Discrete-time Analysis of Multicomponent GI/GI/1 Queueing Networks

Abstract

In this work, we provide initial insights regarding the error introduced into multicomponent queueing systems by assuming the departure processes of arbitrary GI/GI/1-oo queues to be renewal processes. To this end, we compute the sojourn time distribution as well as departure distributions of a linear chain of queueing components and compare the results to a simulation of the same system. By applying the renewal approximation, potential autocorrelations of the departure processes are lost. We investigate the magnitude of this error regarding both the sojourn time as well as interdeparture time distributions for a broad set of parameters. Although more indepth studies are needed, our results show that both distributions can be closely approximated, which allows the application of the model to asses the performance of real world NFV function chains.