An Approach for Bounding Reward Measures in Markov Models Using Aggregation

An ongoing challenge in Markovian analysis is the so-called “state-space explosion,” which is the exponential growth of the size of the state space of a model as the model size increases. We introduce a partial order on the states of a model to facilitate aggregation of states in order to reduce model size while bounding the error introduced by the aggregation. The partial order implies that the current and future behavior of the model is better in one state than another. We develop the theory of the partial order and its properties, show how it is related to monotonicity of matrices and to lumpability, and show how it can be efficiently applied to certain compositionally defined models.