Monte Carlo Summation Applied to Product-Form Loss Networks

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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 27 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.