Discrete-event stochastic systems with copula correlated input processes

Abstract

In this article, we develop a new method based on copulas to model correlated inputs in discrete-event stochastic systems. We first define a type of correlated stochastic process, called Copula Correlated Processes (CCPs), which we then use to model correlated inputs for discrete-event stochastic systems. In general, it is very difficult to analyze discrete-event stochastic systems with correlated inputs. However, we show that discrete-event stochastic systems with CCPs can be discretized and approximated by discrete-event stochastic systems with discrete copula correlated processes, which are equivalent to discrete-event stochastic systems driven by Markov-modulated processes and are much easier to analyze. An illustrative queueing example is provided to demonstrate how our method works.