Paper Info
Title
Deriving the Upper Bound of the Number of Sensors Required to Know All Link Flows in a Traffic Network.
Abstract
It is demonstrated that the minimum number of sensors required to know all link flows in a traffic network can be determined only if path information is available. However, not all paths need to be enumerated but, at most, a small subset defining the rank $r_{w}$ of the link-path incidence matrix ${\\bf W}$. If this rank for a reduced subset of paths is already $m - n$, where $m$ and $n$ are the number of links and noncentroid nodes, respectively, we can conclude that $m - n$ sensors are sufficient. It is also shown that the formulas providing the dependent link flows in terms of the independent link flows can be obtained by the node-based or path-based approaches with the same results only when $r_{w} = m - n$. Finally, an algorithm to obtain the small subsets of linearly independent path vectors is given. The methods are shown by a parallel network example and the Ciudad Real and Cuenca networks, for which the savings in link counts with respect to the $m - n$ bound are larger than 16%. The corresponding savings in path enumeration are larger than 80%.
Year
DOI
Venue
2013
10.1109/TITS.2012.2233474
IEEE Transactions on Intelligent Transportation Systems
Keywords
Field
DocType
mathematical model,traffic flow,estimation,sensors,location,upper bound,algorithms,optimization,observability,vectors,methodology
Discrete mathematics,Linear independence,Traffic flow,Road networks,Upper and lower bounds,Enumeration,Road traffic,Traffic network,Incidence matrix,Mathematics
Journal
Volume
Issue
ISSN
14
2
1524-9050
Citations 
PageRank 
References 
5
0.53
8
Authors
5
Name
Order
Citations
PageRank
Enrique Castillo155559.86
Aida Calvino2685.66
José María Menéndez31098.16
Pilar Jiménez4403.93
Ana Rivas5313.23