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

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