Flow in channel networks may involve a redistribution of flux following the blockage or failure of an individual link. Here we consider a simplified model consisting of N(c) parallel channels conveying a particulate flux. Particles enter these channels according to a homogeneous Poisson process and an individual channel blocks if more than N particles are simultaneously present. The behavior of the composite system depends strongly on how the flux of entering particles is redistributed following a blockage. We consider two cases. In the first, the intensity on each open channel remains constant while in the second the total intensity is evenly redistributed over the open channels. We obtain exact results for arbitrary N(c) and N for a system of independent channels and for arbitrary N(c) and N=1 for coupled channels. For N>1 we present approximate analytical as well as numerical results. Independent channels block at a decreasing rate due to a simple combinatorial effect, while for coupled channels the interval between successive blockages remains constant for N=1 but decreases for N>1. This accelerating cascade is due to the nonlinear dependence of the mean blocking time of a single channel on the entering particle flux that more than compensates for the decrease in the number of active channels.

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 τ b 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.

We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value N, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the n-particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particles, and their time correlation. We generalize previous results for N=2 to an arbitrary distribution of entry times and obtain exact solutions for N=3 for a Poisson distribution and partial results for N≥4.