Braess’ paradox in the uncertain demand and congestion assumed Stochastic Transportation Network Design Problem

In this study, we examine Braess’ paradox in the context of a Stochastic Transportation Network Design Problem (NDP). In conventional NDPs, major variables such as link travel time and traffic flows are considered to be deterministic. However, in the real world, due to variations in traffic patterns, travelers experience different travel times. To account for this variation, in this study Monte Carlo simulation is employed to incorporate the probabilistic nature of travel demand. A new objective function for the NDP is formulated based on the probabilistic definition of link flows, and the design results are compared with the results obtained from conventional formulations. This new model is used to analyze Braess’ paradox, a well-known counter intuitive network phenomenon. Our results indicate that Braess’ paradox is more likely to be observed in our model, as there are more uncertainties in travel demand.