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Erhaltungsgesetze fur das Modell Mr / Gr / 1 / ∞ in der Klasse der konservativen Abfertigungsdisziplinen

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  • Safarian, Mher

Abstract

[Einführung] Die Erhaltungsgesetze sind bedeutende Gesetzmäßigkeiten in der Warteschlangentheorie (oder Bedienungstheorie) [4], [5]. Sie stellen eine invariante Gleichung in der breiten Klasse der Abfertigungsdisziplinen dar. Die Abfertigungsdisziplinen sind die Regeln, welche die Reihenfolge von wartenden Aufträgen innerhalb der Warteschlange bestimmen. Die Erhaltungsgesetze werden meist in der Klasse der konservativen Abfertigungsdisziplinen formuliert unter Annahme, dass innerhalb solcher Klasse der akkumulierte Wert der unvollendeten Arbeit nicht von der zugrundegelegten Abfertigungsdisziplin abhängt [8]. Die Abfertigungsdisziplin heißt also konservativ, falls die Anforderung auf eine belegte Bedieneinheit trifft und in der ersten Position der Warteschlange wartet, bis sie zum Zeitpunkt t bedient wird. In der Klasse von solcher Disziplinen gelten verschiedene Arten von Erhaltungsgesetze, wie z.B. die Erhaltungsgesetze der verbleibenden Aufenthaltszeit der Forderung oder Erhaltungsgesetze der Aufträge usw.. Es gibt auch die Erhaltungsgesetze, die verschiedene Charakteristiken verbinden. Dazu gehört auch das Littles Gesetz, welches einen Zusammenhang zwischen der durchschnittlichen Anzahl von Kunden in einem Wartesystem und der Verweildauer herleitet [6], [7]. Es sei hier noch bemerkt, dass das Littles Gesetz sowohl in der Klasse von nicht konservativen Disziplinen als auch für Netzwerke (wie z. B. die Warteschlangen mehrere Schalter einer Bank oder Check-in-Schalter am Flughafen) aus Wartesystemen gilt. In der vorliegenden Arbeit beschäftigen wir uns mit einer Verallgemeinerung und Präzisierungen des Erhaltungsgesetzes von L. Kleinrock [5] für das Bedienungsmodell Mr / Gr / 1 / ∞ in der Klasse der konservativen Disziplin, wobei die Bedienungsunterbrechungen der Forderungen im Modell zugelassen werden.

Suggested Citation

  • Safarian, Mher, 2014. "Erhaltungsgesetze fur das Modell Mr / Gr / 1 / ∞ in der Klasse der konservativen Abfertigungsdisziplinen," Working Paper Series in Economics 58, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  • Handle: RePEc:zbw:kitwps:58
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