IMPROVEMENTS IN THE LIKELIHOOD RATIO METHOD FOR STEADY-STATE SENSITIVITY ANALYSIS AND SIMULATION

The Likelihood Ratio (LR) method is a potentially powerful tool for performance sensitivity analysis of a stochastic system because of its wide applicability. However, the variance of the estimate from LR increases linearly with the length of the segment path, which makes steady-state performance sensitivity estimation difficult. In our previous paper we proposed using segments defined by an embedded regular Markov chain to increase the chance of finding shorting segments. The condition required on the embedded Markov chain is that the equilibrium distribution of the embedded Markov chain is independent of the parameter perturbed, which is very restrictive. In this paper, we develop an asymptotically consistent LR method using the same kind of segments without the restrictive condition. The new LR method is implemented using A-segments which are defined to be the segments between two adjacent visits to a subset of states, A. Since the restrictive condition is removed, the LR method developed in this paper is much more widely applicable, which in practice extends the scope of applications of the LR method.