On the exact and approximate throughput analysis of closed queuing networks with blocking

A type of blocking is investigated in which, on completion of its service, a job attempts to enter a new station. If, at that moment, the destination station is full, the job is forced to reside in the server of the source station until a place becomes available in the destination station. The server of the source station remains blocked during this period of time. This model is known as a queuing network with transfer blocking. The state space of queuing networks with blocking is reduced by considering finite capacities of the stations. A nonblocking queuing network with the appropriate total number of jobs is derived. The state space of this network is equal to the state space of the blocking queuing network. The transformation of state space is exact for two-station networks and approximate for three-or-more station cases. The approximation has been validated by executing several examples, including stress tests. In all investigated network models, the approximate throughput results deviate, on the average, less than 3% from the simulation results