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.