Linear stochastic fluid networks
| Autor: | David Koops, Onno Boxma, Ewan Jacov Cahen, Michel Mandjes |
|---|---|
| Přispěvatelé: | Stochastic Operations Research, Stochastics (KDV, FNWI) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Importance sampling General Mathematics 0211 other engineering and technologies 02 engineering and technology 01 natural sciences 010104 statistics & probability Stochastic processes Modulation (music) FOS: Mathematics Rare events Applied mathematics 0101 mathematics Queues Queue Mathematics 021103 operations research Stochastic process Probability (math.PR) Recursion (computer science) Exponential function Linear networks Random variable Mathematics - Probability |
| Zdroj: | Methodology and Computing in Applied Probability, 21(1), 125-153. Springer Methodology and Computing in Applied Probability, 21(1). Springer Netherlands |
| ISSN: | 1387-5841 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|