Block renewal processes and their application to modeling

A new stochastic process called block renewal process (or G(m) process) is proposed for modeling auto-correlated arrival processes of queueing systems. This process can be modeled easily by the observable marginal distribution and global auto-correlation index of auto-correlated arrival process. This new process is very simple and tractable, so it is good for both simulation and numerical computation. We also discuss how to obtain analytically the steady-state distribution of queue length of a G(2)/M/1 queue.