TY - JOUR

T1 - Linear stochastic fluid networks

T2 - rare-event simulation and Markov modulation

AU - Boxma, O.J.

AU - Cahen, E.J.

AU - Koops, D.

AU - Mandjes, M.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

KW - Importance sampling

KW - Linear networks

KW - Queues

KW - Rare events

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85047978824&partnerID=8YFLogxK

U2 - 10.1007/s11009-018-9644-1

DO - 10.1007/s11009-018-9644-1

M3 - Article

AN - SCOPUS:85047978824

VL - 21

SP - 125

EP - 153

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 1

ER -