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Mathematical Problems in Engineering
Volume 2016, Article ID 9012724, 10 pages
http://dx.doi.org/10.1155/2016/9012724
Research Article

Sensor Location Problem for Network Traffic Flow Derivation Based on Turning Ratios at Intersection

1Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 200092, China
2China Airport Construction Group Corporation, Beijing 100101, China

Received 28 August 2015; Accepted 28 January 2016

Academic Editor: Luca D’Acierno

Copyright © 2016 Minhua Shao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The sensor location problem (SLP) discussed in this paper is to find the minimum number and optimum locations of the flow counting points in the road network so that the traffic flows over the whole network can be inferred uniquely. Flow conservation system at intersections is formulated firstly using the turning ratios as the prior information. Then the coefficient matrix of the flow conservation system is proved to be nonsingular. Based on that, the minimal number of counting points is determined to be the total number of exclusive incoming roads and dummy roads, which are added to the network to represent the trips generated on real roads. So the task of SLP model based on turning ratios is just to determine the optimal sensor locations. The following analysis in this paper shows that placing sensors on all the exclusive incoming roads and dummy roads can always generate a unique network flow vector for any network topology. After that, a detection set composed of only real roads is proven to exist from the view of feasibility in reality. Finally, considering the roads importance and cost of the sensors, a weighted SLP model is formulated to find the optimal detection set. The greedy algorithm is proven to be able to provide the optimal solution for the proposed weighted SLP model.