Nonparametric inference from the M/G/1 workload

Susan M. Pitts

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

Consider an M/G/1 queue with unknown service-time distribution and unknown traffic intensity ρ. Given systematically sampled observations of the workload, we construct estimators of ρ and of the service-time distribution function, and we study asymptotic properties of these estimators.

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References

1987Applied Probability and Queues 1981Recursive Evaluation of a Family of Compound Distributions 1997Heavy tail modeling and teletraffic data: special invited paper 1995Heavy Tail Modelling and Teletraffic Data 2003Decompounding: an estimation problem for Poisson random sums 1999Non-parametric Estimation for the M/G/∞ Queue 2004Nonparametric Inference About Service Time Distribution from Indirect Measurements

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2017Parameter and State Estimation in Queues and Related Stochastic Models: A Bibliography 2022Estimating Customer Impatience in a Service System With Unobserved Balking 2008Asymptotic Inference for Waiting Times and Patiences in Queues with Abandonment 2019Estimating the input of a Lévy-driven queue by Poisson sampling of the workload process

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