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A survey of parameter and state estimation in queues

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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.

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Acknowledgements

Azam Asanjarani’s and Peter Taylor’s research is supported by the Australian Research Council (ARC) Centre of Excellence for the Mathematical and Statistical Frontiers (ACEMS). Yoni Nazarathy is supported by ARC grant DP180101602. We are grateful to Liron Ravner for feedback on an early version of the manuscript. We also thank Ross McVinish and an anonymous referee for useful feedback. We thank Phil Pollett for contributions to an early version of the associated annotated bibliography [9].

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  1. The University of Auckland, Auckland, New Zealand

    Azam Asanjarani

  2. The University of Queensland, Brisbane, Australia

    Yoni Nazarathy

  3. The University of Melbourne, Melbourne, Australia

    Peter Taylor

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  1. Azam Asanjarani
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Asanjarani, A., Nazarathy, Y. & Taylor, P. A survey of parameter and state estimation in queues. Queueing Syst 97, 39–80 (2021). https://doi.org/10.1007/s11134-021-09688-w

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  • DOI: https://doi.org/10.1007/s11134-021-09688-w

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