Stochastic model of channel blocking with an inhomogeneous flux of entering particles

We study a blocking model where particles enter a narrow channel at random times. A single particle exits in a finite time, but if two particles are present in the channel at the same time a blockage occurs. The arrival times are distributed according to an inhomogeneous Poisson process where the intensity depends explicitly on time. Although it is always possible to transform any one-dimensional Poisson process into a uniform one by introducing a rescaled time, the non-Markovian nature of the blocking process excludes a simple mapping of the results for the homogenenous case. We present a first-principles approach and obtain exact expressions for the survival probability, the number of exiting particles and the mean flux of exiting particles. The theory is applied to three example intensities, namely a simple discontinuity, an exponential decay and a sinusoidally varying function