Customers arrive sequentially to a service system where
the arrival times form a Poisson process of rate λ.
The system offers a choice between a private channel
and a public set of channels. The transmission rate at
each of the public channels is faster than that of the
private one; however, if all of the public channels are
occupied, then a customer who commits itself to using one
of them attempts to connect after exponential periods of
time with mean μ−1. Once connection
to a public channel has been made, service is completed
after an exponential period of time, with mean
ν−1. Each customer chooses one of
the two service options, basing its decision on the number
of busy channels and reapplying customers, with the aim of
minimizing its own expected sojourn time. The best action
for an individual customer depends on the actions taken by
subsequent arriving customers. We establish the existence of
a unique symmetric Nash equilibrium policy and show that its
structure is characterized by a set of threshold-type strategies;
we discuss the relevance of this concept in the context of
a dynamic learning scenario.