Emergency-vehicle drivers who aim to reach their destinations through the fastest possible routes cannot rely solely on expected average travel times. Instead, the drivers should combine this travel-time information with the characteristics of data variation and then select the best or optimal route. The problem can be formulated on a graph in which the origin point and destination point are given. To each arc in the graph a random variable is assigned, characterized by the expected time to traverse the arc and the variance of that time. The problem is then to minimize the total origin-destination expected time, subject to the constraint that the variance of the travel time does not exceed a given threshold. This paper proposes an exact pseudo-polynomial algorithm and an ε-approximation algorithm (so-called FPTAS) for this problem. The model and algorithms were tested using real-life data of travel times under uncertain urban traffic conditions and demonstrated favorable computational results.
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