Accumulation at the Boundary for a One-Dimensional Stochastic Particle System

We consider an infinite particle system on the positive half-line, with particles moving independently of each other. When a particle hits the boundary, it immediately disappears and the boundary moves to the right by some fixed quantity (the particle size). We study the speed of the boundary movement (growth). Possible applications are dynamics of traffic jam growth, growth of a thrombus in a vessel, and epitaxy. Nontrivial mathematics concerns the correlation between particle dynamics and boundary growth.