A Dynamic Network Modeling-Based Approach for Traffic Observability Problem

This paper presents a novel approach for studying the observability problem on a general topology of a traffic freeway network. We develop a new framework, which investigates observability in terms of flow and routing information on the network arcs. We utilize lumped-parameter-based ordinary differential equation (ODE) setting to model traffic (ρ) dynamics on a network arc and then combine it with the ODE model of routing (π) dynamics to develop a state-space model for the network. We then linearize the network dynamics about steady-state flow, calculate the observability matrix, and apply the rank condition test on it. Some of the problems addressed in the paper include the following: identification of essential and redundant measurements in the context of observability, and verification of the sufficiency of a given set of states for the observability of the system. In particular, three different observability problems are formulated and solved using the proposed framework. The methodology is then illustrated by its application on carefully chosen network examples from the commonly encountered traffic freeway scenarios. A theorem and a corollary providing a necessary condition for observability are also proved. Finally, a conjecture based on the observations from the solved network examples is provided.