Abstract
Switched Poisson Processes and Interrupted Poisson Processes are often employed to characterize traffic streams in distributed computer and communications systems, especially in investigations of overflow processes in telecommunication networks. With these processes, input streams having inter-segment correlations and high variance as well as state-dependent traffic can properly be modelled. In this paper we first derive an approximation method to describe the Generalized Switched Poisson processes in conjunction with a renewal assumption. As a special case of this class of processes, the class of Interrupted Poisson processes is also included in the investigation. As a result, a generalization of the well-known class of Interrupted Poisson processes is obtained. It is shown that the renewal property is also given for this general class of Interrupted Poisson processes having generally distributed off-phase. To illustrate the accuracy of the presented renewal approximation of Generalized Switched Poisson processes and to show the major properties of the General Interrupted Poisson processes, applications to some basic queueing systems are discussed by means of numerical results.
Zusammenfassung
Zur Beschreibung von Verkehrsströmen in modernen Rechner- und Kommunikationssystemen werden zunehmend Punktprozesse mit komplexen Charakteristiken benötigt. Die Klassen von unterbrochenen Poisson-Prozessen (IPP: Interrupted Poisson Process) sowie von geschalteten Poisson-Prozessen (SPP: Switched Poisson Process) finden hier häufig Anwendung, z. B. in Untersuchungen von Überlaufverkehr in Fernsprechnetzen, hochvarianzigen Datenströmen in Paketvermittlungssystemen etc. In diesem Beitrag wird zunächst der verallgemeinerte SPP-Prozeß untersucht und dessen Verteilungsfunktion entwickelt, wobei eine Approximation mittels einer Erneuerungsannahme vorgenommen wird. Danach wird eine exakte Beschreibung des verallgemeinerten IPP-Prozesses vorgestellt, in der einige Prozeßbeschreibungen in der Literatur als Sonderfalle enthalten sind. Abschließend werden Parameterstudien anhand einiger einstufiger Verkehrsmodelle durchgeführt.
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This work was done while the author was with Institute of Communications Switching and Data Technics, University of Stuttgart, Seidenstrasse 36, D-7000 Stuttgart 1, FRG.
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Tran-Gia, P. A class of renewal Interrupted Poisson Processes and applications to queueing systems. Zeitschrift für Operations Research 32, 231–250 (1988). https://doi.org/10.1007/BF01928925
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DOI: https://doi.org/10.1007/BF01928925