Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

This study elucidates the effect of congestion avoidance of agents given congestion information on optimizing traffic in a star topology in which the central node is connected to isolated secondary nodes with different preferences. Each agent at the central node stochastically selects a secondary node by referring to the declining preferences based on the congestion rate of the secondary nodes. We investigated two scenarios: (1) repeated visits and (2) a single visit for each node. For (1), we found that multivariate statistics describe well the nonlinear dependence of agent distribution on the number of secondaries, demonstrating the existence of the number of secondaries that makes the distribution the most uniform. For (2), we discovered that congestion avoidance linearizes the travel time for all agents visiting all nodes; in contrast, the travel time increases exponentially with secondaries when not referring to congestion information. Health examination epitomizes this finding; by allowing patients to be preferentially selected for examination in vacant examination sites, we can linearize the time it takes for everyone to complete their examination. We successfully described the optimization effect of congestion avoidance on the collective dynamics of agents in star topologies.