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Sojourn Time Estimation in an M/G/∞ Queue with Partial Information

Part of:Inference from stochastic processesOperations research and management science

Published online by Cambridge University Press:  30 January 2018

Nafna Blanghaps,
Yuval Nov and
Gideon Weiss
Nafna Blanghaps*
Affiliation:
University of Haifa
Yuval Nov*
Affiliation:
University of Haifa
Gideon Weiss*
Affiliation:
University of Haifa
*
∗ Postal address: Department of Statistics, University of Haifa, Haifa, 31905, Israel.
∗ Postal address: Department of Statistics, University of Haifa, Haifa, 31905, Israel.
∗ Postal address: Department of Statistics, University of Haifa, Haifa, 31905, Israel.
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Abstract

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We propose an estimator for the cumulative distribution function G of the sojourn time in a steady-state M/G/∞ queueing system, when the available data consists of the arrival and departure epochs alone, without knowing which arrival corresponds to which departure. The estimator generalizes an estimator proposed in Brown (1970), and is based on a functional relationship between G and the distribution function of the time between a departure and the rth latest arrival preceding it. The estimator is shown to outperform Brown's estimator, especially when the system is heavily loaded.

Keywords

M/G/∞sojourn time estimationSmoluchowski processsemiparametric estimation

MSC classification

Primary:62M09: Non-Markovian processes
Secondary:90B22: Queues and service

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 4 , December 2013, pp. 1044 - 1056
Copyright
© Applied Probability Trust 

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