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November 1998 Uniform acceleration expansions for Markov chains with time-varying rates
William A. Massey, Ward Whitt
Ann. Appl. Probab. 8(4): 1130-1155 (November 1998). DOI: 10.1214/aoap/1028903375

Abstract

We study uniform acceleration (UA) expansions of finite-state continuous-time Markov chains with time-varying transition rates. The UA expansions can be used to justify, evaluate and refine the pointwise stationary approximation, which is the steady-state distribution associated with the time-dependent generator at the time of interest. We obtain UA approximations from these UA asymptotic expansions. We derive a time-varying analog to the uniformization representation of transition probabilities for chains with constant transition rates, and apply it to establish asymptotic results related to the UA asymptotic expansion. These asymptotic results can serve as appropriate time-varying analogs to the notions of stationary distributions and limiting distributions. We illustrate the UA approximations by doing a numerical example for the time-varying Erlang loss model.

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William A. Massey. Ward Whitt. "Uniform acceleration expansions for Markov chains with time-varying rates." Ann. Appl. Probab. 8 (4) 1130 - 1155, November 1998. https://doi.org/10.1214/aoap/1028903375

Information

Published: November 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0937.60066
MathSciNet: MR1661164
Digital Object Identifier: 10.1214/aoap/1028903375

Subjects:
Primary: 60J27 , 60K30

Keywords: asymptotic expansions , Erlang loss model , nonstationary queueing models , pointwise stationary approximation , Poisson's equation , time-inhomogeneous Markov chains

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 4 • November 1998
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