Operations Research: An Introduction (8th Edition)
Operations Research: An Introduction (8th Edition)
Shortest paths in stochastic networks with correlated link costs
Computers & Mathematics with Applications
Risk-aware routing for optical transport networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Information Collection on a Graph
Operations Research
Risk-aware provisioning for optical WDM mesh networks
IEEE/ACM Transactions on Networking (TON)
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Common network parameters, such as number of nodes and arc lengths are frequently subjected to ambiguity as a result of probability law. A number of authors have discussed the calculation of the shortest path in networks with random variable arc lengths. Generally, only a subset of intermediate nodes chosen in accordance with a given probability law can be used to transition from source node to sink node. The determination of a priori path of the minimal length in an incomplete network is defined as a probabilistic shortest path problem. When arc lengths between nodes are randomly assigned variables in an incomplete network the resulting network is known as an incomplete stochastic network. In this paper, the computation of minimal length in incomplete stochastic networks, when travel times between nodes are allowed to be exponentially distributed random variables, is formulated as a linear programming problem. A practical application of the methodology is demonstrated and the results and process compared to the Kulkarni's [V.G. Kulkarni, Shortest paths in networks with exponentially distributed arc lengths, Networks 16 (1986) 255-274] method.