Exact Solutions for Open, Closed and Mixed Queueing Networks with Rejection Blocking

Open, mixed and closed queueing networks with multiple job classes, reversible routing and rejection blocking are investigated in this paper. Jobs may change class membership and general service requirement distributions that depend on the job class are allowed. We prove that the equilibrium state probabilities have product form if at all stations either the scheduling discipline is symmetric or all service requirements at the station have the same exponential distribution. The solution implies insensitivity in this kind of blocking networks, i.e. the distribution of the jobs in equilibrium, irrespective of their remaining service requirements, depends only on their mean service requirement.