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

We consider a single-server queueing system with a finite buffer, $K$ input Poisson flows of intensities $\lambda_i$, and distribution functions $B_i(x)$ of service times for calls of the $i$-th type, $i=1,\dots,K$. If the buffer is overflowed, an arriving call is sent to the orbit and becomes a repeat call. In a random time, which has exponential distribution, the call makes an attempt to reenter the buffer or server, if the latter is free. The maximum number of calls in the orbit is limited; if the orbit is overflowed, an arriving call is lost. We find the relation between steady-state distributions of this system and a system with one Poisson flow of intensity $\lambda=\sum^K_{i=1}\lambda_i$ where type $i$ of a call is chosen with probability $\lambda_i/\lambda$ at the beginning of its service. A numerical example is given.