Have you been stuck in traffic driving a car at the speed of a few meters per hour only to emerge from the traffic jam a while later not certain what caused it in the first place? Traffic experts are likely to attribute the cause to a road construction, a vehicle collision, or any other form of constriction. Physicists, on the other hand, may add that traffic jams may occur due to random fluctuations in driving speed without the presence of any obvious constraint.
Road traffic problems are complex; they involve human nature on one hand and physical laws of time, space, and movement on the other. These problems have been studied using many approaches. One of these approaches explains the traffic jam phenomenon as an example of self-organized criticality (SOC), a concept introduced in the late 1980s by the Danish physicist, Per Bak, to describe how complexity arises in nature. Back argued that complexity may arise as an emergent feature of a system out of simple local interactions among the basic building blocks of the system. The complexity is not in the basic blocks, but rather it is in the way in which they are interconnected and interacted with one another.
Bak and others have shown that Cellular automata (CA) simulation models can produce several characteristic features observed in natural complexity in a robust manner independent from the input parameters of the simulated system. In early 1990s, two other physicists, Kai Nagel and Michael Schreckenberg, created a cellular automaton model for vehicle traffic flow that can reproduce traffic jams. The NaSh model shows that traffic jams can arise as an emergent behavior due to simple interactions between cars on the road. Studying one vehicle behavior cannot provide much insight about the formation of traffic jams, but local interactions between vehicles may cause traffic jams.
Simulation of vehicle traffic using the CA models has shown that vehicle traffic exhibits characteristics similar to the well-known phase transition phenomenon in physics. Considering this point of view, the breakdown of vehicle traffic into traffic jams has properties similar to the phase transition from gas (free-flow traffic) to liquid (traffic jam). The transition from free-flow to a traffic jam happens at a critical vehicle density. It may happen also that vehicles enter a fragile state of co-existence of the two phases beyond the critical density. It is in this state where small fluctuations in speed may push all vehicles into a traffic jam.
One of the fundamental challenges in vehicle communication is the dynamic nature of the ad hoc data network formed among vehicles. The wireless links in this network are continuously created or torn down as vehicles move within or out of range from each other. Intuitively, a wider transmission range results in more stable network since vehicles stay within range longer to complete any exchange of information. However, wide transmission range means not only more power consumption, but also more contention and interference in congested traffic in situations such as traffic jams or traffic stopping at traffic lights. Such conditions deteriorates network performance and thus should be avoided as they create situations not much different from trying to have a conversation with a person in the far corner of a restaurant and the person sitting across the table from you using the same loud voice. Worse yet, imagine everybody else in the restaurant is acting the same way.
To avoid these situations, considerable research effort has been dedicated to estimating the number of vehicles in the road and adjusting the communication strategies accordingly. My doctoral research was focused on estimating the minimum required transmission range to maintain connectivity among vehicles in all traffic phases without relying on any external infrastructure. Nagle’s CA model and other theories from the fields of mobile wireless networks and vehicle traffic helped me derive a mathematical model for estimating the minimum transmission range needed in a vehicle communication network in any traffic phase. I also developed an algorithm to detect traffic conditions and modify the transmission power accordingly so vehicles do not use any more transmission power than needed to remain connected to other vehicles for successful communication.
Vehicles communication may become quite common in only a few years considering the level of interest of governments and car manufacturers over the last decade (more about this in another post). Meanwhile, next time you are sitting in traffic moving nowhere you can blame a driver somewhere down the road for slowing down unexpectedly and dream of a day when your car can tell you to take another route.