The price of anarchy in transportation networks by estimating user cost functions from actual traffic data

We consider a large-scale road network in Eastern Massachusetts. Using real traffic data in the form of spatial average speeds and the flow capacity for each road segment of the network, we convert the speed data to flow data and estimate the origin-destination flow demand matrices for the network. Assuming that the observed traffic data correspond to user (Wardrop) equilibria for different times-of-the-day and days-of-the-week, we formulate appropriate inverse problems to recover the per-road cost (congestion) functions determining user route selection for each month and time-of-day period. Then, we formulate a system-optimum problem in order to find socially optimal flows for the network. We investigate the network performance, in terms of the total latency, under a user-optimal policy versus a system-optimal policy. The ratio of these two quantities is defined as the Price of Anarchy (POA) and quantifies the efficiency loss of selfish actions compared to socially optimal ones. Our findings contribute to efforts for a smarter and more efficient city.