  Service system dynamics occur at the interplay between customer behaviour and
a service provider's response. This kind of dynamics can effectively be modeled
within the framework of queuing theory where customers' arrivals are described
by point process models. However, these approaches are limited by parametric
assumptions as to, for example, inter-event time distributions. In this paper,
we address these limitations and propose a novel, deep neural network solution
to the queuing problem. Our solution combines a recurrent neural network that
models the arrival process with a recurrent generative adversarial network
which models the service time distribution. We evaluate our methodology on
various empirical datasets ranging from internet services (Blockchain, GitHub,
Stackoverflow) to mobility service systems (New York taxi cab).
