The Totally Asymmetric Simple Exclusion Process (TASEP) is a paradigm of
out-of-equilibrium Statistical Physics that serves as a simplistic model for
one-way vehicular traffic. Since traffic is perturbed by cars cruising for
parking in many metropolises, we introduce a variant of TASEP, dubbed SFP, in
which particles are initially cruising at a slower speed and aiming to park on
one of the sites adjacent to the main road, described by a unidimensional
lattice. After parking, they pull out at a finite rate and move at a normal
speed. We show that this model, which breaks many of the conservation rules
applicable in other TASEP variants, exhibits singular features, in particular
non-monotonic variations of the steady-state current with the injection rate
and re-entrant transitions in the phase diagram, for some range of parameters.
These features are robust to variations in the update rule and the boundary
conditions.Neither the slow speed of cruising cars nor the perturbation of the
flow due to pull-out maneuvers, taken in isolation, can rationalize these
observations. Instead, they originate in a cramming (or `paper jam') effect
which results from the coupling of these mechanisms: injecting too many cars
into the system saturates the first sites of the road, which prevents parked
cars from pulling out, thus forcing cruising cars to travel farther along the
road.These strong discrepancies with even the qualitative trends of the
baseline TASEP model highlight the importance of considering the effect of
perturbations on traffic