NDLI: Simulating Tail Probabilities in GI/GI.1 Queues and Insurance Risk Processes with Subexponentail Distributions

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Simulating Tail Probabilities in GI/GI.1 Queues and Insurance Risk Processes with Subexponentail Distributions

Content Provider	Semantic Scholar
Author	Boots, Nam Kyoo Shahabuddin, Perwez
Copyright Year	2001
Abstract	This paper deals with estimating small tail probabilities of thesteady-state waiting time in a GI/GI/1 queue withheavy-tailed (subexponential) service times. The problem ofestimating infinite horizon ruin probabilities in insurancerisk processes with heavy-tailed claims can be transformed into thesame framework. It is well-known that naivesimulation is ineffective for estimating small probabilities andspecial fast simulation techniques like importancesampling, multilevel splitting, etc., have to be used. Though thereexists a vast amount of literature on the rare eventsimulation of queuing systems and networks with light-taileddistributions, previous fast simulation techniques forqueues with subexponential service times have been confined to theM/GI/1 queue. The general approach is to use thePollaczek-Khintchine transformation to convert the problem into thatof estimating the tail distribution of a geometricsum of independent subexponential random variables. However, no suchuseful transformation exists when one goesfrom Poisson arrivals to general interarrival-time distributions. Wedescribe and evaluate an approach that is based ondirectly simulating the random walk associated with the waiting-timeprocess of the GI/GI/1 queue, using a change ofmeasure called delayed subexponential twisting -an importancesampling idea recently developed and found useful inthe context of M/GI/1 heavy-tailed simulations.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://dare.ubvu.vu.nl/bitstream/handle/1871/9457/01012.pdf?isAllowed=y&sequence=1
Alternate Webpage(s)	https://www.econstor.eu/bitstream/10419/85831/1/01012.pdf
Alternate Webpage(s)	http://dare.ubvu.vu.nl/bitstream/handle/1871/9457/01012.pdf?sequence=1
Alternate Webpage(s)	http://papers.tinbergen.nl/01012.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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