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.
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