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K. Cooke and E. Halsey, “The Shortest Route through a Network with Time-Dependent Internodal Transit Times,” Journal of Mathematical Analysis and Applications, Vol. 14, No. 3, 1966, pp. 493-498. doi:10.1016/0022-247X(66)90009-6

has been cited by the following article:

• TITLE: Efficient Routing of Emergency Vehicles under Uncertain Urban Traffic Conditions

  AUTHORS: Amir Elalouf

  KEYWORDS: Fast Routing Algorithm; FPTAS; Dynamic Programming

  JOURNAL NAME: Journal of Service Science and Management, Vol.5 No.3, September 19, 2012

  ABSTRACT: 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.