  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.
