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Simulation Study for the Clan of Ancestors in a Perfect Simulation Scheme of a Continuous One-Dimensional Loss Network

Author

Listed:
  • Nancy L. Garcia

    (UNICAMP)

  • Nevena Marić

    (Syracuse University)

Abstract

Perfect simulation of a one-dimensional loss network on ℝ with length distribution π and cable capacity C is performed using the clan of ancestors method. Previous works estimated the region of convergence of this scheme using a domination by a branching process. In this work, we show that the domination by the branching process is far from sharp and that there is room for improvement. Moreover, we derive an empirical relation concerning the critical value using simulation studies on the number of rectangles present in the clan of ancestors.

Suggested Citation

  • Nancy L. Garcia & Nevena Marić, 2008. "Simulation Study for the Clan of Ancestors in a Perfect Simulation Scheme of a Continuous One-Dimensional Loss Network," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 453-469, September.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:3:d:10.1007_s11009-007-9058-y
    DOI: 10.1007/s11009-007-9058-y
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    References listed on IDEAS

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    1. Ferrari, Pablo A. & Fernández, Roberto & Garcia, Nancy L., 2002. "Perfect simulation for interacting point processes, loss networks and Ising models," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 63-88, November.
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