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Problems of Statistical Inference for Birth and Death Queuing Models

Author

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  • Ronald W. Wolff

    (Department of Industrial Engineering, University of California, Berkeley)

Abstract

A large sample theory for birth and death queuing processes which are ergodic and metrically transitive is applied to make inferences about arrival and service rates. Likelihood ratio tests and maximum likelihood estimators are derived for simple models. Composite hypotheses, for example that the arrival rate does not vary with the number in the system, are considered. A numerical example illustrating these results, based on data generated by simulating a known model, is presented, which includes the testing of both true and false composite hypotheses.

Suggested Citation

  • Ronald W. Wolff, 1965. "Problems of Statistical Inference for Birth and Death Queuing Models," Operations Research, INFORMS, vol. 13(3), pages 343-357, June.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:3:p:343-357
    DOI: 10.1287/opre.13.3.343
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    Cited by:

    1. Frédéric Lavancier & Ronan Le Guével, 2021. "Spatial birth–death–move processes: Basic properties and estimation of their intensity functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 798-825, September.
    2. Anthony Ebert & Ritabrata Dutta & Kerrie Mengersen & Antonietta Mira & Fabrizio Ruggeri & Paul Wu, 2021. "Likelihood‐free parameter estimation for dynamic queueing networks: Case study of passenger flow in an international airport terminal," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 770-792, June.
    3. Saroja Kumar Singh, 2023. "Maximum Likelihood Estimation in Single Server Queues," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 931-947, February.
    4. James Dong & Ward Whitt, 2015. "Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 664-685, December.
    5. Shovan Chowdhury, 2019. "On the Estimation of Performance Measures in a Single M/Ek/1 Queue," Working papers 301, Indian Institute of Management Kozhikode.
    6. Ward Whitt, 2016. "Heavy-traffic fluid limits for periodic infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 111-143, October.

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