We consider a call center model with m input flows and r pools of agents; the m-vector \lambda of instantaneous arrival rates is allowed to be time dependent and to vary stochastically. Seeking to optimize the trade-off between personnel costs and abandonment penalties, we develop and illustrate...

We consider a two-dimensional diffusion process Z(t) = [Z1(t), Z2(t)] that lives in the half strip {0 [less-than-or-equals, slant] Z1 [less-than-or-equals, slant] 1, 0 [less-than-or-equals, slant] Z2 < [infinity]}. 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 [theta] below the normal (0<[theta]<[theta]). 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 --> [infinity], and the marginal distributions of F are computed explicitly. The marginal limit...</[infinity]}.>

Consider a storage system (such as an inventory or bank account) whose content fluctuates as a Brownian Motion X = {X(t), t [greater-or-equal, slanted] 0} in the absence of any control. Let Y = {Y(t), t [greater-or-equal, slanted] 0} and Z = {Z(t), t [greater-or-equal, slanted] 0} be...

We consider a generalization of the classical model of collective risk theory. It is assumed that the cumulative income of a firm is given by a process X with stationary independent increments, and that interest is earned continuously on the firm's assets. Then Y(t), the assets of the firm at...