Cooperative jam mitigation in single-lane traffic

Traffic jams are endemic in both biological and engineered systems when cargo needs to be transported between locations. Various strategies have been proposed to mitigate jams, to improve the efficiency of transportation. We consider jam formation on a single-lane where cars can cooperate and travel as part of a caravan at a speed set by its size, or depart from the travelling end of the caravan at maximum speed. In a periodic setting, when the rate at which cars leave the caravan is large compared to the rate of formation of caravans we observe a diffused, gaseous state. As the density of cars increases or the rate at which cars depart from the caravan decreases, cars coalesce to form a single caravan. We map the regimes in the phase-space and propose a mean-field description of the dynamics through Toner-Tu equations to capture the observed macroscopic behavior.