Stability condition for the queueing model with retrial session arrivals and a finite buffer

Abstract

We consider a single-server finite buffer queueing model with customers arrival in sessions. Sessions admission into the system is regulated by granting so called tokens. The pool of tokens is finite. Session, which arrives when tokens are not available, leaves the system forever or joins the orbit and retries for the access later on. Session admission implies further arrival of a random number of customers in random time intervals. Customers are lost if" the buffer is full upon their arrival moments. Sufficient condition for existence of the stationary state distribution for this model is proven.