@conference {1508845,
	title = {A Fast Analytical Algorithm for Solving Markov Decision Processes with Continuous Resources },
	booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)},
	year = {2007},
	abstract = {Agents often have to construct plans that obey deadlines
or, more generally, resource limits for real-valued resources whose consumption can only be characterized
by probability distributions, such as execution time or
battery power. These planning problems can be modeled with continuous state Markov decision processes
(MDPs) but existing solution methods are either inefficient or provide no guarantee on the quality of the resulting policy. We therefore present CPH, a novel solution method that solves the planning problems by first
approximating with any desired accuracy the probability
distributions over the resource consumptions with phasetype distributions, which use exponential distributions as
building blocks. It then uses value iteration to solve the
resulting MDPs by exploiting properties of exponential
distributions to calculate the necessary convolutions accurately and efficiently while providing strong guarantees on the quality of the resulting policy. Our experimental feasibility study in a Mars rover domain demonstrates a substantial speedup over Lazy Approximation,
which is currently the leading algorithm for solving continuous state MDPs with quality guarantees.},
	author = {Janusz Marecki and Sven Koenig and Tambe, Milind}
}
