Parametric Analysis of Queuing Networks

TLDR

The study examines a queuing network comprising M exponential service stations and N customers. The aim is to analyze how varying parameters affect the behavior of a single‑node input/output subsystem σ. The authors construct an equivalent network where all queues outside subsystem σ are replaced by a single composite queue, enabling analysis of subsystem σ and its application to open exponential networks. For specific parameter classes, subsystem σ behaves identically in the equivalent and original networks, illustrating an analogy to Norton's theorem in circuit theory.

Abstract

We consider a queuing network with M exponential service stations and with N customers. We study the behavior of a subsystem σ, which has a single node as input and a single node as output, when the subsystem parameters are varied. An "equivalent" network is constructed in which all queues except those in subsystem σ are replaced by a single composite queue. We show that for certain classes of system parameters, the behavior of subsystem σ in the equivalent network is the same as in the given network. The analogy to Norton's theorem in electrical circuit theory is demonstrated. In addition, the equivalent network analysis can be applied to open exponential networks.