Towards mesoscale analysis of inter-vehicle communications

Cooperative traffic systems renew much research interest with the rapid development of communication technologies. This paper considers a finite number of vehicles moving in a single lane from a mesoscale perspective and explores the spectral properties of such a cooperative system, in particular how the communication range and the coupling weights influence the eigenvalues of the global disturbance transition matrix (DTM), i.e., disturbance modes of the traffic system. Dynamics of these vehicles are described by a modified coupled-map car-following model under periodic boundaries with inter-vehicle communications. From a state-space approach, a system DTM is established from a global view and a closed-form solution of its eigenvalues is derived. Linear stability conditions are subsequently obtained. It is found that the eigenvalue distribution of system DTM is essentially dominated by the communication range and the coupling weights, but nearly independent of the system size. By analyzing the magnitudes of the dominant poles, the synchronization of the traffic system is enhanced if the weights of the vehicles within the communication range are more evenly distributed or the communication range is increased. Particularly, it is shown that the optimal communication network tends to be a mean-field network w.r.t. global synchronization, indicating that a communication network emphasizing uniform importance among vehicles within each vehicle's communication range is helpful for improving the synchronizability. Finally, numerical simulations verify the results.