Efficient heuristics for simulating rare events in queuing networks
نویسندگان
چکیده
Resumé / Ðåçþìå In this thesis we propose state-dependent importance sampling heuristics to estimate the probability of population overflow in queuing networks. These heuristics capture state-dependence along the boundaries (when one or more queues are almost empty) which is crucial for the asymptotic efficiency of the change of measure. The approach does not require difficult (and often intractable) mathematical analysis or costly optimization involved in adaptive importance sampling methodologies. Experimental results on tandem, parallel, feed-forward, and a 2-node feedback Jackson queuing networks as well as a 2-node tandem non-Markovian network suggest that the proposed heuristics yield asymptotically efficient estimators, sometimes with bounded relative error. For these queuing networks no state-independent importance sampling techniques are known to be efficient. In dit proefschrift introduceren we toestandsafhankelijke importance sampling heuristieken om de waarschijnlijkheid van overflow van de totale populatie in netwerken van wachtrijsystemen te schatten. Deze heuristieken hebben de juiste toestandsafhankelijkheid langs de grenzen (als een of meer wachtrijen bijna leeg zijn). Dit is cruciaal voor de asymptotische efficiëntie van de kansmaatverandering. De aanpak vereist geen moeilijke (en vaak ingewikkelde) wiskundige analyse of kostbare optimalisatie zoals in adaptieve importance sampling methodieken. Experimentele resultaten voor tandem, parallel, feed-forward en 2-node feedback Jackson wachtrijnetwerken alsook voor een 2-node tandem non-Markov netwerk suggereren dat de voorgestelde heuristieken asymptotisch efficiënte schatters opleveren, soms met begrensde relatieve fout. Voor deze wachtrijnetwerken zijn geen efficiënte toestandsonafhankelijke importance sampling technieken bekend.  äàííîé ðàáîòå ïðåäëàãàþòñÿ ýâðèñòè÷åñêèå ìåòîäû ïîëó÷åíèÿ îöåíêè âåðîÿòíîñòè ïåðåïîëíåíèÿ ñåòè ñ ïîìîùüþ çàâèñèìîé îò ñîñòîÿíèÿ ñåòè âûáîðêè ïî âàæíîñòè. Ìåòîäû îòðàæàþò çàâèñèìîñòü âäîëü ãðàíèö ïðîñòðàíñòâà ñîñòîÿíèé ñåòè (â ñëó÷àå, êîãäà îäíà èëè áîëåå î÷åðåäè ïî÷òè ïóñòû), èìåþùóþ ðåøàþùåå çíà÷åíèå äëÿ àñèìïòîòè÷åñêîé ýôôåêòèâíîñòè çàìåíû ìåðû. Ïîäõîä íå òðåáóåò ñëîæíîãî (è ÷àñòî íåðàçðåøèìîãî) ìàòåìàòè÷åñêîãî àíàëèçà è îïòèìèçàöèîííûõ çàòðàò, ó÷àñòâóþùèõ â àäàïòàòèâíûõ ìåòîäèêàõ íàõîæäåíèÿ âûáîðêè ïî âàæíîñòè. Ðåçóëüòàòû ýêñïåðèìåíòîâ íà òàíäåìíûõ, ïàðàëëåëüíûõ, ñåòÿõ ñ ïðÿìîé ñâÿçüþ, è 2-õ óçåëíûõ Äæåêñîí ñåòÿõ ñ îáðàòíîé ñâÿçüþ, à òàêæå 2-õ óçåëíûõ òàíäåìíûõ íå-Äæåêñîí ñåòÿõ, ïîäòâåðæäàþò, ÷òî ïðåäëàãàåìûé ýâðèñòè÷åñêèé ïîäõîä äàåò àñèìïòîòè÷åñêè ýôôåêòèâíûå îöåíêè, â íåêîòîðûõ ñëó÷àÿõ äàæå
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Extension of heuristics for simulating population overflow in Jackson tandem queuing networks to non-Markovian tandem queuing networks
In this paper we extend previously proposed state-dependent importance sampling heuristics for simulation of population overflow in Markovian tandem queuing networks to nonMarkovian tandem networks, and experimentally demonstrate the asymptotic efficiency of the resulting heuristics.
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