Alternative estimators of blocking probability in retrial queuing system

The presented retrial system with constant rate can be used to describe, for instance, behavior of ALOHA type multiple access protocol or short TCP transfers. Arrivals who find the server busy join to infinite capacity orbit, and then return to the system after exponentially distributed retrial time.

The goal of the research is to estimate the blocking probability P_orb (the probability to join the orbit) in a single server system with Poisson input and no buffer (an M/G/1/1-type retrial system) both in the stability and instability region.

The analysis is based on the regenerative method. Various estimators are presented. In particularly, a regenerative estimator which is based on residual-cycle time is applied for estimation of P_orb in unstable mode.

The variance reduction effect and efficiency of estimators are studied. Numerical results of simulation are consistent with known analytical results and corresponding results for loss systems.