A Robust Queueing Network Analyzer Based on Indices of Dispersion

TL;DR

This paper introduces a robust queueing network analysis method that uses indices of dispersion to approximate steady-state performance, accommodating complex arrival and service processes with proven effectiveness through simulations.

Contribution

It presents a novel algorithm that incorporates indices of dispersion for counts to analyze queueing networks with general inputs and feedback, improving robustness and flexibility.

Findings

Effective in approximating steady-state performance.

Handles non-renewal arrivals and general service times.

Validated by extensive simulations and heavy-traffic analysis.

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.