Statistical Properties of the Regenerative Processes with Networking Applications

Renewal and regenerative processes play a very significant role in applied probability. Models relied on regenerative process theory are very useful in a big variety of fields including telecommunication systems. It is especially important to notice that regenerative approach may be used for confident estimating while modeling of queueing systems.

We discuss main statistical properties of regenerative processes with focus on the regenerative simulation which is one of the basic methods in simulation output analysis estimating steady-state parameters. Indeed the regenerative simulation produces asymptotically valid confidence intervals for point estimators of time average both for continuous-time and discrete-time regenerative processes. Note that the latter is typically based on simulation of an integer number of the regenerative cycles.

The main purpose of the work is to present a survey of the basic properties of the regenerative variance estimators and the minimal sufficient conditions for the regenerative central limit theorem to be held. To illustrate the regenerative method, we study regenerative structure of a general queueing system with a finite buffer. In particular, we present non-standard regeneration instants and simulation results related to the output of the served customers and the overflow output, respectively.