A theory of traffic congestion at moving bottlenecks

The physics of traffic congestion occurring at a moving bottleneck on a multi-lane road is revealed based on the numerical analyses of vehicular traffic with a discrete stochastic traffic flow model in the framework of three-phase traffic theory. We find that there is a critical speed of a moving bottleneck at which traffic breakdown, i.e. a first-order phase transition from free flow to synchronized flow, occurs spontaneously at the moving bottleneck, if the flow rate upstream of the bottleneck is great enough. The greater the flow rate, the higher the critical speed of the moving bottleneck. A diagram of congested traffic patterns at the moving bottleneck is found, which shows regions in the flow-rate-moving-bottleneck-speed plane in which congested patterns emerge spontaneously or can be induced through large enough disturbances in an initial free flow. A comparison of features of traffic breakdown and resulting congested patterns at the moving bottleneck with known ones at an on-ramp (and other motionless) bottleneck is made. Nonlinear features of complex interactions and transformations of congested traffic patterns occurring at on- and off-ramp bottlenecks due to the existence of the moving bottleneck are found. The physics of the phenomenon of traffic congestion due to 'elephant racing' on a multi-lane road is revealed.