Characteristics of Optimal Solutions to the Sensor Location Problem

TL;DR

This paper refines the understanding of optimal traffic sensor placement by establishing a stronger necessary condition for flow determination, which is sufficient in many practical road network configurations, aiding sensor deployment strategies.

Contribution

It introduces a new necessary condition for sensor placement that is also sufficient in certain graph classes, improving upon previous criteria for traffic flow observability.

Findings

Counterexample shows previous condition is not sufficient

New stronger necessary condition proposed

Condition is sufficient for tree-like subgraphs in road networks

Abstract

In [Bianco, L., Giuseppe C., and P. Reverberi. 2001. "A network based model for traffic sensor location with implications on O/D matrix estimates". Transportation Science 35(1):50-60.], the authors present the Sensor Location Problem: that of locating the minimum number of traffic sensors at intersections of a road network such that the traffic flow on the entire network can be determined. They offer a necessary and sufficient condition on the set of monitored nodes in order for the flow everywhere to be determined. In this paper, we present a counterexample that demonstrates that the condition is not actually sufficient (though it is still necessary). We present a stronger necessary condition for flow calculability, and show that it is a sufficient condition in a large class of graphs in which a particular subgraph is a tree. Many typical road networks are included in this category, and we show how our condition can be used to inform traffic sensor placement.