Analysis of Time and Distance Delays in Car Following Models

In this paper we consider two types of car following models: models where the follower maintain safe distance headway and models where the follower maintains safe time headway. We analyze distance delays and time delays, caused by influence of the leading vehicle to the follower. We show that delays satisfy an equation similar to the Lindley equation for the waiting time in the single server queue. This equation is well studied in queueing theory and in many important cases has explicit solution. It opens up possibilities to apply many available results on single server queues for the analysis shock wave propagation in time and space.