A Survey of Parameter and State Estimation in Queues

TL;DR

This paper provides a comprehensive survey of various inference methods and paradigms used for parameter and state estimation in queueing systems, covering classical, Bayesian, and online approaches.

Contribution

It categorizes and explains different estimation paradigms in queueing theory, offering a structured overview and key references for future research.

Findings

Multiple inference paradigms are systematically categorized.

Key principles and ideas for each estimation approach are outlined.

Numerical experiments illustrate the discussed methods.

Abstract

We present a broad literature survey of parameter and state estimation for queueing systems. Our approach is based on various inference activities, queueing models, observations schemes, and statistical methods. We categorize these into branches of research that we call estimation paradigms. These include: the classical sampling approach, inverse problems, inference for non-interacting systems, inference with discrete sampling, inference with queueing fundamentals, queue inference engine problems, Bayesian approaches, online prediction, implicit models, and control, design, and uncertainty quantification. For each of these estimation paradigms, we outline the principles and ideas, while surveying key references. We also present various simple numerical experiments. In addition to some key references mentioned here, a periodically-updated comprehensive list of references dealing with parameter and state estimation of queues will be kept in an accompanying annotated bibliography.