Stability of regional traffic networks employing maximum throughput demand management

This paper considers the stability and optimality properties of traffic demand management schemes, motivated by the integration of smart monitoring and control technologies in traffic networks. First, a suitable optimization problem is formulated that aims to obtain demand input values that maximize the throughput within traffic networks adhering to regional traffic dynamics with triangular macroscopic fundamental diagrams. We show that optimal solutions to this problem may lead to unstable behaviour, revealing a trade-off between stability and optimality. To address this issue, we analytically study the stability properties of traffic networks at the presence of constant demand input and provide suitable local conditions that guarantee stability when the system's equilibrium densities are strictly within the free-flow region, but not at the critical density. The latter case is significant, since the maximum throughput behaviour coincides in many cases with the local critical density. We resolve this by proposing a decentralized proportional demand control scheme and suitable local design conditions such that stability is guaranteed. Our analytic results are validated with numerical simulations in a 3-region system that demonstrate the effectiveness and practicality of the proposed approach.