Stochastic Modeling and Solution Techniques in a Time-Varying Environment

摘要

The randomization technique, which solves the Kolmogorov differential equations by viewing the continuous time Markov process as a uniformized embedded discrete parameter Markov chaian randomized by a Poisson process, was fully developed and published. The numerical randomization technique was compared to a variety of simulation methods, including a brute force approach and others taking advantage to varying degrees of the uniformized embedded chain structure. Some initial progress has been made in studying optimization problems in a time varying environment. Unlike the steady state situations examined, the constraint functions are not monotone in all decision variables for all cases, which makes for less efficient use of implicit enumeration schemes. Nevertheless, implicit enumeration still appears to hold the most promise for our types of problems.