Doubly Stochastic Generative Arrivals Modeling

Abstract

We propose a new framework named DS-WGAN that integrates the doubly stochastic (DS) structure and the Wasserstein generative adversarial networks (WGAN) to model, estimate, and simulate a wide class of arrival processes with non-stationary and stochastic arrival rates. We prove statistical consistency for the estimator solved by the DS-WGAN framework. We then discuss and address challenges from the computational aspect in the model estimation procedures. We show that the DS-WGAN framework can facilitate what-if simulation and predictive simulation for scenarios that have never happened before in the historical data. Numerical experiments with synthetic and real data sets are implemented to demonstrate the performance of DS-WGAN, both from a statistical perspective and from an operational performance evaluation perspective.Numerical experiments suggest that the successful model estimation for DS-WGAN only requires a moderate size of data, which can be appealing in the contexts of operational management.