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September 2014 Nonparametric inference for queueing networks of GEOMX/G/∞ queues in discrete time
Dominic Edelmann, Cornelia Wichelhaus
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Adv. in Appl. Probab. 46(3): 790-811 (September 2014). DOI: 10.1239/aap/1409319560

Abstract

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.

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Dominic Edelmann. Cornelia Wichelhaus. "Nonparametric inference for queueing networks of GEOMX/G/∞ queues in discrete time." Adv. in Appl. Probab. 46 (3) 790 - 811, September 2014. https://doi.org/10.1239/aap/1409319560

Information

Published: September 2014
First available in Project Euclid: 29 August 2014

zbMATH: 1306.60136
MathSciNet: MR3254342
Digital Object Identifier: 10.1239/aap/1409319560

Subjects:
Primary: 60K25
Secondary: 62M05

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 3 • September 2014
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