  We study the Braess paradox in the transport network as originally proposed
by Braess with totally asymmetric exclusion processes (TASEPs) on the edges.
The Braess paradox describes the counterintuitive situation in which adding an
edge to a road network leads to a user optimum with higher travel times for all
network users. Travel times on the TASEPs are nonlinear in the density, and
jammed states can occur due to the microscopic exclusion principle, leading to
a more realistic description of trafficlike transport on the network than in
previously studied linear macroscopic mathematical models. Furthermore, the
stochastic dynamics allows us to explore the effects of fluctuations on network
performance. We observe that for low densities, the added edge leads to lower
travel times. For slightly higher densities, the Braess paradox occurs in its
classical sense. At intermediate densities, strong fluctuations in the travel
times dominate the system's behavior due to links that are in a domain-wall
state. At high densities, the added link leads to lower travel times. We
present a phase diagram that predicts the system's state depending on the
global density and crucial path-length ratios.
