An Average Study of the Signalized Link-Transmission-Model

In this paper we present an average study between the continuous-time signalized T-periodic Link Transmission Model (LTM), and its time-averaged version. Those are macroscopic models capturing the time-evolution of the vehicles densities in urban traffic networks controlled by periodic traffic light of period T. In this paper, we formalize the mathematic sense in which the solutions of the periodic signalized LTM model are approximated by the solutions of its averaged version. In particular, we shown that the error norm between the solutions of the signalized and the averaged models is bounded, in both a finite and infinite time-intervals, by a constant proportional to the the ratio, T/L, between the traffic light time-cycle T, and the considered road segment (link) length, L. This result confirm the intuition that the precision of the averaged models improves with the increase of traffic light frequencies and link road lengths.