A stochastic shortest path problem is an undiscounted infinite-horizon Markov decision process with an absorbing and costree target state, where the objective is to reach the target state while optimizing total expected cost. In almost all cases, the objective in solving a stochastic shortest path problem is to minimize the total expected cost to reach the target state. But in probabilistic model checking, it is also useful to solve a problem where the objective is to maximize the expected cost to reach the target state. This thesis considers the maximum-time stochastic shortest path problem, which is a special case of the maximum-cost stochastic shortest path problem where actions have unit cost. The contribution is an efficient approach to computing high-quality bounds on the optimal solution for this problem. The bounds are useful in themselves, but can also be used by other algorithms to accelerate search for an optimal solution.

A stochastic shortest path (SSP) problem is an undiscounted Markov decision process with an absorbing and zero-cost target state, where the objective is to reach the target state with minimum expected cost. This problem provides a foundation for algorithms for decision-theoretic planning and probabilistic model checking, among other applications. This thesis describes an implementation and evaluation of recently developed error bounds for SSP problems. The bounds can be used in a test for convergence of iterative dynamic programming algorithms for solving SSP problems, as well as in action elimination procedures that can accelerate convergence by excluding provably suboptimal actions that do not need to be re-evaluated each iteration. The techniques are shown to be effective for both decision-theoretic planning and probabilistic model checking.