## Traffic Congestion in India

A flyover over the College of Engineering, Pune – an engineering college in Pune, Maharashtra, India – has been recently commissioned. Although the flyover intends to significantly improve traffic congestion in Pune, some traffic planning experts have raised doubts about the flyover’s potential to meet this goal. Previous flyovers that were constructed at universities like Swargate and Savitribai Phule Pune University were regarded as failures by experts. Moreover, program manager Pranjali Deshpande-Agashe argues that flyovers will only “increase vehicular traffic”; for reasons other than flaws in the newly commissioned flyover’s design, other officials express concerns that the flyover could result in traffic jams in neighboring junctions.

The doubts about the future effectiveness of the flyover relate to the topics of Network Traffic and Game Theory. More specifically, the idea that the construction of the flyover will increase traffic congestion is an example of Braess’ Paradox, a theory by Mathematician Dietrich Braess that the addition of a road or resource to an existing transportation network could increase average total travel time. Using concepts related to Braess’ Paradox, we can provide a brief explanation as to why the recently commissioned flyover could worsen traffic congestion in Pune. Let’s assume that the traffic network below (Figure 1.1) is a simplified model of the traffic in Pune prior to the construction of the flyover:

In this network (Figure 1.1), 2000 cars want to travel from node A to B. It takes a travel time of 45 minutes to travel on edges C-B and A-D and x/50 minutes to travel on edges A-C and D-B, where x denotes the number of cars traveling along the edge. Nash Equilibrium states that total travel time should be the same for every path used from node A-B. For that reason, total travel time for all travelers, under Nash Equilibrium, should be (1000/50)+45=65 minutes.

The flyover is now added over the College of Engineering, Pune (Figure 1.2), connecting nodes C and D. Cars, however, can only travel from C to D in one direction. For simplicity’s sake, we can assume that the travel time along the flyover is 0 minutes and that edge C-D is a significantly faster route than edges A-C, D-B, etc.. This traffic network may come across as more attractive and efficient to that in Figure 1.1 – a possible reason behind the “psychological illusion that the commissioning of the new flyover is easing traffic flow around the junction.” However, here, the only dominant strategy that exists for all travelers is the path A-C-D-B. In Figure 1.2, Nash Equilibrium – where if one traveler were to switch routes he or she would be strictly worse off given that the rest do not change routes – produces a total travel time of (2000/50) + 0 + (2000/50) = 80 minutes, which is more than the total travel time in the traffic network prior to the flyover construction in Figure 1.1. To conclude, the increase in total travel time and the simplified models in Figure 1.1 and 1.2 illustrate Braess’ Paradox and offer an explanation for the traffic planning experts’ warnings that the future flyover in Pune could very likely worsen traffic congestion.