Input parameters to achieve target performance in stochastic systems: A simulation-based approach

The use of simulation as an engineering tool to design complex stochastic systems is often inhibited by cost. Extensive computer processing is needed to solve the inverse problem which deals with the calculation of a design parameter given a desired target for the performance measure of a given system. The designer simulates the process numerically and obtains an approximation for that same output. The goal is to match the numerical and experimental results as closely as possible by varying the values of input parameters in the numerical simulation. The most obvious difficulty in solving the inverse problem is that one cannot simply calculate a straightforward solution and be done. Since the output has to be matched by varying the input, an iterative method of solution is implied. This paper proposes a ‘stochastic approximation’ algorithm to estimate the necessary controllable input parameters within a desired accuracy given a target value for the performance function. The proposed solution algorithm is based on Newton's methods using a single-run simulation approach to estimate the needed derivative. The proposed approach may be viewed as an optimization scheme, where a loss function must be minimized. The solution algorithm properties and the validity of the estimates are examined by applying it to some reliability and queueing systems with known analytical solutions.