Traffic monitoring in urban transportation systems can be carried out based on vehicular sensor networks. Probe vehicles (PVs), such as taxis and buses, and floating cars (FCs), such as patrol cars for surveillance, can act as mobile sensors for sensing the urban traffic and send the reports to a traffic-monitoring center (TMC) for traffic estimation. In the TMC, sensing reports are aggregated to form a traffic matrix, which is used to extract traffic information. Since the sensing vehicles cannot cover all the roads all the time, the TMC needs to estimate the unsampled data in the traffic matrix. As this matrix can be approximated to be of low rank, matrix completion (MC) is an effective method to estimate the unsampled data. However, our previous analysis on the real traces of taxis in Shanghai reveals that MC methods do not work well due to the uneven samples of PVs, which is common in urban traffic. To exploit the intrinsic relationship between the unevenness of samples and traffic estimation error, we study the temporal and spatial entropies of samples and successfully define the important criterion, i.e., average entropy of the sampling process. A new sampling rule based on this relationship is proposed to improve the performance of estimation and monitoring. With the sampling rule, two new patrol algorithms are introduced to plan the paths of controllable FCs to proactively participate in traffic monitoring. By utilizing the patrol algorithms for real-data-set analysis, the estimation error reduces from 35% to about 10%, compared with the random patrol or interpolation method in traffic estimation. Both the validity of the exploited relationship and the effectiveness of the proposed patrol control algorithms are demonstrated.
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