The Almost Regenerative Method for Stochastic System Simulations

The regenerative method for simulations of stochastic systems allows data collection at the entry times to a single recurrent state of the process of interest. Estimates of estimator variance are then easily computed since the generated observations have the desirable property of being independent and identically distributed. Relative to a fixed run length, however, the mean time between entries into this single state may be excessively long for complicated stochastic systems (e.g., a congested network of queues), thus providing few observations and poor variance estimates. The almost regenerative method, a relaxation of the regenerative method, can, under frequently encountered conditions, alleviate this problem by allowing data collection at the entry times to a set of states of the process of interest. Empirical evidence from simulations of simple queueing networks supports the intuitive notion that the almost regenerative method can provide more accurate estimates of estimator variance than the regenerative method. Similar results hold when the almost regenerative method is compared to the frequently used fixed time increment method for event-oriented simulations.