Estimation of the workload correlation in a Markov fluid queue

This paper considers a Markov fluid queue, focusing on the correlation function of the stationary workload process. A simulation-based computation technique is proposed, which relies on a coupling idea. Then an upper bound on the variance of the resulting estimator is given, which reveals how the coupling time and the busy period of the Markov fluid queue affect the performance of the computation procedure. A numerical assessment, in which we compare the proposed technique with naive simulation, gives an indication of the achievable efficiency gain in various scenarios.