# Rare-Event Simulation for Distribution Networks

arXiv: https://arxiv.org/abs/1706.05602 · HTML: https://mlsanity.com/paper/1706.05602/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Achieving Efficiency in Black Box Simulation of Distribution Tails with Self-structuring Importance Samplers](https://mlsanity.com/paper/2102.07060/) (2021)

## Abstract (arXiv)

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.