Managing Information in Queues: The Impact of Giving Delayed Information   to Customers
  Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the performance of the system. To this end, we construct and 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 Model, however, the queue length information the customer receives is delayed by a constant $\Delta$. We show that the delay can cause oscillations or asynchronous behavior in the model based on the value of $\Delta$. 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 in the work of Dong et al., we analytically and mathematically show for the first time that the moving average fluid model can exhibit oscillations and determine their dependence on the moving average window. Thus, our analysis provides new insight on how managers of service systems information systems should report queue length information to customers and how delayed information can produce unwanted behavior. 
Jamol Pender, Richard H. Rand and Elizabeth Wesson
math.OC math.DS