Abstract:Optimal path problems are important in many science and engineering fields. Performance criteria may vary in coping with uncertainty, such as expectation, reliability, value at risk, etc. In this paper, we will first summarize our recent work on a dynamic programming based optimal path algorithm for maximizing the time reliability. We then study the convergence properties of the algorithm by introducing two special successive approximation sequences. Finally we will show the connection between the maximum reliability problem and the shortest and k-shortest path problems.

Keywords: Shortest path problem, Dynamic programming, Stochastic networks, Reliability, Successive approximation