  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.
