Markov Chain Based Algorithms for City-Scale Pollution-Aware Traffic Routing

Air pollution is a growing concern across the world. Long-term exposure to severe pollution can cause serious health issues. Outdoor air pollution accounts for an estimated 4.2 million deaths per year, primarily due to stroke, heart disease, lung cancer, and chronic respiratory diseases. Low and middleincome countries suffer the most, especially in the Western Pacific and South-East Asia regions. A significant cause of air pollution in urban areas worldwide is the high volume of road traffic. Studies have shown that people are willing to choose greener routes when credible information is provided One of the approaches to solve this problem is to design a transportation policy that balances multiple objectives of • Avoiding extreme pollution in any part of the road network • Enabling short transit times for the vehicles that follow the policy • Making effective use of the road capacities to route the traffic. We propose a novel sampling-based approach for this problem. We provide the first construction of a Markov Chain that can sample integer max flow solutions of a planar graph, with theoretical guarantees that the probabilities depend on the aggregate transit length. We designed a traffic policy using diverse samples and simulated traffic on real-world road maps using the SUMO traffic simulator. We designed the MaxFlow-MCMC algorithm that used the Markov Chain to sample max flow solutions and generate a k-optimal set. We observe a considerable decrease in areas with severe pollution when experimented with maps of large cities across the world compared to other approaches. Extending the above work, we also propose a significantly faster extension to the MaxFlow-MCMC algorithm without compromising on the performance involving the following contributions.We provide the first construction of a Markov Chain to sample a set of k-optimal max flow solutions directly from a planar graph. We also provide theoretical guarantees that the stationary distribution probabilities depend on both the k-optimality value and the aggregate transit length. We simulate traffic on large-scale realworld roadmaps using the SUMO traffic simulator. We observe a significant speed improvement in the range of 22 to 242 times in our experiments while obtaining lesser average pollution compared to the MaxFlow-MCMC algorithm. To summarize, we present two novel Markov Chain based algorithms to generate a diverse set of max flow solutions from a planar graph, while being scalable to large road networks. We provide theo-