  Upon arrival to a ticket queue, a customer is offered a slip of paper with a
number on it and is told the number of the customer currently in service. The
arriving customer then chooses whether to take the slip or balk, a decision
based on the perceived queue length and associated waiting time. Even after
taking a ticket, a customer may abandon the queue, an event that will be
unobservable until the abandoning customer would have begun service. In
contrast, a standard queue has a physical waiting area so that abandonment is
apparent immediately when it takes place and balking is based on the actual
queue length at the time of arrival. We prove heavy tra?c limit theorems for
the generalized ticket and standard queueing processes, discovering that the
processes converge together to the same limit, a regulated Ornstein-Uhlenbeck
(ROU) process. One conclusion is that for a highly utilized service system with
a relatively patient customer population, the ticket and standard queue
performances are asymptotically indistinguishable on the scale typically
uncovered under heavy tra?c approaches. Next, we heuristically estimate several
performance metrics of the ticket queue, some of which are of a sensitivity
typically undetectable under diffusion scaling. The estimates are tested using
simulation and are shown to be quite accurate under a general collection of
parameter settings.

Probability