Are Pre-Processing and Prioritization Preferable in Service Systems?

The simplest option for a service system is to serve customers in the order of arrival by a "processor". However, another option involves employing "sorters" to gather information prior to processing. Sorting primarily prioritizes customers. For example, in emergency rooms, triage nurses act as sorters, and determine who should get priority. Prioritization itself might help reduce the overall waiting cost. Further, information gathered in the sorting step can reduce the need to gather the same information later. While these benefits of prioritization can be substantial, we find that its costs can be large too. First, sorters are paid salaries. Second, waiting for a sorter can be costly to customers having high waiting costs. We model a system with two classes of customers, and show that the heterogeneity in the waiting cost and the relative sizes of these customer classes play a pivotal role in determining when prioritizing is useful.