Structural Observability of Traffic Density Dynamics on a Motorway Ring Road

In order to control and reduce the congestion in motorway traffic networks, it is required to measure important traffic variables, e.g. densities, that can be observed by sensors. However, to reduce the operational costs, one should look for the most efficient methods to place the minimum number of sensors in a given network. In this paper, we discuss the structural observability of a traffic system, namely, the density dynamics defined on a motorway ring road. For this purpose, LWR theory in a spatial discretization form is employed, and the nonlinear dynamics of the traffic density associated with different cells of the network have been derived. Then, by considering a linearization of the ordinary differential equations (ODEs), we derive the minimum number of sensors that are needed to render the network weakly or strongly structurally observable. In this framework, the parameters of the system can have any nonzero value, and the exact value of nonzero elements (weights) is not of interest. In this work, we also discuss optimal locations in the traffic network to place the minimum set of sensors.