Have you ever found yourself; while waiting at a traffic signal, watching the timer count down to zero; wondering precisely why traffic signals last as long as they do? The numbers are fairly inane. The signal near my house lasts for 53 seconds, 53! Why not a minute, or 10 seconds. Well, the answer to this and a lot of other questions regarding traffic lie in the realm of Traffic Engineering. Today we will discuss a few dimensions that make up the patchwork quilt that is this hybrid discipline. Traffic engineering considers two primary problems; How to reduce congestion on the roads and how to reduce accidents.
Of course, these problems have varied nuances. How does one reduce congestion while still maintaining a reasonable speed limit, can one reduce the amount of time that drivers have to wait at traffic signals, toll bridges etc. The science is a mixture of mathematics, physics and human psychology.
One of the fundamental concepts is the lane-flow equation. The relationship between lane flow (Q, vehicles per hour), maximum speed (V, kilometers per hour) and density (K, vehicles per kilometer) is Q=K.V
Observation suggests that up to a maximum flow, speed does not decline while density increases. However, above a critical threshold, increased density reduces speed. Additionally, beyond a further threshold, increased density reduces flow as well.
Road systems are designed using queuing theory. Queuing theory is the mathematical modeling of lines and a sequence of interconnected queues is a queuing network. When an object (in this case a car) crosses a queuing node(intersection, traffic light etc) it can either proceed to the next queue or leave the network. Once a network has been designed, it can be optimized on the basis of the lane flow equation. The optimization rule used is usually Kerners Breakdown Minimization principal.
The final network may be improved further by three-phase traffic analysis. This considers the physics of traffic jams. The theory states that there are 3 states that may exist; Free flow, synchronized flow and wide moving jam. The theory considers breakdowns that may occur when transitioning from one state to another.
Traffic management is a really exhilarating field, particularly for math junkies, like this author. 🙂