Large deviations and fast simulation in the presence of boundaries

Søren Asmussen, Pascal Fuckerieder, Manfred Jobmann and Hans-Peter Schwefel

Stochastic Processes and their Applications, 2002, vol. 102, issue 1, 1-23

Abstract: Let [tau](x)=inf{t>0: Q(t)[greater-or-equal, slanted]x} be the time of first overflow of a queueing process {Q(t)} over level x (the buffer size) and . Assuming that {Q(t)} is the reflected version of a Lévy process {X(t)} or a Markov additive process, we study a variety of algorithms for estimating z by simulation when the event {[tau](x)[less-than-or-equals, slant]T} is rare, and analyse their performance. In particular, we exhibit an estimator using a filtered Monte Carlo argument which is logarithmically efficient whenever an efficient estimator for the probability of overflow within a busy cycle (i.e., for first passage probabilities for the unrestricted netput process) is available, thereby providing a way out of counterexamples in the literature on the scope of the large deviations approach to rare events simulation. We also add a counterexample of this type and give various theoretical results on asymptotic properties of , both in the reflected Lévy process setting and more generally for regenerative processes in a regime where T is so small that the exponential approximation for [tau](x) is not a priori valid.

Keywords: Buffer; overflow; Exponential; change; of; measure; Filtered; Monte; Carlo; Importance; sampling; Lévy; process; Local; time; Queueing; theory; Rare; event; Reflection; Regenerative; process; Saddlepoint (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (2)

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