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Nonparametric Inference for Queueing Networks of GeomX/G/∞ Queues in Discrete Time

Part of: Special processes Inference from stochastic processes

Published online by Cambridge University Press:  22 February 2016

Dominic Edelmann  and
Cornelia Wichelhaus
Dominic Edelmann*
Affiliation:
University of Heidelberg
Cornelia Wichelhaus*
Affiliation:
University of Heidelberg
*
∗ Postal address: Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany.
∗ Postal address: Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany.
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Abstract

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We study nonparametric estimation problems for discrete-time stochastic networks of GeomX/G/∞ queues. We assume that we are only able to observe the external arrival and external departure processes at the nodes over a stretch of time. Based on such incomplete information of the system, we aim to construct estimators for the unknown general service time distributions at the nodes without imposing any parametric condition. We propose two different estimation approaches. The first approach is based on the construction of a so-called sequence of differences, and a crucial relation between the expected number of external departures at a node and specific sojourn time distributions in the network. The second approach directly utilizes the structure of the cross-covariance functions between external arrival and departure processes at the nodes. Both methods lead to deconvolution problems which we solve explicitly. A detailed simulation study illustrates the numerical performances of our estimators and shows their advantages and disadvantages.

Keywords

Cross-covariancediscrete deconvolutiondiscrete-time queueing systemnonparametric statistics for queuessojourn time estimation

MSC classification

Primary: 60K25: Queueing theory
Secondary: 62M05: Markov processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 790 - 811
Copyright
© Applied Probability Trust 

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