  We consider a system of ordered cars moving in $\R$ from right to left.
  Each car is represented by a point in $\R$; two or more cars can occupy the
same point but cannot overpass. Cars have two possible velocities: either 0 or
1. An unblocked car needs an exponential random time of mean 1 to pass from
speed 0 to speed 1 (\emph{slow-to-start}). Car $i$, say, travels at speed 1
until it (possibly) hits the stopped car $i-1$ to its left. After the departure
of car $i-1$, car $i$ waits an exponential random time to change its speed to
1, travels at this speed until it hits again stopped car $i-1$ and so on.
Initially cars are distributed in $\R$ according to a Poisson process of
parameter $\lambda<1$. We show that every car will be stopped only a finite
number of times and that the final relative car positions is again a Poisson
process with parameter $\lambda$. To do that, we relate the trajectories of the
cars to a $M/M/1$ stationary queue as follows. Space in the traffic model is
time for the queue. The initial positions of the cars coincide with the arrival
process of the queue and the final relative car positions match the departure
process of the queue.
