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An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure

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  • Lothar Breuer

Abstract

Although the concept of Batch Markovian Arrival Processes (BMAPs) has gained widespread use in stochastic modelling of communication systems and other application areas, there are few statistical methods of parameter estimation proposed yet. However, in order to practically use BMAPs for modelling, statistical model fitting from empirical time series is an essential task. The present paper contains a specification of the classical EM algorithm for MAPs and BMAPs as well as a performance comparison to the computationally simpler estimation procedure recently proposed by Breuer and Gilbert. Furthermore, it is shown how to adapt the latter to become an estimator for hidden Markov models. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Lothar Breuer, 2002. "An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure," Annals of Operations Research, Springer, vol. 112(1), pages 123-138, April.
    • Handle: RePEc:spr:annopr:v:112:y:2002:i:1:p:123-138:10.1023/a:1020981005544
    DOI: 10.1023/A:1020981005544
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    Cited by:

    1. Andrzej Chydzinski & Pawel Mrozowski, 2016. "Queues with Dropping Functions and General Arrival Processes," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-23, March.
    2. Mark, Brian L. & Ephraim, Yariv, 2013. "An EM algorithm for continuous-time bivariate Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 504-517.
    3. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. B. Houdt & J. Velthoven & C. Blondia, 2008. "QBD Markov chains on binomial-like trees and its application to multilevel feedback queues," Annals of Operations Research, Springer, vol. 160(1), pages 3-18, April.
    5. Dimitri frosinin & L. Breuer, 2006. "Threshold policies for controlled retrial queues with heterogeneous servers," Annals of Operations Research, Springer, vol. 141(1), pages 139-162, January.
    6. Casale, Giuliano & Sansottera, Andrea & Cremonesi, Paolo, 2016. "Compact Markov-modulated models for multiclass trace fitting," European Journal of Operational Research, Elsevier, vol. 255(3), pages 822-833.
    7. Lin, Lei & Wang, Qian & Sadek, Adel W., 2014. "Border crossing delay prediction using transient multi-server queueing models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 64(C), pages 65-91.
    8. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
    9. Hautphenne, Sophie & Fackrell, Mark, 2014. "An EM algorithm for the model fitting of Markovian binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 19-34.
    10. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.
    11. Peter Buchholz & Jan Kriege, 2017. "Fitting correlated arrival and service times and related queueing performance," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 337-359, April.
    12. 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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