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Sengupta's invariant relationship and its application to waiting time inference

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  14 July 2016

Hiroshi Toyoizumi
Hiroshi Toyoizumi*
Affiliation:
NTT Telecommunication Networks Laboratories
*
∗Postal address: NTT Multimedia Networks Laboratories, 3–9–11, Midori-cho, Musashino-shi, Tokyo 180, Japan. E-mail: toyo@hashi.tn1.ntt.jp
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Abstract

This paper presents a new proof of Sengupta's invariant relationship between virtual waiting time and attained sojourn time and its application to estimating the virtual waiting time distribution by counting the number of arrivals and departures of a G/G/1 FIFO queue. Since this relationship does not require any parametric assumptions, our method is non-parametric. This method is expected to have applications, such as call processing in communication switching systems, particularly when the arrival or service process is unknown.

Keywords

G/G/1 QUEUESENGUPTA'S INVARIANT RELATIONSHIPVIRTUAL WAITING TIMEATTAINED SOJOURN TIMECOMMUNICATION SWITCHING SYSTEMQUEUE INFERENCE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G55: Point processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 795 - 799
Copyright
Copyright © Applied Probability Trust 1997 

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