Summary
In this paper we study theE k /D/r queueing system. The steady state equations are derived and the queue lenth probability generating function is determined. The average number of customers in the system and other related quantities are determined in closed form in terms of the roots of an equation, which can be easily obtained by standard numerical techniques. Also a computational procedure for evaluating the steady state probability distribution of the number of customers in the system is developed. Numerical results of the average queueing times are given fork=2,r=1, 2, ..., 10 and the whole range of utilization factors.
Zusammenfassung
Für das WartemodellE k /D/r wird über die „steady state Gleichungen“ die erzeugende Funktion der Verteilung der Warte Schlangenlänge hergeleitet. Die mittlere Zahl der Einheiten im System und verwandte Größen werden in geschlossener Form mit Hilfe der Wurzeln einer transzendenten Gleichung dargestellt. Diese Wurzeln können leicht mit numerischen Standard-verfahren bestimmt werden. Ein Algorithmus zur Bestimmung der stationären Verteilung der Zahl der Einheiten im System wird entwickelt. Numerische Ergebnisse für die mittleren Wartezeiten werden fürk=2,r=1, 2, ..., 10, und variable Verkehrsintensität angegeben.
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An erratum to this article is available at http://dx.doi.org/10.1007/BF01720223.
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Xerocostas, D.A., Demertzes, C. Steady state solution of theE k /D/r queueing model. OR Spektrum 4, 47–51 (1982). https://doi.org/10.1007/BF01837024
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DOI: https://doi.org/10.1007/BF01837024