An Error Bound for Infinite Approximations of Queueing Networks with Large Finite Stations under RSRD Protocol

Queueing networks with stations having finite but relatively large buffers are studied. The protocol is the repetitive service random destination (RSRD) protocol. A simple infinite product approximation is suggested to evaluate the system. An analytic error bound is established for the accuracy of this approximation. This error bound is shown to be of the order of the steady state probability to exceed the buffer limits computed by product form expressions for the infinite system. This probability can often be thought as being quite small and thus provides a practical error bound. Some numerical support is provided. To establish the error bound, a new method consisting of introducing an intermediate model is used. This approach seems of interest for wider application to obtain error bounds. Keywords : Repetitive Service, Approximation, Product Form, Error Bound. 1 Motivation Queueing network modelling has become a general tool to evaluate the performances of manufacturing, computer..