Parameter and State Estimation in Queues and Related Stochastic Models: A Bibliography

TL;DR

This bibliography compiles and categorizes the literature on parameter and state estimation in queues and related stochastic models, spanning seminal developments from the 1950s to 2017. It surveys approaches including $MLE$, Bayesian and nonparametric methods, and online/sequential techniques across a range of queueing models such as $M/M/1$, $GI/G/1$, $M/G/1$, and networked systems, with data regimes from full observation to probing and passive measurements. The document highlights the role of model structure (e.g., $PH$/$ME$ service times) and sampling regime in estimator design, performance, and asymptotics, and connects methodological advances to practical applications in telecommunications, manufacturing, traffic, and health care. By organizing the literature along models, data regimes, paradigms, and applications, it serves as a reference for researchers and practitioners seeking to locate results, compare methods, and identify gaps for future work.

Abstract

This is an annotated bibliography on estimation and inference results for queues and related stochastic models. The purpose of this document is to collect and categorise works in the field, allowing for researchers and practitioners to explore the various types of results that exist. Our focus is on papers that deal with mathematical queueing models as well as related stochastic models motivated by queues. We attempted to make this bibliography exhaustive, yet there are possibly some papers that we have missed. As it is updated continuously, additions and comments are welcomed. Note that this bibliography is also a companion to our survey of parameter and state estimation in queues [20].