A receiver of “particles” has two cells each of which may contain only one particle. The cells are empty at the initial time. Particles arrive at a Poisson rate of λ. If one cell is occupied, no departures are possible. Once both cells are occupied, particles from outside do not enter the receiver; while each particle in the system, being considered separately and independently of the other, leaves its cell in the random time exponentially distributed with a parameter of μ. However, once one particle leaves the receiver (whichever comes first), the departure for the other particle is terminated, and the system comes back to the state with one particle.
Describe how the process X_t will run, and find the limiting probabilities. (Advice: You may use Proposition 4 assuming μ₁ = ε > 0 and letting ε→0 at the very end.)