TY - GEN

T1 - A conditional Monte Carlo method for estimating the failure probability of a distribution network with random demands

AU - Blanchet, Jose

AU - Li, Juan

AU - Nakayama, Marvin K.

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - We consider a model of an irreducible network in which each node is subjected to a random demand, where the demands are jointly normally distributed. Each node has a given supply that it uses to try to meet its demand; if it cannot, the node distributes its unserved demand equally to its neighbors, which in turn do the same. The equilibrium is determined by solving a linear program (LP) to minimize the sum of the unserved demands across the nodes in the network. One possible application of the model might be the distribution of electricity in an electric power grid. This paper considers estimating the probability that the optimal objective function value of the LP exceeds a large threshold, which is a rare event. We develop a conditional Monte Carlo algorithm for estimating this probability, and we provide simulation results indicating that our method can significantly improve statistical efficiency.

AB - We consider a model of an irreducible network in which each node is subjected to a random demand, where the demands are jointly normally distributed. Each node has a given supply that it uses to try to meet its demand; if it cannot, the node distributes its unserved demand equally to its neighbors, which in turn do the same. The equilibrium is determined by solving a linear program (LP) to minimize the sum of the unserved demands across the nodes in the network. One possible application of the model might be the distribution of electricity in an electric power grid. This paper considers estimating the probability that the optimal objective function value of the LP exceeds a large threshold, which is a rare event. We develop a conditional Monte Carlo algorithm for estimating this probability, and we provide simulation results indicating that our method can significantly improve statistical efficiency.

UR - http://www.scopus.com/inward/record.url?scp=84863294168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863294168&partnerID=8YFLogxK

U2 - 10.1109/WSC.2011.6148075

DO - 10.1109/WSC.2011.6148075

M3 - Conference contribution

AN - SCOPUS:84863294168

SN - 9781457721083

T3 - Proceedings - Winter Simulation Conference

SP - 3832

EP - 3843

BT - Proceedings of the 2011 Winter Simulation Conference, WSC 2011

T2 - 2011 Winter Simulation Conference, WSC 2011

Y2 - 11 December 2011 through 14 December 2011

ER -