article

Parameter estimation for Markov modulated Poisson processes via the EM algorithm with time discretization

Authors:

Li Deng,

Jon W. MarkAuthors Info & Claims

Telecommunications Systems, Volume 1, Issue 1

Pages 321 - 338

https://doi.org/10.1007/BF02136167

Published: 01 December 1993 Publication History

Abstract

The Markov modulated Poisson process (MMPP) has been proposed as a suitable model for characterizing the input traffic to a statistical multiplexer [6]. This paper describes a novel method of parameter estimation for MMPPs. The idea is to employ time discretization to convert an MMPP from the continuous-time domain into the discrete-time domain and then to use a powerful statistical inference technique, known as the EM algorithm, to obtain maximum-likelihood estimates of the model parameters. Tests conducted through a series of simulation experiments indicate that the new method yields results that are significantly more accurate compared to the method described in [8]. In addition, the new method is more flexible and general in that it is applicable to MMPPs with any number of states while retaining nearly constant simplicity in its implementation. Detailed experimental results on the sensitivity of the estimation accuracy to (1) the initialization of the model, (2) the size of the observation interarrival interval data available for the estimation, and (3) the inherent separability of the MMPP states are presented.

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Cited By

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Ngoc HNakagawa K(2018)Online Estimation for Packet Loss Probability of MMPP/D/1 Queuing by Importance SamplingProceedings of the 9th International Symposium on Information and Communication Technology10.1145/3287921.3287928(145-149)Online publication date: 6-Dec-2018
https://dl.acm.org/doi/10.1145/3287921.3287928
Mrozowski PChydzinski A(2018)Queues with Dropping Functions and Autocorrelated ArrivalsMethodology and Computing in Applied Probability10.1007/s11009-016-9534-320:1(97-115)Online publication date: 1-Mar-2018
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Okamura HYi ZDohi T(2015)Network survivability modeling and analysis for power-aware MANETs by Markov regenerative processesTelecommunications Systems10.1007/s11235-015-9989-560:4(471-484)Online publication date: 1-Dec-2015
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Published In

Telecommunications Systems Volume 1, Issue 1

December 1993

395 pages

ISSN:1018-4864

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Kluwer Academic Publishers

United States

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Published: 01 December 1993

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Ngoc HNakagawa K(2018)Online Estimation for Packet Loss Probability of MMPP/D/1 Queuing by Importance SamplingProceedings of the 9th International Symposium on Information and Communication Technology10.1145/3287921.3287928(145-149)Online publication date: 6-Dec-2018
https://dl.acm.org/doi/10.1145/3287921.3287928
Mrozowski PChydzinski A(2018)Queues with Dropping Functions and Autocorrelated ArrivalsMethodology and Computing in Applied Probability10.1007/s11009-016-9534-320:1(97-115)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s11009-016-9534-3
Okamura HYi ZDohi T(2015)Network survivability modeling and analysis for power-aware MANETs by Markov regenerative processesTelecommunications Systems10.1007/s11235-015-9989-560:4(471-484)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1007/s11235-015-9989-5
Okamura HKishikawa HDohi T(2013)Application of deterministic annealing EM algorithm to MAP/PH parameter estimationTelecommunications Systems10.1007/s11235-013-9717-y54:1(79-90)Online publication date: 1-Sep-2013
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Chen ZVijayan SBarbieri RWilson MBrown E(2009)Discrete-and continuous-time probabilistic models and algorithms for inferring neuronal up and down statesNeural Computation10.1162/neco.2009.06-08-79921:7(1797-1862)Online publication date: 1-Jul-2009
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Okamura HDohi TTrivedi K(2009)Markovian arrival process parameter estimation with group dataIEEE/ACM Transactions on Networking10.1109/TNET.2008.200875017:4(1326-1339)Online publication date: 1-Aug-2009
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Chydzinski A(2007)Time to buffer overflow in an MMPP queueProceedings of the 6th international IFIP-TC6 conference on Ad Hoc and sensor networks, wireless networks, next generation internet10.5555/1772322.1772416(879-889)Online publication date: 14-May-2007
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Okamura HKamahara YDohi TGlynn P(2007)Estimating Markov-modulated compound Poisson processesProceedings of the 2nd international conference on Performance evaluation methodologies and tools10.5555/1345263.1345299(1-8)Online publication date: 22-Oct-2007
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Klemm ALindemann CLohmann M(2003)Modeling IP traffic using the batch Markovian arrival processPerformance Evaluation10.1016/S0166-5316(03)00067-154:2(149-173)Online publication date: 1-Oct-2003
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