Non-Markovian Models of Blocking in Concurrent and Countercurrent Flows

We investigate models in which blocking can interrupt a particulate flow process at any time. Filtration, and flow in micro or nanochannels 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.