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

Jack Haddad and Nikolas Geroliminis

Transportation Research Part B: Methodological, 2012, vol. 46, issue 9, 1159-1176

Abstract: In 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.

Keywords: Stability characterization; Macroscopic fundamental diagram; State-feedback control; Traffic congestion (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (40)

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DOI: 10.1016/j.trb.2012.04.004

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