Computational algorithms for networks of queues with rejection blocking

Abstract

Open, closed and mixed queueing networks with reversible routing, multiple job classes and rejection blocking are investigated. In rejection blocking networks blocking event occurs when upon completion of its service of a particular station's server, a job attempts to proceed to its next station. If, at that moment, its destination station is full, the job is rejected. The job goes back to the server of the source station and immediately receives a new service. This is repeated until the next station releases a job and a place becomes available. In the model jobs may change their class membership and general service time distributions depending on the job class are allowed. Two station types are considered: Either the scheduling discipline is symmetric, in which case the service time distributions are allowed to be general and dependent on the job class or the service time distributions at a station are all identical exponential distributions, in which case more general scheduling disciplines are allowed. An exact product form solution for equilibrium state probabilities is presented. Using the exact product form solution of the equilibrium state distribution, algorithms for computation of performance measures, such as mean number of jobs and throughputs, are derived. The complexity of the algorithms is discussed.