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

Author

Listed:
  • Wenwen Li

    (University of Haifa
    East China Normal University)

  • Alexander Goldenshluger

    (University of Haifa)

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.

Suggested Citation

  • Wenwen Li & Alexander Goldenshluger, 2024. "Adaptive minimax estimation of service time distribution in the $$M_t/G/\infty $$ M t / G / ∞ queue from departure data," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 81-123, October.
    • Handle: RePEc:spr:queues:v:108:y:2024:i:1:d:10.1007_s11134-024-09921-2
    DOI: 10.1007/s11134-024-09921-2
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