Stochastic model of single-file flow with reversible blockage

We introduce a stochastic model for reversible blockage in particulate flow through a channel. A blockage forms whenever two particles are in the channel simultaneously. The process restarts after a waiting time and both particles exit the channel. We obtain exact expressions for the steady-state particle flux out of the channel, the probability that the channel is open at time t and the probability distribution that n particles have exited the channel at time t when the channel is closed.