Analysis and design of a stationary ring road with two signals
The signalized ring road is an important model to understand the properties of signal setting on road networks. Stationary states exist on signalized ring road with a minimum period of multiple times of the cycle length. In this study, we extend the homogeneous one-signal ring road to the rotationally symmetric two-signal ring road, and set offsets between signals to reveal coordination effects. First, we apply link transmission model (LTM) to solve bound- ary flows at signals under stationery states, which is an equilibrium state of the dynamics networks. Then, we derive the critical densities influenced by signal settings, including the cycle length and the green ratio, to determine the conditions for maximum flow-rates of networks. Based on critical densities, an approximate macroscopic fundamental diagram (MFD) is obtained, relating average flow-rate and density of networks. The capacity drop of networks caused by offsets is also analyzed for different ratios of road length and cycle length. We then find the optimal cycle length for various congestion conditions based on the approximate MFD and properties of critical densities. Numerical LTM simulations are run to verify theoretical results and further explore the minimum periods of stationery states.