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Road accidents or maintenance often lead to the blockage of roads, causingsevere traffic congestion. Diverted routes after road blockage are oftendecided individually and have no coordination. Here, we employ the cavityapproach in statistical physics to obtain both analytical results andoptimization algorithms to optimally divert and coordinate individual vehicleroutes after road blockage. Depending on the number and the location of theblocked roads, we found that there can be a significant change in travelingpath of individual vehicles, and a large increase in the average travelingdistance and cost. Interestingly, traveling distance decreases but travelingcost increases for some instances of diverted traffic. By comparing networkswith different topology and connectivity, we observe that the number ofalternative routes play a crucial role in suppressing the increase in travelingcost after road blockage. We tested our algorithm using the England highwaynetwork and found that coordinated diversion can suppress the increase intraveling cost by as much as 66$\%$ in the scenarios studied. These resultsreveal the advantages brought by the optimally coordinated traffic diversionafter road blockage.

Optimally coordinated traffic diversion by statistical physics