Bad air quality due to free pollutants such as particulate matter (PM), carbon dioxide (CO ${}_2$ ), nitrogen oxides (NO ${}_x$ ) and volatile organic components (VOC) increases the risk of long- term health diseases. The impact of traffic-calming measures on air quality has been studied using specialized equipment at control sites or mounted on cars to monitor pollutants levels. However, this approach suffers from a large number of variables on the experiments such as vehicles types, number of monitored vehicles, driver’s behavior, traffic density, time of the day, elapsed monitoring time, road conditions and weather. In this work, we use a cellular automata and an instantaneous traffic emissions model to capture the effect of speed humps on traffic flow and on the generation of CO ${}_2$ , NO ${}_x$ , VOC and PM pollutants. This approach allows us to study and characterize the effect of many speed humps on a single lane. We found that speed humps significantly promote the generation of pollutants when the number of vehicles on a lane is low. Our results may provide insight into urban planning strategies to reduce the generation of traffic emissions and lower the risk of long-term health diseases.

The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify how vulnerable a graph is to contagion. This paper introduces three mathematical formulations of the problem: an integer linear program (ILP) and two constraint satisfaction problems (CSP1 and CSP2). Thanks to off-the-shelf optimization software, these formulations can be solved optimally over arbitrary graphs; this is relevant because the only algorithms designed to date for this problem are approximation algorithms and heuristics, which do not guarantee to find optimal solutions. We empirically compared the proposed formulations using random graphs and off-the-shelf optimization software. The results show that CSP1 and CSP2 tend to reach optimal solutions in less time than the ILP. Therefore, we executed them over some benchmark graphs of order at most 5908. The previously best-known solutions for some of these graphs were improved. We draw some empirical observations from the experimental results. For instance, we find the tendency: the larger the graph’s optimal solution, the more difficult it is to find it. Finally, the resulting set of optimal solutions might be helpful as a benchmark dataset for the performance evaluation of non-exact algorithms.