  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.
