On a New Finite Perturbation Analysis Algorithm
Consider a random variable X θ(t,ω) on a countable state space χ which describes the evolution of a discrete event dynamic system (DEDS), e.g., a queueing network. It is assumed that the distribution of X θ(t,ω) depends on, for simplification, one parameter θ with θ ∈ Θ. In performance analysis of DEDS the most interesting question is to determine l xo,T (θ) = E(Ψ(X Ψ(T,ω))|x o) (resp. l(θ) = lim T→∞ E(Ψ(X θ(T,ω))|x o )), where Ψ is the so-called performance-generating function, x 0 ∈ χ the state of the DEDS for t = 0, and [0, T] the observation horizon. Especially in the first step of the optimization of a DEDS it is important to determine the sensitivity of l x0,T (θ) with respect to θ, i.e., the derivation l′ x0,T (θ)=dl x0,T (θ)/dθ. Usually, neither for l x0,T (θ) nor for l′ x0,T (θ) analytic solutions are available; only estimates are accessible by an always time consuming simulation experiment. (Le., you have to perform simulation runs under fixed θ to produce trajectories x θ(t, ω) from X θ(t, ω)). Methods to reduce total simulation time are needed and important.
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