Abstract
The paper deals with the observability problem in traffic networks, including route, origin–destination and link flows, based on number plate scanning and link flow observations. A revision of the main observability concepts and methods is done using a small network. Starting with the full observability of the network based only on number plate scanning on some links, the number of scanned links is reduced and replaced by counted link flows, but keeping the full observability of all flows in the network. In this way, the cost can be substantially reduced. To this end, several methods are given and discussed, and two small and one real case of networks are used to illustrate the proposed methodologies. Finally, some conclusions and final recommendations are included.
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Notes
At this stage, the reader may ask how the route flows can be observed in practice. We will see later on that the number plate scanning technique allows this to be done.
Castillo et al. (2008a) deals with this problem in detail and gives methods to solve it.
Castillo et al. (2008b) deal with the observability problem in traffic networks and provide some algorithms to transform the conservation laws written in terms of OD flows in order to solve the OD and link flow observability problem, based on counted links.
The reason why they are observable is because all coefficients in the corresponding row associated with unknown flows are null.
In this particular example, and because all sets are different, the index s coincides with the route number r, but otherwise, s ≤ r (see Examples 1, 2 or 3 for cases with \( s \ne r \)).
The automatic number plate recognition technique goes further that OD-pair flow identification; in fact, it identifies route flows. If the number of scanned links is not sufficient, the only problem is that two or more route flows become confounded, that is, we identify the join flow but not the individual route flows.
Note that from a computational point of view, the same pair of routes does not need to be compared twice.
On a DELL Optiplex 755 computer.
We note that these times correspond to the computer programs written in Matlab only with the purpose of presenting the examples in this paper. So, important reductions in time can be achieved if a programming expert writes the code, and must be used only as bounds and to illustrate how the relative cpu times depend on the size of the network.
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Acknowledgments
The authors are indebted to the Spanish Ministry of Science and Technology (Projects BIA2005-07802-C02-01 and TRA2010-17818) and to the Council of Education and Science of Castilla-La Mancha (A06-016) for partial support of this work, and to Prof. Antonio Conejo (University of Castilla La Mancha) for providing computer resources.
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Castillo, E., Rivas, A., Jiménez, P. et al. Observability in traffic networks. Plate scanning added by counting information. Transportation 39, 1301–1333 (2012). https://doi.org/10.1007/s11116-012-9390-0
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DOI: https://doi.org/10.1007/s11116-012-9390-0