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New Results About Weakly Equivalent MAP 2 and MAP 3 Processes

Author

Listed:
  • Pepa Ramírez-Cobo

    (IMUS, Institute of Mathematics of University of Seville)

  • Rosa E. Lillo

    (University Carlos III of Madrid)

Abstract

In Ramírez-Cobo et al. (J Appl Probab 47(3):630–649, 2010b), weakly equivalent second order Markovian arrival processes (noted MAP 2s) are introduced and partially characterized. In this work we look into weak equivalence in detail and provide a complete characterization of weakly equivalent MAP 2s. The analogous problem for the MAP 3 case is partially solved.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9227-x
    DOI: 10.1007/s11009-011-9227-x
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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.
    2. 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.
    3. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael & del Carmen Segovia, Maria, 2009. "Replacement policy in a system under shocks following a Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 497-502.
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