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We consider two applied discrete-time Markov control models: waiting times process in GI j D j 1 j ¥ queues with a controlled service rate and water release control in a simple dam model with independent water inflows. The stochastic dynamics of both models is determinated by a sequence of independent and identically distributed random variables with a distribution function F . In the situation when an available approximation F̃ is used in place of the unknown F , we estimate the deterioration of performance of control policies optimal with respect to the total discounted cost and the average cost per unit of time. For this purpose we introduce a stability index and find uppers bounds for this index expressed in terms of the Prokhorov distance between the distributions functions F and F̃ . When F̃ F̃m is the empirical distribution function obtained from a sample of size m in average the stability index is less than a constant times m 1=3.

Quantitative Estimates of Stability in Controlled GI | D | 1 | #INF# Queueing Systems and in Control of Water Release in a Simple Dam Model