A hybrid analysis approach for finite-capacity queues with general inputs and phase type service

A new analysis method for queueing systems with general input stream and phase type service time distributions is introduced. The approach combines discrete event simulation and numerical analysis of continuous time Markov chains. Simulation is used to represent the arrival process, whereas the service process is analyzed with numerical techniques. In this way the state of the system is characterized by a probability vector rather than by a single state. The use of a distribution vector reduces the variance of result estimators such that the width of confidence intervals is often reduced compared to discrete event simulation. This, in particular, holds for measures based on rare events or states with a small probability. This analysis approach can be applied for a wide variety of result measures including stationary, transient and accumulated measures.