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Statistical inference for Mt/G/Infinity queueing systems under incomplete observations

Author

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  • Li, Dongmin
  • Hu, Qingpei
  • Wang, Lujia
  • Yu, Dan

Abstract

Mt/G/Infinity queueing systems have been widely used to analyse complex systems, such as telephone call centres, software testing systems, and telecommunication systems. Statistical inferences of performance measures, such as the expected cumulative numbers of arrivals and departures, are indispensable for decision makers in analysing the current scenario, predicting future scenarios, and making cost-effective decisions. In most scenarios, we only obtain interval censored data, namely, counts in fixed time intervals, instead of complete data because we either do not want or are not able to monitor arrivals and departures. We provide a general framework for statistical inference in Mt/G/Infinity queueing systems given interval censored data. A maximum-likelihood estimation (MLE) method is proposed for inferring the arrival rate and service duration. This method is applicable to general forms of the arrival rate functions and general service duration distributions. More importantly, we propose a combination of the bootstrap method and the delta method for inferring the expected cumulative numbers of arrivals and departures. The results of the simulation study demonstrate that the point and interval estimates of the proposed MLE method are satisfactory overall. As the number of intervals increases, the estimates based on the proposed MLE approach the estimates based on MLE with complete data. Our procedure enables estimates to be obtained without the need to keep track of each item, thereby substantially reducing resource consumption for monitoring items and storing data. An application in a software testing system demonstrates that the goodness-of-fit performance of the proposed MLE method is satisfactory.

Suggested Citation

  • Li, Dongmin & Hu, Qingpei & Wang, Lujia & Yu, Dan, 2019. "Statistical inference for Mt/G/Infinity queueing systems under incomplete observations," European Journal of Operational Research, Elsevier, vol. 279(3), pages 882-901.
  • Handle: RePEc:eee:ejores:v:279:y:2019:i:3:p:882-901
    DOI: 10.1016/j.ejor.2019.06.055
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    References listed on IDEAS

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    1. Andersen, Anders Reenberg & Nielsen, Bo Friis & Reinhardt, Line Blander & Stidsen, Thomas Riis, 2019. "Staff optimization for time-dependent acute patient flow," European Journal of Operational Research, Elsevier, vol. 272(1), pages 94-105.
    2. Stephen G. Eick & William A. Massey & Ward Whitt, 1993. "The Physics of the Mt/G/∞ Queue," Operations Research, INFORMS, vol. 41(4), pages 731-742, August.
    3. Okamura, Hiroyuki & Dohi, Tadashi & Osaki, Shunji, 2013. "Software reliability growth models with normal failure time distributions," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 135-141.
    4. Aktekin, Tevfik, 2014. "Call center service process analysis: Bayesian parametric and semi-parametric mixture modeling," European Journal of Operational Research, Elsevier, vol. 234(3), pages 709-719.
    5. Park, Juhyun, 2007. "On the choice of an auxiliary function in the M/G/[infinity] estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5477-5482, August.
    6. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    7. P. A. W Lewis & G. S. Shedler, 1979. "Simulation of nonhomogeneous poisson processes by thinning," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 403-413, September.
    8. Bertsimas, Dimitris & Doan, Xuan Vinh, 2010. "Robust and data-driven approaches to call centers," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1072-1085, December.
    9. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    10. U. Narayan Bhat, 1969. "Sixty Years of Queueing Theory," Management Science, INFORMS, vol. 15(6), pages 280-294, February.
    11. Ibrahim, Rouba & L’Ecuyer, Pierre & Shen, Haipeng & Thiongane, Mamadou, 2016. "Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers," European Journal of Operational Research, Elsevier, vol. 250(2), pages 480-492.
    12. Coolen, F. P. A. & Coolen-Schrijner, P., 2003. "A nonparametric predictive method for queues," European Journal of Operational Research, Elsevier, vol. 145(2), pages 425-442, March.
    13. Dhingra, Vibhuti & Kumawat, Govind Lal & Roy, Debjit & Koster, René de, 2018. "Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations," European Journal of Operational Research, Elsevier, vol. 267(3), pages 855-876.
    14. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    15. Lujia Wang & Qingpei Hu & Jian Liu, 2016. "Software reliability growth modeling and analysis with dual fault detection and correction processes," IISE Transactions, Taylor & Francis Journals, vol. 48(4), pages 359-370, April.
    16. Peter Hall & Juhyun Park, 2004. "Nonparametric inference about service time distribution from indirect measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 861-875, November.
    17. Pender, Jamol, 2016. "Risk measures and their application to staffing nonstationary service systems," European Journal of Operational Research, Elsevier, vol. 254(1), pages 113-126.
    18. N. Bingham & Susan Pitts, 1999. "Non-parametric Estimation for the M/G/∞ Queue," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 71-97, March.
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