Rare-Event Simulation for Distribution Networks

Autor:	Blanchet, Jose, Li, Juan, Nakayama, Marvin K.
Rok vydání:	2017
Předmět:	Mathematics - Optimization and Control Mathematics - Numerical Analysis 65C05 (Primary) 90B15 (Secondary) 90C35 (Tertiary)
Druh dokumentu:	Working Paper
Popis:	We model equilibrium allocations in a distribution network as the solution of a linear program (LP) which minimizes the cost of unserved demands across nodes in the network. The constraints in the LP dictate that once a given node's supply is exhausted, its unserved demand is distributed among neighboring nodes. All nodes do the same and the resulting solution is the equilibrium allocation. Assuming that the demands are random (following a jointly Gaussian law), our goal is to study the probability that the optimal cost (i.e. the cost of unserved demands in equilibrium) exceeds a large threshold, which is a rare event. Our contribution is the development of importance sampling and conditional Monte Carlo algorithms for estimating this probability. We establish the asymptotic efficiency of our algorithms and also present numerical results which illustrate strong performance of our procedures. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1706.05602 Zobrazit plný text záznamu View this record from Arxiv