  Giving customers queue length information about a service system has the
potential to influence the decision of a customer to join a queue. Thus, it is
imperative for managers of queueing systems to understand how the information
that they provide will affect the performance of the system. To this end, we
construct and analyze a two-dimensional deterministic fluid model that
incorporates customer choice behavior based on delayed queue length
information. All of the previous literature assumes that all queues have
identical parameters and the underlying dynamical system is symmetric. However,
in this paper, we relax this symmetry assumption by allowing the arrival rates,
service rates, and the choice model parameters to be different for each queue.
Our methodology exploits the method of multiple scales and asymptotic analysis
to understand how to break the symmetry. We find that the asymmetry can have a
large impact on the underlying dynamics of the queueing system.
