Uninterrupted traffic flow refers to flow of those streams where vehicular motion is not interrupted by stoppages. Movement of vehicles on expressways and certain arterial sections can be classified as uninterrupted traffic flow. In fact, to some extent, all flows except at or near intersections can be said to be within the scope of uninterrupted traffic flow.
Our discussion on uninterrupted traffic flow is divided into four sections. The first section presents the fundamental relation of traffic flow. The second section talks about certain macroscopic relations between speed and density. The third section deals with viewing the traffic stream as an outcome of interactions between drivers; this section is titled "Microscopic Models". The fourth section analyzes situations when two different traffic streams meet.
Fundamental Relation
The fundamental relation of traffic flow is valid for interrupted as well as uninterrupted traffic flow. It is discussed here as this is the first instance we discuss models of traffic flow. Consider the following traffic stream;
Assume that vehicle V1 is touching section A-A and vehicle Vn is touching B-B at time, t = 0. Also assume that the average speed of the stream is u kmph. For simplicity, assume that each vehicle in the stream is moving with u kmph. Further assume that the density of vehicles between A-A and B-B is k vpkm (vehicles per km).
Now, if an observer standing at A-A starts counting vehicles at time, t = 0 the first vehicle he/she would count is V1. Since, Vn is u km away from A-A and since every vehicle is moving with u kmph Vn will reach A-A exactly at t = 1 hr (press replay button to see). Hence in one hour the observer will count all vehicles between A-A and B-B. That is, it will count all vehicles over the distance u km (see Figure).
Now, as per our initial assumption, there are k vpkm (i.e. density = k vpkm). That is, the number of vehicles between V1 and Vn (including both), N is given by
N = u (the distance between A-A and B-B) x k(density)
Hence in one hour the observer will count N or u x k vehicles. By definition, number of vehicles counted in an hour is flow, q in vph (vehicles per hour).
Hence, in this case, q = N
or q = u x k
The last equation, which says flow of a traffic stream is equal to average speed of the stream times the average density of the stream is called the fundamental relation of traffic flow.
