Submitted to manuscript ( Please , provide the manuscript number ! ) Priority Scheduling of Jobs with Unknown Types

In service systems, prioritization with respect to the relative “importance” of jobs helps allocate the limited resources efficiently. However, the information that is crucial to determine the importance level of a job may not be available immediately, but can be revealed through some preliminary investigation. While investigation provides useful information, it also delays the provision of services. Therefore, it is not clear if and when such an investigation should be carried out. To provide insights into this question, we consider a service system where finitely many jobs, all available at time zero, belong to one of the two possible types, where each type is characterized by its waiting cost and expected service time. Jobs’ type identities are initially unknown, but the service provider has the option to spend time on investigation to determine the type of a job albeit with a possibility of making an incorrect determination. Our objective is to identify policies that balance the time spent on information extraction with the time spent on service. Our study reveals that investigation is less likely to be beneficial when one of the types is significantly dominated by the other in terms of numbers, or the two types of jobs are not significantly different from each other with respect to their importance. More interestingly, we find that if the server decides to do investigation for all jobs, it is possible that more accurate information might result in higher costs. We also provide a complete characterization of the optimal dynamic policy. In particular, we show that the optimal dynamic policy that specifies when to carry out investigation is determined by a switching curve and we provide a mathematical expression for this switching curve. One insight that comes out of this characterization is that the server should start with performing investigation when there are sufficiently many jobs at the beginning and never perform investigation when there are few jobs.