  We introduce a novel single-server queue with general retrial times and
event-dependent arrivals. This is a versatile model for the study of service
systems, in which the server needs a non-negligible time to retrieve waiting
customers upon a service completion, while future arrivals depend on the last
realized event. Such a model is motivated by the customers' behaviour in
service systems where they decide to join based on the last realized event. We
investigate the necessary and sufficient stability condition and derive the
stationary distribution both at service completion epochs, and at an arbitrary
epoch using the supplementary variable technique. We also study the asymptotic
behaviour under high rate of retrials. Performance measures are explicitly
derived and extensive numerical examples are performed to investigate the
impact of event-dependency. Moreover, constrained optimisation problems are
formulated and solved with ultimate goal to investigate the admission control
problem.
