Markov Decision Petri Nets with Uncertainty

Abstract

Markov Decision Processes (MDPs) are a well known mathematical formalism that combines probabilities with decisions and allows one to compute optimal sequences of decisions, denoted as policies, for fairly large models in many situations. However, the practical application of MDPs is often faced with two problems: the specification of large models in an efficient and understandable way, which has to be combined with algorithms to generate the underlying MDP, and the inherent uncertainty on transition probabilities and rewards, of the resulting MDP. This paper introduces a new graphical formalism, called Markov Decision Petri Net with Uncertainty (MDPNU), that extends the Markov Decision Petri Net (MDPN) formalism, which has been introduced to define MDPs. MDPNUs allow one to specify MDPs where transition probabilities and rewards are defined by intervals rather than constant values. The resulting process is a Bounded Parameter MDP (BMDP). The paper shows how BMDPs are generated from MDPNUs, how analysis methods can be applied and which results can be derived from the models.