  We consider a one-dimensional infinite lattice where at each site there sits
an agent carrying a velocity, which is drawn initially for each agent
independently from a common distribution. This system evolves as a Markov
process where a pair of agents at adjacent sites exchange their positions with
a specified rate, while retaining their respective velocities, only if the
velocity of the agent on the left site is higher. We study the statistics of
the net displacement of a tagged agent $m(t)$ on the lattice, in a given
duration $t$, for two different kinds of rates: one in which a pair of agents
at sites $i$ and $i+1$ exchange their sites with rate $1$, independent of the
velocity difference between the neighbors, and another in which a pair exchange
their sites with a rate equal to their relative speed. In both cases, we find
$m(t)\sim t$ for large $t$. In the first case, for a randomly picked agent,
$m/t$, in the limit $t\to \infty$, is distributed uniformly on $[-1,1]$ for all
continuous distributions of velocities. In the second case, the distribution is
given by the distribution of the velocities itself, with a Galilean shift by
the mean velocity. We also find the large time approach to the limiting forms
and compare the results with numerical simulations. In contrast, if the
exchange of velocities occurs at unit rate, independent of their values, and
irrespective of which is faster, $m(t)/t$ for large $t$ is has a gaussian
distribution, whose width varies as $t^{-1/2}$.
