To obtain adequate traffic information, the density of traffic sensors should be sufficiently high to cover the entire transportation network. However, deploying sensors densely over the entire network may not be realistic for practical applications due to the budgetary constraints of traffic management agencies. This paper describes several possible spatial distributions of traffic information credibility and proposes corresponding different sensor information credibility functions to describe these spatial distribution properties. A maximum benefit model and its simplified model are proposed to solve the traffic sensor location problem. The relationships between the benefit and the number of sensors are formulated with different sensor information credibility functions. Next, expanding models and algorithms in analytic results are performed. For each case, the maximum benefit, the optimal number and spacing of sensors are obtained and the analytic formulations of the optimal sensor locations are derived as well. Finally, a numerical example is proposed to verify the validity and availability of the proposed models for solving a network sensor location problem. The results show that the optimal number of sensors of segments with different model parameters in an entire freeway network can be calculated. Besides, it can also be concluded that the optimal sensor spacing is independent of end restrictions but dependent on the values of model parameters that represent the physical conditions of sensors and roads.
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