A Simple Throughput Bound for Large Closed Queueing Networks with Finite Capacities

Arbitrary closed exponential queueing networks are examined such as with finite capacities and blocking or dynamic routing. Conditions are provided from which a simple upper bound on the system throughput and an error bound for its accuracy can be concluded. These conditions are illustrated for a Jackson network with finite entrance buffer and overflow station. An explicit error bound for this application is derived of order M", where M is the number of jobs.