Statistical inference for mean-field queueing systems

TL;DR

This paper develops a statistical inference framework for discrete mean-field queueing models, specifically the supermarket model, using asymptotic analysis and numerical validation to estimate system parameters from observed data.

Contribution

It introduces a novel inference method for discrete mean-field models, extending existing continuous model techniques to jump processes like the supermarket model.

Findings

Asymptotic inference scheme based on approximate least squares estimation.

Estimator is consistent and asymptotically normal as system size and observations grow.

Numerical results demonstrate the efficiency and accuracy of the proposed estimator.

Abstract

Mean-field limits have been used now as a standard tool in approximations, including for networks with a large number of nodes. Statistical inference on mean-filed models has attracted more attention recently mainly due to the rapid emergence of data-driven systems. However, studies reported in the literature have been mainly limited to continuous models. In this paper, we initiate a study of statistical inference on discrete mean-field models (or jump processes) in terms of a well-known and extensively studied model, known as the power-of-L, or the supermarket model, to demonstrate how to deal with new challenges in discrete models. We focus on system parameter estimation based on the observations of system states at discrete time epochs over a finite period. We show that by harnessing the weak convergence results developed for the supermarket model in the literature, an asymptotic inference scheme based on an approximate least squares estimation can be obtained from the mean-field limiting equation. Also, by leveraging the law of large numbers alongside the central limit theorem, the consistency of the estimator and its asymptotic normality can be established when the number of servers and the number of observations go to infinity. Moreover, numerical results for the power-of-two model are provided to show the efficiency and accuracy of the proposed estimator.