Delays in Traffic Flow Models

In this chapter, we present how time-delays arise in traffic flow dynamics, mainly focusing on human reaction delays, mechanical delays, and delay time of vehicle motion. We clarify the differences in notions of time constant versus time-delay, also known as dead-time, and provide definitions of discrete delays and distributed delays. This is followed by a quantitative measure of time-delay as reported in the literature and as measured under certain driving conditions. We give examples of linear and nonlinear microscopic traffic flow models that include time-delays, with various discussions, comparisons, and interpretations. Additional insights on driver behavior modeling can be found in [1].