Simulating tail probabilities in GI/GI.1 queues and insurance risk processes with subexponentail distributions
Nam Kyoo Boots; Perwez Shahabuddin
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.
Year of publication: |
2001
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Authors: | Boots, Nam Kyoo ; Shahabuddin, Perwez |
Publisher: |
Rotterdam [u.a.] : Tinbergen Inst. |
Subject: | importance sampling | rare event simulation | subexponential distributions | insurance risk | GI/GI/1 queues | Simulation | Wahrscheinlichkeitsrechnung | Probability theory | Warteschlangentheorie | Queueing theory | Statistische Verteilung | Statistical distribution |
Saved in:
freely available
Extent: | Online-Ressource (36 S.) |
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Series: | Discussion paper / Tinbergen Institute. - Rotterdam [u.a.] : [Verlag nicht ermittelbar], ISSN 0929-0834, ZDB-ID 2435783-2. - Vol. 2001,012 |
Type of publication: | Book / Working Paper |
Type of publication (narrower categories): | Arbeitspapier ; Working Paper ; Graue Literatur ; Non-commercial literature |
Language: | English |
Notes: | Systemvoraussetzungen: Acrobat Reader |
Other identifiers: | hdl:10419/85831 [Handle] |
Source: | ECONIS - Online Catalogue of the ZBW |
Persistent link: https://www.econbiz.de/10011313925