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

Abstract

Abstract This article deals with the problem of estimating the service time distribution of the $$M_t/G/\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>G</mml:mi> <mml:mo>/</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> 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.

Locations

• Queueing Systems - View - PDF