Self-Selecting Priority Queues with Burr Distributed Waiting Costs

Service providers, in the presence of congestion and heterogeneity of customer waiting costs, often introduce a fee-based premier option using which the customers self-segment themselves. Examples of this practice are found in health care, amusement parks, government (consular services), and transportation. Using a single-server queuing system with customer waiting costs modeled as a Burr Distribution, we perform a detailed analysis to (i) determine the conditions (fees, cost structure, etc.) under which this strategy is profitable for the service provider, (ii) quantify the benefits accrued by the premier customers; and (iii) evaluate the resulting impact on the other customers. We show that such self-selecting priority systems can be pareto-improving in the sense that they are beneficial to everyone. These benefits are larger when the variance in the customer waiting costs is high and the system utilization is high. We use income data from the poorest and richest areas (identified by zipcode) in the United States along with the countrywide income distribution to illustrate our results. Numerical results indicate that planning for a 20-40% enrollment in the high-priority option is robust in ensuring that all the stakeholders benefit from the proposed strategy.