Optimal stochastic scheduling of connected queues with switching costs

Structural properties of optimal policies for the problem of scheduling a single server in a forest network of N queues (without arrivals) subject to switching penalties are presented. In addition to linear holding costs, either lump sum switching costs or batch set-up delays that are incurred at each instant the server processes a job in a queue different than the previous one are composed. Reward rate notions are used to unearth conditions on the holding costs and service distributions for which an exhaustive policy is optimal. For the case of two nodes connected probabilistically in tandem, an optimal policy under similar conditions is explicitly defined