On the stability of traffic perimeter control in two-region urban cities

Abstract

a b s t r a c tIn this paper, stability analysis of traffic control for two-region urban cities is treated. It is known in control theory that optimality does not imply stability. If the optimal control is applied in a heavily congested system with high demand, traffic conditions might not change or the network might still lead to gridlock. A city partitioned in two regions with a Macroscopic Fundamental Diagram (MFD) for each of the regions is considered. Under the assumption of triangular MFDs, the two-region MFDs system is modeled as a piecewise second-order system. Necessary and sufficient conditions are derived for stable equilibrium accumulations in the undersaturated regimes for both MFDs. Moreover, the traffic perimeter control problem for the two-region MFDs system is formulated. Phase portraits and stability analysis are conducted, and a new algorithm is proposed to derive the boundaries of the stable and unstable regions. Based on these regions, a state-feedback control strategy is derived. Trapezoidal shape of MFDs are also addressed with numerical solutions.

Optimal Perimeter Control for Two Urban Regions With Macroscopic Fundamental Diagrams: A Model Predictive Approach

“…Therefore, the objective function (14) in the optimal open-loop problem (14)- (22) is modified as follows: The role of β in (31) and u jump in (29) and (30) are similar in terms of making a balance between the desired smoothness and trip completion. Nevertheless, the calibration of u jump is easier than β, because it represents a physical measure.…”

“…However, in case of multiregion cities with multiple centers of congestion and/or attraction, control policies are more complicated and not well understood. For stability analysis of controlling two urban regions, see [14].…”

On the spatial partitioning of urban transportation networks

“…(1) is important for modeling purposes as details in individual links are not needed to describe the congestion level of cities and its dynamics. It can also be utilized to introduce simple control strategies to improve mobility in homogeneous city centers building on the concept of an MFD, like in Daganzo (2007), Geroliminis and Daganzo (2007), and Haddad and Geroliminis (2012). The main logic of the strategies is that they try to decrease the inflow in regions with points in the decreasing part of an MFD.…”

A three-dimensional macroscopic fundamental diagram for mixed bi-modal urban networks

“…While one bus traditionally creates more congestion than a moving car, the additional delay 39 per passenger carrying is smaller for large bus occupancies, making buses a more sustainable mode of 40 transport compared to cars. 41 To understand the physics of urban mobility, traffic dynamics of multimodal urban networks need to be 1 analyzed under various network structures. As multiple modes compete for limited urban space, conflicts and 2 interactions are developed resulting in congestion.…”