A New Variable-length Cell Model for Traffic Systems

In this paper we propose a new variable-length cell model (V-CTM) consisting of only three state lumped variables: two densities associated to two cells of variable length: a downstream congested one, of length, $l$, and an upstream free one, of length $L-l$, where $L$ is the total length of the sector. The former one is characterized by the congested (lumped or averaged) density, the latter one by the free (lumped or averaged) density. The third state, $l$ described the position of the congestion wave front. The paper investigates also several mathematical properties of this model ensuring the consistency with respect its inherent mass (or vehicle) conservation law. A comparison with respect to the standard fixed-cell CTM is also provided.