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
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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 -