Universal behavior in a model of city traffic with unequal green/red times

The effect of green/red asymmetry is studied for the single-car traffic model proposed in B.A. Toledo, V. Muñoz, J. Rogan, C. Tenreiro, J.A. Valdivia, Modeling traffic through a sequence of traffic lights, Phys. Rev. E 70 (1) (2004) 016107], on two different signal synchronization strategies, namely, all signals in phase, and a green wave. The asymmetry is characterized by the parameter g=_tgr/T$g=t_{\text{gr}}/T$, where _tgr$t_{\text{gr}}$ is the green time and T$T$ the signal period. Although the car dynamics turns simpler or more complex, as compared with the equivalent situation for the symmetric case g=0.5$g=0.5$, critical behavior around resonance is shown to be preserved. However, unlike the case g=0.5$g=0.5$, critical exponents at both sides of the resonance are not equal and depend on g$g$. Analytical expressions for them are found, and shown to be both consistent with simulation results and independent of the distribution of distances between signals for the green wave case. Also, it is found that the green wave strategy is more robust to changes in g$g$, with respect to the synchronized lights strategy, in the sense that larger departures from g=0.5$g=0.5$ are needed to have noticeable effects on the car dynamics.