Abstract We study the new problem of stochastic programs over trees with dependent random arc capacities. This problem can be used as a subproblem in decomposition methods that solve multi‐stage networks with independent random arc capacities and random travel times. An efficient algorithm is provided to compute the expected total cost. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 157–163 2007

Network Address Translation (NAT) commonly prevents nodes without globally valid IP addresses from establishing direct Internet paths. In peer-to-peer networks, peers may utilize intermediate nodes as relays for this NAT traversal. We develop a stochastic relay routing algorithm for selecting appropriate relay nodes. The proposed relay routing algorithm is constructed in a stochastic programming framework by leveraging the actual delay of local links and the statistical delay distributions of non-local overlay links. Single or multiple paths are established via relays between two peers for achieving packet delivery with low delay and small loss. The simulation results showed that the proposed stochastic single/multi-path routing algorithm achieved a much lower packet delay than deterministic shortest path algorithms, which utilize average link delays. We demonstrated the effectiveness of the path diversity provided by our algorithm in reducing packet loss significantly via simulations. Our algorithm is fully distributed and requires only accurate local information. The employment of our algorithm is beneficial for provisioning real-time streaming applications in peer-to-peer networks.