Efficient estimation of blocking probabilities in non-stationary loss networks

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Abstract

This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages21
Publication statusPublished - 2002

Publication series

NameMemorandum Faculty of Mathematical Sciences
PublisherUniversity of Twente, Department of Applied Mathematics
No.1648
ISSN (Print)0169-2690

Keywords

  • MSC-90B18
  • MSC-90B22
  • IR-65834
  • EWI-3468
  • METIS-212329
  • MSC-60K25

Cite this

Boucherie, R. J., & Lassila, P. (2002). Efficient estimation of blocking probabilities in non-stationary loss networks. (Memorandum Faculty of Mathematical Sciences; No. 1648). Enschede: University of Twente, Department of Applied Mathematics.
Boucherie, Richardus J. ; Lassila, P. / Efficient estimation of blocking probabilities in non-stationary loss networks. Enschede : University of Twente, Department of Applied Mathematics, 2002. 21 p. (Memorandum Faculty of Mathematical Sciences; 1648).
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abstract = "This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method.",
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author = "Boucherie, {Richardus J.} and P. Lassila",
note = "Imported from MEMORANDA",
year = "2002",
language = "Undefined",
series = "Memorandum Faculty of Mathematical Sciences",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1648",

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Boucherie, RJ & Lassila, P 2002, Efficient estimation of blocking probabilities in non-stationary loss networks. Memorandum Faculty of Mathematical Sciences, no. 1648, University of Twente, Department of Applied Mathematics, Enschede.

Efficient estimation of blocking probabilities in non-stationary loss networks. / Boucherie, Richardus J.; Lassila, P.

Enschede : University of Twente, Department of Applied Mathematics, 2002. 21 p. (Memorandum Faculty of Mathematical Sciences; No. 1648).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Efficient estimation of blocking probabilities in non-stationary loss networks

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AU - Lassila, P.

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N2 - This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method.

AB - This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method.

KW - MSC-90B18

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KW - IR-65834

KW - EWI-3468

KW - METIS-212329

KW - MSC-60K25

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BT - Efficient estimation of blocking probabilities in non-stationary loss networks

PB - University of Twente, Department of Applied Mathematics

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Boucherie RJ, Lassila P. Efficient estimation of blocking probabilities in non-stationary loss networks. Enschede: University of Twente, Department of Applied Mathematics, 2002. 21 p. (Memorandum Faculty of Mathematical Sciences; 1648).