Deterministic microscopic three-phase traffic flow models

Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow or synchronized flow or else wide moving jam traffic phase. In a speed adaptation model (SA model), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATD and SA models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATD and SA models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATD and SA models are studied. A comparison of the ATD and SA models with stochastic models in the context of three-phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented.