  In this paper, we apply a supervised machine-learning approach to solve a
fundamental problem in queueing theory: estimating the transient distribution
of the number in the system for a G(t)/GI/1. We develop a neural network
mechanism that provides a fast and accurate predictor of these distributions
for moderate horizon lengths and practical settings. It is based on using a
Recurrent Neural Network (RNN) architecture based on the first several moments
of the time-dependant inter-arrival and the stationary service time
distributions; we call it the Moment-Based Recurrent Neural Network (RNN)
method (MBRNN ). Our empirical study suggests MBRNN requires only the first
four inter-arrival and service time moments. We use simulation to generate a
substantial training dataset and present a thorough performance evaluation to
examine the accuracy of our method using two different test sets. We show that
even under the configuration with the worst performance errors, the mean number
of customers over the entire timeline has an error of less than 3%. While
simulation modeling can achieve high accuracy, the advantage of the MBRNN over
simulation is runtime, while the MBRNN analyzes hundreds of systems within a
fraction of a second. This paper focuses on a G(t)/GI/1; however, the MBRNN
approach demonstrated here can be extended to other queueing systems, as the
training data labeling is based on simulations (which can be applied to more
complex systems) and the training is based on deep learning, which can capture
very complex time sequence tasks. In summary, the MBRNN can potentially
revolutionize our ability to perform transient analyses of queueing systems.
