On a Retrial Single-Server Queueing System with Finite Buffer and Poisson Flow

A retrial single-server queueing system with finite buffer is considered. The primary incoming flow is Poissonian. If the buffer is overflown, a call entering the system becomes a repeat call and joins the group of repeat calls referred to as an orbit. The maximum number of calls that can simultaneously be contained in the orbit is limited. A call from the orbit makes new attempts to enter the system until a vacancy occurs. Time between repeat attempts for each call is an exponentially distributed random variable. At the initial moment of service, a type of a call is defined: with probability $a_i$ it becomes a call of type $i$ and its service time in this case has distribution function $B_i(x)$, $i=1,\dots,K$. For this system, the stationary joint distribution of queues in the buffer and orbit is found. Numerical examples are given.