Three-phase theory of city traffic: Moving synchronized flow patterns in under-saturated city traffic at signals

• Three-phase traffic theory of city traffic.
• Moving synchronized flow patterns (MSP) at traffic signal.
• Random features of MSP emergence and evolution.
• Effect of MSP characteristics on green-wave breakdown.

Three-phase traffic flow theory of city traffic has been developed. Based on simulations of a stochastic microscopic traffic flow model, features of moving synchronized flow patterns (MSP) have been studied, which are responsible for a random time-delayed breakdown of a green-wave (GW) organized in a city. A possibility of GW control leading to the prevention of GW breakdown has been demonstrated. A diagram of traffic breakdown in under-saturated traffic (transition from under- to over-saturated city traffic) at the signal has been found; the diagram presents regions of the average arrival flow rate, within which traffic breakdown can occur, in dependence of parameters of the time-function of the arrival flow rate or/and signal parameters. Physical reasons for a crucial difference between results of classical theory of city traffic and three-phase theory are explained. In particular, we have found that under-saturated traffic at the signal can exist during a long time interval, when the average arrival flow rate is larger than the capacity of the classical theory; the classical capacity is equal to a minimum capacity in three-phase theory. Within a range of the average arrival flow rate between the minimum and maximum signal capacities, under-saturated traffic is in a metastable state with respect to traffic breakdown. We have distinguished the following possible causes for the metastability of under-saturated traffic: (i) The arrival flow rate during the green phase is larger than the saturation flow rate. (ii) The length of the upstream front of a queue at the signal is a finite value. (iii) The outflow rate from a MSP (the rate of MSP discharge) is larger than the saturation flow rate.