  We present methodology for estimating the stochastic intensity of a doubly
stochastic Poisson process. Statistical and theoretical analyses of traffic
traces show that these processes are appropriate models of high intensity
traffic arriving at an array of service systems. The statistical estimation of
the underlying latent stochastic intensity process driving the traffic model
involves a rather complicated nonlinear filtering problem. We develop a novel
simulation methodology, using deep neural networks to approximate the path
measures induced by the stochastic intensity process, for solving this
nonlinear filtering problem. Our simulation studies demonstrate that the method
is quite accurate on both in-sample estimation and on an out-of-sample
performance prediction task for an infinite server queue.
