Optimal Capacity Planning in Stochastic Loss Networks with Time-Varying Workloads

We consider a capacity planning optimization problem in a general theoretical framework that extends the classical Erlang loss model and related stochastic loss networks to support time-varying workloads. The time horizon consists of a sequence of coarse time intervals, each of which involves a stochastic loss network under a fixed multi-class workload that can change in a general manner from one interval to the next. The optimization problem consists of determining the capacities for each time interval that maximize a utility function over the entire time horizon, finite or infinite, where rewards gained from servicing customers are offset by penalties associated with deploying capacities in an interval and with changing capacities among intervals. We derive a state-dependent optimal policy within the context of a particular limiting regime of the optimization problem, and we prove this solution to be asymptotically optimal. Then, under fairly mild conditions, we prove that a similar structural property holds for the optimal solution of the original stochastic optimization problem, and we show how the optimal capacities comprising this solution can be efficiently computed.