Comparing Markov Chains: Aggregation and Precedence Relations Applied to Sets of States, with Applications to Assemble-to-Order Systems
针对状态空间巨大的马尔可夫链，提出一种基于马尔可夫报酬理论的新边界方法，通过重定向转移集构造可分析的小模型，为按订单装配系统提供单调性证明和性能边界。
Solving Markov chains is, in general, difficult if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward theory: Our method constructs bounds by redirecting selected sets of transitions, facilitating an intuitive interpretation of the modifications of the original system. We show that our method is compatible with strong aggregation of Markov chains; thus we can obtain bounds for an initial chain by analyzing a much smaller chain. We illustrate our method by using it to prove monotonicity results and bounds for assemble-to-order systems.