Wide-sense regeneration for Harris recurrent Markov processes: an open problem

Harris recurrence is a widely used tool in the analysis of queueing systems. For discrete-time Harris chains, such systems automatically exhibit wide-sense regenerative structure, so that renewal theory can be applied to questions related to convergence of the transition probabilities to the equilibrium distribution. By contrast, in continuous time, the question of whether all Harris recurrent Markov processes are automatically wide-sense regenerative is an open problem. This paper reviews the key structural results related to regeneration for discrete-time chains and continuous time Markov processes, and describes the key remaining open problem in this subject area.