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Nonidentifiability of the Two-State BMAP

Author

Listed:
  • Joanna Rodríguez

    (Universidad Carlos III)

  • Rosa E. Lillo

    (Universidad Carlos III)

  • Pepa Ramírez-Cobo

    (Universidad de Cádiz)

Abstract

The capability of modeling non-exponentially distributed and dependent inter-arrival times as well as correlated batches makes the Batch Markovian Arrival Processes (BMAP) suitable in different real-life settings as teletraffic, queueing theory or actuarial contexts. An issue to be taken into account for estimation purposes is the identifiability of the process. This paper explores the identifiability of the stationary two-state BMAP noted as BMAP 2 (k), where k is the maximum batch arrival size, under the assumptions that both the interarrival times and batches sizes are observed. It is proven that for k ≥ 2 the process cannot be identified. The proof is based on the construction of an equivalent BMAP 2(k) to a given one, and on the decomposition of a BMAP 2 (k) into k BMAP 2 (2)s.

Suggested Citation

  • Joanna Rodríguez & Rosa E. Lillo & Pepa Ramírez-Cobo, 2016. "Nonidentifiability of the Two-State BMAP," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 81-106, March.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:1:d:10.1007_s11009-014-9401-z
    DOI: 10.1007/s11009-014-9401-z
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    References listed on IDEAS

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    1. Bodrog, L. & Heindl, A. & Horváth, G. & Telek, M., 2008. "A Markovian canonical form of second-order matrix-exponential processes," European Journal of Operational Research, Elsevier, vol. 190(2), pages 459-477, October.
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    4. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    5. Falin, G.I., 2010. "A single-server batch arrival queue with returning customers," European Journal of Operational Research, Elsevier, vol. 201(3), pages 786-790, March.
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    Cited by:

    1. 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.
    2. Yera, Yoel G. & Lillo, Rosa E. & Nielsen, Bo F. & Ramírez-Cobo, Pepa & Ruggeri, Fabrizio, 2021. "A bivariate two-state Markov modulated Poisson process for failure modeling," Reliability Engineering and System Safety, Elsevier, vol. 208(C).

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