On a 2-class polling model with reneging and $$k_i$$ k i -limited service

Abstract

This paper analyzes a 2-class, single-server polling model operating under a $$k_i$$ -limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of $$(k_1,k_2)$$ which minimizes a cost function involving the expected time a customer spends waiting in the queue and an additional penalty cost should reneging take place.