  Road accidents or maintenance often lead to the blockage of roads, causing
severe traffic congestion. Diverted routes after road blockage are often
decided individually and have no coordination. Here, we employ the cavity
approach in statistical physics to obtain both analytical results and
optimization algorithms to optimally divert and coordinate individual vehicle
routes after road blockage. Depending on the number and the location of the
blocked roads, we found that there can be a significant change in traveling
path of individual vehicles, and a large increase in the average traveling
distance and cost. Interestingly, traveling distance decreases but traveling
cost increases for some instances of diverted traffic. By comparing networks
with different topology and connectivity, we observe that the number of
alternative routes play a crucial role in suppressing the increase in traveling
cost after road blockage. We tested our algorithm using the England highway
network and found that coordinated diversion can suppress the increase in
traveling cost by as much as 66$\%$ in the scenarios studied. These results
reveal the advantages brought by the optimally coordinated traffic diversion
after road blockage.
