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The Impact of Autocorrelation on Queuing Systems

Author

Listed:
  • Miron Livny

    (Department of Computer Sciences, University of Wisconsin-Madison, Madison, Wisconsin 53706)

  • Benjamin Melamed

    (NEC USA, Inc., C&C Research Laboratories, Princeton, New Jersey 08540)

  • Athanassios K. Tsiolis

    (Department of Computer Sciences, University of Wisconsin-Madison, Madison, Wisconsin 53706)

Abstract

The performance of single-server queues with independent interarrival intervals and service demands is well understood, and often analytically tractable. In particular, the M/M/1 queue has been thoroughly studied, due to its analytical tractability. Little is known, though, when autocorrelation is introduced into interarrival times or service demands, resulting in loss of analytical tractability. Even the simple case of an M/M/1 queue with autocorrelations does not appear to be well understood. Such autocorrelations do, in fact, abound in real-life systems, and worse, simplifying independence assumptions can lead to very poor estimates of performance measures. This paper reports the results of a simulation study of the impact of autocorrelation on performance in an FIFO queue. The study used two computer methods for generating autocorrelated random sequences, with different autocorrelation characteristics. The simulation results show that the injection of autocorrelation into interarrival times, and to a lesser extent into service demands, can have a dramatic impact on performance measures. From a performance viewpoint, these effects are generally deleterious, and their magnitude depends on the method used to generate the autocorrelated process. The paper discusses these empirical results and makes some recommendations to practitioners of performance analysis of queuing systems.

Suggested Citation

  • Miron Livny & Benjamin Melamed & Athanassios K. Tsiolis, 1993. "The Impact of Autocorrelation on Queuing Systems," Management Science, INFORMS, vol. 39(3), pages 322-339, March.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:3:p:322-339
    DOI: 10.1287/mnsc.39.3.322
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    Cited by:

    1. Li, Ming, 2017. "Record length requirement of long-range dependent teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 164-187.
    2. Civelek, Ismail & Biller, Bahar & Scheller-Wolf, Alan, 2021. "Impact of dependence on single-server queueing systems," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1031-1045.
    3. Girish, Muckai K. & Hu, Jian-Qiang, 2001. "Approximations for the departure process of the G/G/1 queue with Markov-modulated arrivals," European Journal of Operational Research, Elsevier, vol. 134(3), pages 540-556, November.
    4. Raed Kontar & Shiyu Zhou & John Horst, 2017. "Estimation and monitoring of key performance indicators of manufacturing systems using the multi-output Gaussian process," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2304-2319, April.
    5. Henry Lam, 2018. "Sensitivity to Serial Dependency of Input Processes: A Robust Approach," Management Science, INFORMS, vol. 64(3), pages 1311-1327, March.
    6. Petra Tomanová & Vladimír Holý, 2021. "Clustering of arrivals in queueing systems: autoregressive conditional duration approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 859-874, September.
    7. Nielsen, Erland Hejn, 2004. "Streams of events and performance of queuing systems: The basic anatomy of arrival/departure processes, when focus is set on autocorrelation," CORAL Working Papers L-2004-02, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    8. Sousa-Vieira, M.E. & Suárez-González, A. & López-García, C. & Fernández-Veiga, M. & López-Ardao, J.C. & Rodríguez-Rubio, R.F., 2010. "Fast simulation of self-similar and correlated processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2040-2061.
    9. Justus Arne Schwarz & Martin Epp, 2016. "Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6251-6264, October.
    10. Benjamin Melamed & Xiang Zhao, 2013. "MARM Processes Part I: General Theory," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 1-35, March.
    11. Marne C. Cario & Barry L. Nelson, 1998. "Numerical Methods for Fitting and Simulating Autoregressive-to-Anything Processes," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 72-81, February.
    12. Hejn Nielsen, Erland, 2007. "Autocorrelation in queuing network-type production systems--Revisited," International Journal of Production Economics, Elsevier, vol. 110(1-2), pages 138-146, October.
    13. David Heath & Sidney Resnick & Gennady Samorodnitsky, 1998. "Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 145-165, February.
    14. Van Nyen, Pieter L. M. & Van Ooijen, Henny P. G. & Bertrand, J.W.M.J. Will M., 2004. "Simulation results on the performance of Albin and Whitt's estimation method for waiting times in integrated production-inventory systems," International Journal of Production Economics, Elsevier, vol. 90(2), pages 237-249, July.
    15. Nima Manafzadeh Dizbin & Barış Tan, 2019. "Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes," Flexible Services and Manufacturing Journal, Springer, vol. 31(4), pages 1042-1076, December.

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