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On the identifiability of the two-state BMAP

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  • Rodríguez César, Joanna Virginia
  • Ramírez-Cobo, Pepa

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 is an open problem concerning BMAP-related processes. This paper explores the identifiability issue of the two-state BMAP noted BMAP2(k), where k is the maximum batch arrival size. It is proven that for k = 2 the process cannot be identified, under the assumptions that both the interarrival times and batches sizes are observed. Additionally, a method to obtain an equivalent BMAP2(2) to a given one is provided.

Suggested Citation

  • Rodríguez César, Joanna Virginia & Ramírez-Cobo, Pepa, 2012. "On the identifiability of the two-state BMAP," DES - Working Papers. Statistics and Econometrics. WS ws120201, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws120201
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    References listed on IDEAS

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    1. Qi-Ming He & Hanqin Zhang, 2008. "An Algorithm for Computing Minimal% Coxian Representations," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 179-190, May.
    2. 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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