Likelihood Ratio Derivative Estimation for Finite-Time Performance Measures in Generalized Semi-Markov Processes
研究广义半马尔可夫过程中有限时间性能指标的似然比导数估计方法，给出了易于验证的适用条件，并证明这些条件在排队和可靠性模型中成立。
This paper investigates the likelihood ratio method for estimating derivatives of finite-time performance measures in generalized semi-Markov processes (GSMPs). We develop readily verifiable conditions for the applicability of this method. Our conditions mainly place restrictions on the basic building blocks (i.e., the transition probabilities, the distribution and density functions of the event lifetimes, and the initial distribution) of the GSMP, which is in contrast to the structural conditions needed for infinitesimal perturbation analysis. We explicitly show that our conditions hold in many practical settings, and in particular, for large classes of queueing and reliability models. One intermediate result we obtain in this study, which is of independent value, is to formally show that the random variable representing the number of occurring events in a GSMP in a finite time horizon, has finite exponential moments in a neighborhood of zero.