Adaptive minimax estimation of service time distribution in the $$M_t/G/\infty $$ M t / G / ∞ queue from departure data

Wenwen Li and Alexander Goldenshluger ()
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Wenwen Li: University of Haifa
Alexander Goldenshluger: University of Haifa

Queueing Systems: Theory and Applications, 2024, vol. 108, issue 1, No 3, 123 pages

Abstract: Abstract This article deals with the problem of estimating the service time distribution of the $$M_t/G/\infty $$ M t / G / ∞ queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure.

Keywords: $$M_t/G/\infty $$ M t / G / ∞ queue; Deconvolution; Poisson process; Laplace transform; Minimax risk; Adaptive estimation; 60K25; 62G05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11134-024-09921-2

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