A Robust Server-Effort Policy for Fluid Processing Networks
Multi-Class Processing Networks describe a set of servers that performs multiple classes of jobs on different items. The useful and tractable way to find an optimal control for such a network is to approximate it by a fluid network. Clearly arrival and servicing processes in such systems are affected by inherent uncertainty. A recent study addressed this issue by formulating a Robust Counterpart for a Separated Contin- uous Linear Programming model with budgeted uncertainty. The aforementioned approach provides a solution in terms of processing rates, which is transformed into a sequencing policy. However in cases where servers can process several jobs simultaneously, instead of a sequencing policy, we must implement a resource allocation policy. The existing approach cannot be implemented in this case. In this paper, we discuss situations where the implementation requires control of the proportion of server effort per class. We formulate Robust Counterparts of both processing rates and server-effort model in four types of uncertainty sets: box, budgeted, one-sided budgeted, and polyhedral. We prove that server-effort model provides a better solution than any algebraic transformation of the solution of the processing rates model. Finally, to get a grasp of how much our new model improves on the processing rates model, we provide the results of some numerical experiments.