Bayesian Inference in Queueing Systems

Bayesian inference offers a principled framework for estimating the key parameters of queueing models by combining prior knowledge with observed data. In service and manufacturing environments, accurate estimation of arrival rates, service rates and associated performance measures is essential for capacity planning, resource allocation and quality control. The Bayesian paradigm accommodates uncertainty through prior distributions, naturally quantifies parameter variability and enables coherent updating as new data become available. Recent methodological advances have addressed challenges such as limited sample sizes, non-standard arrival processes and customer behaviour phenomena like balking. Modern computational techniques, notably Markov Chain Monte Carlo (MCMC) algorithms, facilitate the practical implementation of complex posterior analyses. The result is a suite of flexible, data-driven tools that support decision-making in contexts as diverse as call centres, healthcare triage systems and cloud computing platforms.

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Research from all publishers

Recent work has demonstrated that Bayesian estimators can outperform classical methods in finite-sample settings. One study examined single-server queues with limited capacity, showing that the use of a Jeffreys’ prior yields lower mean-squared error in estimating traffic intensity across a broad parameter range, even for sample sizes below 200. Another contribution introduced a fully Bayesian framework for queues with balking, comparing inverted beta, gamma and Jeffreys priors under squared-error and precautionary loss criteria. By employing MCMC simulations, the authors quantified the trade-off between estimation accuracy and risk aversion, offering practitioners guidelines for selecting priors in service systems where some customers may decline to join. A third line of research proposed flexible likelihood formulations based on binomial-negative and discrete uniform assumptions, enabling Bayesian inference in models with bulk arrivals and general service distributions. This approach broadens the applicability of Bayesian queueing analysis to settings with grouped customer arrivals and non-exponential service patterns, and it leverages conjugate structures for computational efficiency.

Bayesian Inference in Queueing Systems publication trend

The graph below shows the total number of articles in bayesian inference in queueing systems across all publications each year (not limited to Nature Index journals).

Technical terms

Bayesian inference: A statistical framework that updates prior beliefs about parameters using observed data to obtain posterior distributions.

Traffic intensity (ρ): The ratio of the arrival rate to the service rate in a queue, indicating system utilisation.

Prior distribution: A probability distribution representing initial beliefs about a parameter before observing data.

Jeffreys’ prior: A non-informative prior derived from the Fisher information, often used to yield objective Bayesian estimates.

Markov Chain Monte Carlo (MCMC): A class of algorithms for sampling from complex posterior distributions by constructing a Markov chain that converges to the target distribution.

Balking: Behaviour in which arriving customers choose not to join a queue based on its perceived length or waiting time.

References

1. Traffic Intensity Estimation in Finite Markovian Queueing Systems. Mathematical Problems in Engineering (2018).
2. Modeling and Estimation of Traffic Intensity in M/M/1 Queueing System with Balking: Classical and Bayesian Approaches. AppliedMath (2025).
3. Bayesian queue modelling with likelihood binomial negative and uniform discrete. Journal of Mathematical and Computational Science (2022).