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Networks of channels conveying particles are often subject to blockages dueto the limited carrying capacity of the individual channels. If the channelsare coupled, blockage of one causes an increase in the flux entering theremaining open channels leading to a cascade of failures. Once all channels areblocked no additional particle can enter the system. If the blockages are offinite duration, however, the system reaches a steady state with an exitingflux that is reduced compared to the incoming one. We propose a stochasticmodel consisting of $N_c$ channels each with a blocking threshold of $N$particles. Particles enter the system according to a Poisson process with theentering flux of intensity $\Lambda$ equally distributed over the openchannels. Any particle in an open channel exits at a rate $\mu$ and a blockedchannel unblocks at a rate $\mu^*$. We present a method to obtain the exitingflux in the steady state, and other properties, for arbitrary $N_c$ and $N$ andwe present explicit solutions for $N_c=2,3$. We apply these results to comparethe efficiency of conveying a particulate stream of intensity $\Lambda$ usingdifferent channel configurations. We compare a single "robust" channel with alarge capacity with multiple "fragile" channels with a proportionately reducedcapacity. The "robust" channel is more efficient at low intensity, whilemultiple, "fragile" channels have a higher throughput at large intensity. Wealso compare $N_c$ coupled channels with $N_c$ independent channels, both withthreshold $N=2$. For $N_c=2$ if $\mu^*/\mu>1/4$, the coupled channels arealways more efficient. Otherwise the independent channels are more efficientfor sufficiently large $\Lambda$.

Stochastic models of multi-channel particulate transport with blockage