Symmetric Monotone Embedding of Traffic Flow Networks with First-In-First-Out Dynamics

Abstract

Abstract: We study a flow network model for vehicular traffic that captures congestion effects at diverging junctions. Standard approaches which rely on monotonicity of the flow dynamics do not immediately apply to such first-in-first-out models. The network model nonetheless exhibits a mixed monotonicity property. Mixed monotonicity enables the original system to be embedded in a system of twice the dimension that is monotone and symmetric. The dynamics of the original system are recovered on a subspace of the embedding system, and we prove global asymptotic stability for a class of networks by considering convergence properties of the embedding system.