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Matchmaking and Testing for Exponentiality in the M/G/∞ Queue

Part of: Special processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Rudolf Grübel  and
Hendrik Wegener
Rudolf Grübel*
Affiliation:
Leibniz Universität Hannover
Hendrik Wegener*
Affiliation:
Leibniz Universität Hannover
*
∗ Postal address: Institut für Mathematische Stochastik, Leibniz Universität Hannover, Postfach 6009, D-30060 Hannover, Germany.
∗ Postal address: Institut für Mathematische Stochastik, Leibniz Universität Hannover, Postfach 6009, D-30060 Hannover, Germany.
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Abstract

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Customers arrive sequentially at times x 1 < x 2 < · · · < x n and stay for independent random times Z 1, …, Z n > 0. The Z-variables all have the same distribution Q. We are interested in situations where the data are incomplete in the sense that only the order statistics associated with the departure times x i + Z i are known, or that the only available information is the order in which the customers arrive and depart. In the former case we explore possibilities for the reconstruction of the correct matching of arrival and departure times. In the latter case we propose a test for exponentiality.

Keywords

AsymptoticsKendall's τlog-concave densitylog-convex densityqueuepredictionpermutation

MSC classification

Secondary: 60K25: Queueing theory 62M07: Non-Markovian processes 62M20: Prediction

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 131 - 144
Copyright
Copyright © Applied Probability Trust 2011 

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