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A mixed-integer linear program for optimizing sensor locations along freeway corridors

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  • Danczyk, Adam
  • Liu, Henry X.
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    Abstract

    How to optimally allocate limited freeway sensor resources is of great interest to transportation engineers. In this paper, we focus on the optimal allocation of point sensors, such as loop detectors, to minimize performance measurement errors. Although it has been shown that the minimization problem can be intuitively formulated as a nonlinear program, the formulation is so complex that only heuristic approaches can be used to solve the problem. In this paper, we transform the nonlinear program into an equivalent mixed-integer linear model. The linearized model is shown to have a graphical interpretation and can be solved using resource constrained shortest path algorithms. A customized Branch-and-Bound technique is then proposed to solve the resource constrained shortest path problem. Numerical experiments along an urban freeway corridor demonstrate that this sensor location model is successful in allocating loop detectors to improve the accuracy of travel time estimation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 45 (2011)
    Issue (Month): 1 (January)
    Pages: 208-217

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    Handle: RePEc:eee:transb:v:45:y:2011:i:1:p:208-217

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    Related research

    Keywords: Sensor location problem Mixed-integer linear program Branch-and-Bound techniques Loop detectors;

    References

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    1. Zhang, Xiaoning & Yang, Hai, 2004. "The optimal cordon-based network congestion pricing problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 517-537, July.
    2. Sherali, Hanif D. & Desai, Jitamitra & Rakha, Hesham, 2006. "A discrete optimization approach for locating Automatic Vehicle Identification readers for the provision of roadway travel times," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 857-871, December.
    3. Yang, Hai & Zhou, Jing, 1998. "Optimal traffic counting locations for origin-destination matrix estimation," Transportation Research Part B: Methodological, Elsevier, vol. 32(2), pages 109-126, February.
    4. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    5. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    6. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
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    Cited by:
    1. Xing, Tao & Zhou, Xuesong & Taylor, Jeffrey, 2013. "Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 66-90.

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