Analysis of two-server queueing model with phase-type service time distribution and common phases of service

Abstract

We consider two server queueing system with an infinite buffer. Customers arrive to the system according to the Markovian Arrival Process. Service time of a customer has a phase-type distribution. The servers use the same equipment (phases of PH) for customers processing. So, if service of a customer transits to the phase, at which another server is currently providing the service, the service of the customer is suspended until the phase will become available. Behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is derived. Expressions for computation of the main performance measures are derived.