An Extension of Norton's Theorem for Queueing Networks

Given a closed BCMP queueing network, the problem is considered of studying the behavior of any subsystem σ without solving for the entire system. This paper proves that this is possible for σ consisting of any number of queues, arbitrarily interfacing the rest of the system, thus generalizing the classic CHW theorem, also known as Norton's theorem. A general flow-equivalent solution procedure is given and its computational complexity is compared with that of the product-form and the exact aggregation procedure. The relative merits of these procedures are also expressed in terms of σ's cardinality. Copyright © 1982 by The Institute of Electrical and Electronics Engineers, Inc