Managing Queues with Different Resource Requirements
Queueing models that are used to capture various service settings typically assume that customers require a single unit of resources (servers) to be processed. However, there are many service settings where such an assumption may fail to capture the heterogeneity in resource requirements of different customers. For instance, clinical guidelines suggest that patients should be classified based on the level of medical attention/supervision required.
We propose a multi-server queueing model with multiple customer classes in which customers from different classes may require different amounts of resources to be served. We study the optimal scheduling policy for such systems. To balance the holding cost, the service rate, the resource requirement, and the priority-induced idleness, we develop a class of index-based policies which we refer to as the idle-aware cµ/m rule. We establish the asymptotic optimality of this class of policies in the many-server heavy-traffic regime. For a two-class two-server model, where policy-induced idleness can have a big impact on system performance, we establish a uniform performance bound on the amount of sub-optimality incurred by the idle-avoid cµ/m rule (a special case of the idle-aware cµ/m rule). This theoretical bound, along with numerical experiments, provides support for the robustness of our proposed class of policies.