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The Queue Inference Engine: Deducing Queue Statistics from Transactional Data

Author

Listed:
  • Richard C. Larson

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

The transactional data of a queueing system are the recorded times of service commencement and service completion for each customer served. With increasing use of computers to aid or even perform service one often has machine readable transactional data, but virtually no information about the queue itself. In this paper we propose a way to deduce the queueing behavior of Poisson arrival queueing systems from only the transactional data and the Poisson assumption. For each congestion period in which queues may form (in front of a single or multiple servers), the key quantities obtained are mean wait in queue, time-dependent mean number in queue, and probability distribution of the number in queue observed by a randomly arriving customer. The methodology builds on arguments of order statistics and usually requires a computer to evaluate a recursive function. The results are exact for a homogeneous Poisson arrival process (with unknown parameter) and approximately correct for a slowly time varying Poisson process.

Suggested Citation

  • Richard C. Larson, 1990. "The Queue Inference Engine: Deducing Queue Statistics from Transactional Data," Management Science, INFORMS, vol. 36(5), pages 586-601, May.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:5:p:586-601
    DOI: 10.1287/mnsc.36.5.586
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    Citations

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    Cited by:

    1. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    2. Lee K. Jones, 1999. "Inferring Balking Behavior From Transactional Data," Operations Research, INFORMS, vol. 47(5), pages 778-784, October.
    3. Richard Charles Larson, 2002. "Public Sector Operations Research: A Personal Journey," Operations Research, INFORMS, vol. 50(1), pages 135-145, February.
    4. David Simchi-Levi, 2014. "OM Forum —OM Research: From Problem-Driven to Data-Driven Research," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 2-10, February.
    5. Yijie Peng & Michael C. Fu & Bernd Heidergott & Henry Lam, 2020. "Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling," Operations Research, INFORMS, vol. 68(6), pages 1896-1912, November.
    6. Rouba Ibrahim & Ward Whitt, 2009. "Real-Time Delay Estimation Based on Delay History," Manufacturing & Service Operations Management, INFORMS, vol. 11(3), pages 397-415, May.
    7. Edward H. Kaplan, 2012. "OR Forum---Intelligence Operations Research: The 2010 Philip McCord Morse Lecture," Operations Research, INFORMS, vol. 60(6), pages 1297-1309, December.
    8. Azam Asanjarani & Yoni Nazarathy & Peter Taylor, 2021. "A survey of parameter and state estimation in queues," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 39-80, February.

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