IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws120201.html
   My bibliography  Save this paper

On the identifiability of the two-state BMAP

Author

Listed:
  • Rodríguez César, Joanna Virginia
  • Lillo Rodríguez, Rosa Elvira
  • 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 & Lillo Rodríguez, Rosa Elvira & 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
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/14546/ws120201.pdf?sequence=1
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. Pepa Ramírez-Cobo & Rosa E. Lillo, 2012. "New Results About Weakly Equivalent MAP 2 and MAP 3 Processes," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 421-444, September.
    4. Pepa Ramírez-Cobo & Rosa Lillo & Michael Wiper, 2014. "Identifiability of the MAP 2 /G/1 queueing system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 274-289, April.
    5. Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2015. "Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 126-133.
    6. 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).
    7. Sunkyo Kim, 2016. "Minimal LST representations of MAP(n)s: Moment fittings and queueing approximations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(7), pages 549-561, October.
    8. 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.
    9. Qi-Ming He & Hanqin Zhang & Jungong Xue, 2011. "Algorithms for Coxianization of Phase-Type Generators," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 153-164, February.
    10. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:ws120201. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.