  We investigate models in which blocking can interrupt a particulate flow
process at any time. Filtration, and flow in micro/nano-channels and traffic
flow are examples of such processes. We first consider concurrent flow models
where particles enter a channel randomly. If at any time two particles are
simultaneously present in the channel, failure occurs. The key quantities are
the survival probability and the distribution of the number of particles that
pass before failure. We then consider a counterflow model with two opposing
Poisson streams. There is no restriction on the number of particles passing in
the same direction, but blockage occurs if, at any time, two opposing particles
are simultaneously present in the passage.
