### Traffic Jam I

Sometimes traffic jams occur for seemingly no reason. It has long been my theory that this is due to the comparatively slow response of driver to varying traffic environment to adjust his/her car's speed, thus failure to adapt fast to the traffic resulting in never ending loop of typical traffic jam. Some scientists in Japan have come up with a brilliant setup that might show the development of traffic situations and here is the outcome.

The drivers were asked to maintain a constant speed at all times in the loop. Initially there was little sign of disturbance as to the traffic flow. Nevertheless, wave-packets slowly began to develop within the constant traffic. That is, a cruising speed of some cars were slower than the car behind them which forced some drivers to reduce their speed. However, since there is always a delay in which the driver reacts to the outside conditions, the driver always overshoots by a certain distance before he steps on his brake and this makes him force to reduce speed at a faster rate. This propagates through the drivers behind him causing a series of disturbances in the traffic flow. Now moving on to the third car after this car. This time, the driver notices a reduced speed of the second car and steps on a brake to slow down but also with a lagged response. He must decelerate even faster than the car in front. This propagates and imagine what will happen to the eleventh car?

This theory and experiment can be in fact explained with a common controls and feedback theory. In the theory of controls, if a rate of response at which the system reacts to the changes in the environment (or variables) has a significant lag or at least more than what is demanded for maintaining system stability, the result is either overshooting or undershooting of the output of the system.

I can think of a great analogy to the feedback theory that may just explain this in plain English. Think of a long shower hose and your objective is to turn on water that is in a decent temperature range. Initially, you will position the knob between hot and cold (a constant cruising speed) where you think is the most likely position to give out warm temperature water. In reality, the initial water coming out of the hose will be colder (unexpected speed gradient). So in response to what you observed, you will turn the knob more close to hot (your response to the speed gradient). Since the length of the shower hose is too long (lagging response), by the time you felt hot water coming out, you are forced to reposition the knob back to somewhere closer to cold. Again, the length of hose prevents instant change in water stream temperature (lagging response) and therefore you move the knob a little bit closer to cold only to realize a second later that the water is too cold again. This is an analogy given by a professor during my controls class.