DOIAbstract
AbstractWe consider a two-dimensional diffusion process Z(t) = [Z1(t), Z2(t)] that lives in the half strip {0 ⩽ Z1 ⩽ 1, 0 ⩽ Z2 < ∞}. On the interior of this state space, Z behaves like a standard Brownian motion (independent components with zero drift and unit variance), and there is instantaneous reflection at the boundary. The reflection is in a direction normal to the boundary at Z1 = 1 and Z2 = 0, but at Z1 = 0 the reflection is at an angle θ below the normal (0<θ<12θ). This process Z is shown to arise as the diffusion limit of a certain tandem storage or queuing system. It is shown that Z(t) has a nondefective limit distribution F as t → ∞, and the marginal distributions of F are computed explicitly. The marginal limit distribution for...
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