A slow-to-start traffic model related to a M/M/1 queue

J. Stat. Mech. (2007) P07008 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