Estimating Loynes' exponent

  • Authors:
  • Ken R. Duffy;Sean P. Meyn

  • Affiliations:
  • Hamilton Institute, National University of Ireland Maynooth, Maynooth, Ireland;Department of Electrical and Computer Engineering, and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, USA 61801

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2011

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Abstract

Loynes' distribution, which characterizes the one dimensional marginal of the stationary solution to Lindley's recursion, possesses an ultimately exponential tail for a large class of increment processes. If one can observe increments but does not know their probabilistic properties, what are the statistical limits of estimating the tail exponent of Loynes' distribution? We conjecture that in broad generality a consistent sequence of non-parametric estimators can be constructed that satisfies a large deviation principle. We present rigorous support for this conjecture under restrictive assumptions and simulation evidence indicating why we believe it to be true in greater generality.