The slow-to-start mechanism is known to play an important role in the
particular shape of the Fundamental diagram of traffic and to be associated to
hysteresis effects of traffic flow.We study this question in the context of
exclusion and queueing processes,by including an asymmetry between deceleration
and acceleration in the formulation of these processes. For exclusions
processes, this corresponds to a multi-class process with transition asymmetry
between different speed levels, while for queueing processes we consider
non-reversible stochastic dependency of the service rate w.r.t the number of
clients. The relationship between these 2 families of models is analyzed on the
ring geometry, along with their steady state properties. Spatial condensation
phenomena and metastability is observed, depending on the level of the
aforementioned asymmetry. In addition we provide a large deviation formulation
of the fundamental diagram (FD) which includes the level of fluctuations, in
the canonical ensemble when the stationary state is expressed as a product form
of such generalized queues.Comment: 28 pages, 8 figure
