Air pollution is a growing concern across the world. Road traffic is one of the major contributors to air pollution in urban areas. One of the approaches to solve this problem is to design a transportation policy that i) avoids extreme pollution in any area, ii) enables short transit times, and iii) makes effective use of the road capacities. Previous work to address this problem named MaxFlow-MCMC algorithm, proposed a novel sampling-based approach for this problem. In this work, we propose a significantly faster extension to the algorithm without compromising on the performance involving the following contributions: (a) We provide the first construction of a Markov Chain to sample a set of k-optimal max flow solutions directly from a planar graph. (b) We simulate traffic on large-scale real-world 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.