  We study the following interacting particle system. There are $\rho n$
particles, $\rho < 1$, moving clockwise ("right"), in discrete time, on $n$
sites arranged in a circle. Each site may contain at most one particle. At each
time, a particle may move to the right-neighbor site according to the following
rules. If its right-neighbor site is occupied by another particle, the particle
does not move. If the particle has unoccupied sites ("holes") as neighbors on
both sides, it moves right with probability $1$. If the particle has a hole as
the right-neighbor and an occupied site as the left-neighbor, it moves right
with probability $0<p<1$. (We refer to the latter rule as a "holdback"
property.) The main question we address is: what is the system steady-state
flux (or throughput) when $n$ is large, as a function of density $\rho$? The
most interesting range of densities is $0\le \rho < 1/2$. We define the system
{\em typical flux} as the limit in $n\to\infty$ of the steady-state flux in a
system subject to additional random perturbations, when the perturbation rate
vanishes. Our main results show that: (a) the typical flux is different from
the formal flux, defined as the limit in $n\to\infty$ of the steady-state flux
in the system without perturbations, and (b) there is a phase transition at
density $h=p/(1+p)$. If $\rho<h$, the typical flux is equal to $\rho$, which
coincides with the formal flux. If $\rho>h$, a {\em condensation} phenomenon
occurs, namely the formation and persistence of large particle clusters; in
particular, the typical flux in this case is $p(1-\rho) < h < \rho$, which
differs from the formal flux when $h < \rho < 1/2$. Our results include both
steady-state and transient analysis. In particular, we derive a version of the
Ballot Theorem, and show that the key "reason" for large cluster formation for
densities $\rho > h$ is described by this theorem.
