When to Triage in Service Systems with Hidden Customer Class Identities?

In service systems with heterogeneous customers, prioritization with respect to the relative importance of customers is known to improve certain performance measures. However, in many applications, information necessary to determine the importance level of a customer may not be available immediately but can be revealed only through some preliminary investigation, which is sometimes called triage. This triage process is typically error-prone and may take substantial amount of time, and hence, it is not always clear if and when it should be implemented for purposes of priority assignment. To provide insights into this question, we study a stylized queueing model with a single server and two types of customers with hidden type identities, which differ in their rates of service and waiting costs. By means of a Markov decision formulation, we first show that the optimal dynamic policy on triage is characterized by a switching curve. The comparison of two state-independent policies (no-triage and triage-all) shows that the information from triage is more beneficial when the traffic intensity is neither too low nor too high. Our numerical results show that the system manager should consider implementing a state-dependent triage policy when the probability of classifying a customer into the important class and the mean triage time are of moderate size, when the difference between the importance levels of the two classes of customers is large, and/or when the traffic intensity is high.