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The Impact of Delay Announcements in Many-Server
Queues with Abandonment
Mor Armony
ABSTRACT
In this work we develop methods to study the impact upon aggregate system
performance of state-dependent delay announcements to arriving customers in a
many-server queue with customer abandonment. We assume that the queue is not
visible to waiting customers, as in most customer contact centers, when contact
is made by telephone, email or instant messaging. As a function of the
announced delay customers may balk or have new abandonment behavior. To perform
a rough-cut analysis, prior to a more detailed study, we use a fluid model, which
provides an approximate and highly simplified description of large systems in
an overloaded regime. In the fluid model, all customers are faced with the same
delay and consequently can be given the same delay announcement. At the same
time, the time-to-abandon distribution plays a critical role.
We show that the resulting approximate description of aggregate performance is
effective by comparing to (1) a numerical algorithm approximating the
steady-state performance of an M/GI/s+GI queueing model with a constant delay announcement and (2)
simulations with state-dependent announcements. Specifically, customers who
cannot enter service immediately are told the delay of the last customer to
enter service. Within the fluid model framework, we find conditions under which
there exists a unique equilibrium delay, where the actual delay coincides with
the announced delay, and for a natural iteration to converge to that
equilibrium delay. We further consider the effect of providing biased delay
information, and show how the fluid model can be applied to do further studies.
* This is joint work with Nahum Shimkin and Ward
Whitt
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