Flexible Server Allocation and Customer Routing Policies for Two Parallel Queues When Service Rates Are Not Additive

We consider the question of how routing and allocation can be coordinated to meet the challenge of demand variability in a parallel queueing system serving two types of customers. A decision maker decides whether to keep customers at the station at which they arrived or to reroute them to the other station. At the same time, the decision maker has two servers and must decide where to allocate their effort. We analyze this joint decision-making scenario with both routing and station-dependent holding costs, but add an important twist. We allow the combined service rate (when the servers work at the same station) to be superadditive or subadditive. This captures positive or negative externalities that arise during collaboration. We seek an optimal control policy under the discounted or long-run average cost criteria. Our results show that in the superadditive case jobs should never be routed away from the lower-cost queue. When jobs are rerouted from the higher-cost queue to the low-cost queue the optimal c...