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- Title
Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation.
- Authors
Boxma, O. J.; Cahen, E. J.; Koops, D.; Mandjes, M.
- Abstract
We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient importance sampling algorithms with provable performance guarantees. For linear stochastic fluid networks without modulation, we prove that the number of runs needed (so as to obtain an estimate with a given precision) increases polynomially (whereas the probability under consideration decays essentially exponentially); for networks operating in the slow modulation regime, our algorithm is asymptotically efficient. Our techniques are in the tradition of the rare-event simulation procedures that were developed for the sample-mean of i.i.d. one-dimensional light-tailed random variables, and intensively use the idea of exponential twisting. In passing, we also point out how to set up a recursion to evaluate the (transient and stationary) moments of the joint storage level in Markov-modulated linear stochastic fluid networks.
- Subjects
STOCHASTIC processes; SIMULATION methods &; models; MARKOV processes; PROBABILITY theory; SET theory; STATISTICAL sampling
- Publication
Methodology & Computing in Applied Probability, 2019, Vol 21, Issue 1, p125
- ISSN
1387-5841
- Publication type
Article
- DOI
10.1007/s11009-018-9644-1