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Optimal route selection with reliable expected travel time has been a focus of research in transportation networks where the reliability is subject to many uncertainty factors such as traffic incidents or recurring traffic congestions. In this paper we develop an approximation method to obtain the reliability of a route travel time in a stochastic time-dependent traffic network. The proposed method takes into consideration the probabilistic nature of the travel time on individual links and their spatial correlation between adjacent links of a selected route. Reliability calculations and the accuracy of our approximation are discussed via a simple illustrative example and a larger network.