Center for Applied Mathematics Colloquium
Delay or queue length information has the potential to influence the decision of a customer to join a queue. Therefore, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. In this talk, we will analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on delayed queue length information. In the first fluid model, customers join each queue according to a Multinomial Logit Choice Model, however, the queue length information the customer receives is delayed by a constant amount of time which we call the delay. We show that oscillations or asynchronous behavior in the queueing model can occur based on the size of the delay. In the second model, customers receive information about the queue length through a moving average of the queue length. Although it has been shown empirically that giving patients moving average information causes oscillations and asynchronous behavior to occur in U.S. hospitals. We will also show that the moving average fluid model can exhibit oscillations and determine its dependence on the moving average window. Thus, our analysis provides new insight on how managers of queueing systems should report queue length information to customers and how delayed information can produce unwanted behavior.