Traffic congestion reconstruction with Kerner's three-phase theory

Vehicular traffic can be either free or congested. Traffic occurs in time and space, i.e., it is a spatiotemporal process. However, usually traffic can be measured only at some road locations (for example, via road detectors, video cameras, probe vehicle data, or phone data). For efficient traffic control and other intelligent transportation systems, the reconstruction of traffic congestion is necessary at all other road locations at which traffic measurements are not available. Traffic congestion can be reconstructed in space and time (Fig. 1) based on Boris Kerner’s three-phase traffic theory with the use of the ASDA and FOTO models introduced by Kerner. Kerner's three-phase traffic theory and, respectively, the ASDA/FOTO models are based on some common spatiotemporal features of traffic congestion observed in measured traffic data. Vehicular traffic can be either free or congested. Traffic occurs in time and space, i.e., it is a spatiotemporal process. However, usually traffic can be measured only at some road locations (for example, via road detectors, video cameras, probe vehicle data, or phone data). For efficient traffic control and other intelligent transportation systems, the reconstruction of traffic congestion is necessary at all other road locations at which traffic measurements are not available. Traffic congestion can be reconstructed in space and time (Fig. 1) based on Boris Kerner’s three-phase traffic theory with the use of the ASDA and FOTO models introduced by Kerner. Kerner's three-phase traffic theory and, respectively, the ASDA/FOTO models are based on some common spatiotemporal features of traffic congestion observed in measured traffic data. Common spatiotemporal empirical features of traffic congestion are those spatiotemporal features of traffic congestion, which are qualitatively the same for different highways in different countries measured during years of traffic observations. In particular, common features of traffic congestion are independent on weather, road conditions and road infrastructure, vehicular technology, driver characteristics, day time, etc. Kerner's definitions and , respectively, for the synchronized flow and wide moving jam phases in congested traffic are examples of common spatiotemporal empirical features of traffic congestion. In empirical observations, traffic congestion occurs usually at a highway bottleneck as a result of traffic breakdown in an initially free flow at the bottleneck. A highway bottleneck can result from on- and off-ramps, road curves and gradients, road works, etc. In congested traffic (this is a synonym term to traffic congestion), a phenomenon of the propagation of a moving traffic jam (moving jam for short) is often observed. A moving jam is a local region of low speed and great density that propagates upstream as a whole localized structure. The jam is limited spatially by two jam fronts. At the downstream jam front, vehicles accelerate to a higher speed downstream of the jam. At the upstream jam front, vehicles decelerate while approaching the jam. A wide moving jam is a moving jam that exhibits the characteristic jam feature , which is a common spatiotemporal empirical feature of traffic congestion. The jam feature defines the wide moving jam traffic phase in congested traffic as follows. A wide moving jam is a moving traffic jam, which exhibits the characteristic jam feature to propagate through any bottlenecks while maintaining the mean velocity of the downstream jam front denoted by v g {displaystyle v_{g}} . Kerner's jam feature can be explained as follows. The motion of the downstream jam front results from acceleration of drivers from a standstill within the jam to traffic flow downstream of the jam. After a vehicle has begun to accelerate escaping from the jam, to satisfy safety driving, the following vehicle begins to accelerate with a time delay. We denote the mean value of this time delay in vehicle acceleration at the downstream jam front by τ d e l , j a m ( a ) {displaystyle au _{del,jam}^{(a)}} . Because the average distance between vehicles within the jam, including average vehicle length, equals 1 ρ m a x {displaystyle {frac {1}{ ho _{max}}}} (where ρ m a x {displaystyle ho _{max}} is the average vehicle density within the jam), the mean velocity of the downstream jam front v g {displaystyle v_{g}} is v g = − 1 ρ m a x τ d e l , j a m ( a ) ( 1 ) {displaystyle v_{g}=-{frac {1}{ ho _{max} au _{del,jam}^{(a)}}}qquad qquad (1)} .