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Monte Carlo Summation Applied to Product-Form Loss Networks

Published online by Cambridge University Press:  27 July 2009

Keith W. Ross  and
Jie Wang
Keith W. Ross
Affiliation:
Department of SystemsUniversity of Pennsylvania Philadelphia, Pennsylvania 19104
Jie Wang
Affiliation:
Department of SystemsUniversity of Pennsylvania Philadelphia, Pennsylvania 19104
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Abstract

Loss networks with direct routing have a product-form solution for their equilibrium probabilities. The product-form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. We propose the application of Monte Carlo summation in order to determine the normalization constant, the blocking probabilities, and the revenue sensitivities. We show that if the proper sampling technique is employed, then the computational effort of Monte Carlo summation is independent of link capacities. We also discuss the application of importance sampling, antithetic variates, and indirect estimation via Little's formula. The method is illustrated with a four-leaf star network supporting multirate traffic.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 3 , July 1992 , pp. 323 - 348
Copyright
Copyright © Cambridge University Press 1992

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