Phénomènes Physiques et
Modèles
Mathématiques en Sciences de l'Univers
Le séminaire a lieu le lundi 10 mai 2004 de 14h00 à
15h00
dans la salle de réunion
du PHC (Observatoire de Nice).
Hysteresis
phenomenon in traffic flows
Michael Blank, Russian Academy of
Sciences and Nice Observatory
A simple ``particle-hopping'' model for traffic flow will be
presented. The model is related to the Nagel-Schreckenburg model,
but is mathematically more tractable and includes it as a special
case. The model has several distinct ergodic (unmixed) phases
with two critical values. When traffic density is below the lowest
critical value, the steady state of the model corresponds to the
``free-flowing'' (or ``gaseous'') phase. When the density exceeds
the second critical value the model produces large, persistent,
well-defined traffic jams, which corresponds to the ``jammed''
(or ``liquid'') phase. Between these two critical values each of
the ``free-flowing'' and the ``jammed'' phase may take place, which
can be considered as an ``overcooled gas'' phase when a small
perturbation can drastically change gas into liquid. Mathematical
analysis is accomplished in part by the exact derivation of the
life-time of individual traffic jams for a given configuration of
particles.