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Convergence of ODE approximations and bounds on performance models in the steady-state

Richard Hayden

National Workshop Paper
9th Workshop on Process Algebra and Stochastically Timed Activities (PASTA 2010)
September, 2010
Abstract

We present a limiting convergence result for differential equation approximations of continuous-time Markovian performance models in the stationary (steady-state) regime. This extends existing results for convergence up to some finite time. We show how, for a large class of performance models, this result can be inexpensively exploited to make strong statements about the stationary behaviour of massive continuous-time Markov chains. Furthermore, we present a new technique based on Lyapunov functions which has the potential to allow the efficient computation of tight guaranteed bounds on the stationary distribution.

Keywords
Fluid and ODE analysis
Performance Modelling and Analysis
Petri Nets
Process Algebra
Queueing theory
Stochastic Modelling
AESOP
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