A Robust Queueing Network Analyzer Based on Indices of Dispersion

Abstract

We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival processes, general service-time distributions and customer feedback. We focus on the customer flows, defined as the continuous-time processes counting customers flowing into or out of the network, or flowing from one queue to another. Each flow is partially characterized by its rate and a continuous function that measures the stochastic variability over time. This function is a scaled version of the variance-time curve, called the index of dispersion for counts (IDC). The required IDC functions for the flows can be calculated from the model primitives, estimated from data or approximated by solving a set of linear equations. A robust queueing technique is used to generate approximations of the mean steady-state performance at each queue from the IDC of the total arrival flow and the service specification at that queue. The algorithm effectiveness is supported by extensive simulation studies and heavy-traffic limits.

Supervised learning-based approximation method for single-server open queueing networks with correlated interarrival and service times

“…These studies do not provide an approximation for the departure process mean, coe cient of variation, and autocorrelation for the general correlated interevent times. Whitt and You (2020) introduce a queuing network analysis method based on robust queuing and using the indices of dispersion for counts that is closely related to the autocorrelation function of a process. This method, referred as Rob-QNA in this study, assumes renewal service times and a first come first serve queuing discipline.…”

“…The supervised learning approach yields more accurate cycle time prediction compared to analytical approximations (Kingman 1961, Marchal 1976, Krämer and Langenbach-Belz 1976, Buzacott and Shanthikumar 1993) and the robust queueing approximation (Whitt and You 2020).…”

“…In the following, we give the summary of the SLQNA, MAPQNA, and QNA algorithms used in this work. For details on the Rob-QNA algorithm for tree-structured networks, we refer the reader to (Whitt and You 2020).…”