A Markov Model for Measuring Service Levels in Nonstationary G(t)/G(t)/s(t)+G(t) Queues

Abstract

We present a Markov model to approximate the queueing behavior at the G(t)=G(t)=s(t) + G(t) queue with exhaustive discipline and abandonments. The performance measures of interest are: (1) the average number of customers in queue, (2) the variance of the number of customers in queue, (3) the average number of abandonments and (4) the virtual waiting time distribution of a customer when arriving at an arbitrary moment in time. We use acyclic phase-type distributions to approximate the general interarrival, service and abandonment time distributions. An ecient, iterative algorithm allows the accurate analysis of small- to medium-sized problem instances. The validity and accuracy of the model are assessed using a simulation study.