a Poisson process and customers may abandon service after entering the queue for an exponentially distributed duration with distinct rates. In this paper, we consider last come-first served (LCFS) and first come-first served (FCFS), and service time is assumed to be distributed exponentially among all customers. Deriving the Laplace transforms of the defined random variables and applying the matrix geometric method with direct truncation makes it possible to obtain an approximation of the stationary distribution in order to calculate the expected waiting time for both classes of customers. For each class of customer, we derive performance measures related to stationary probability distributions and conditional waiting times.