A single-server retrial queue system with multidimensional Poisson flow

A single-server bufferless queue system with It independent Poisson input flows and arbitrary service distribution functions is investigated. A customer of any type denied service joins the queue afresh, retaining his type. Three modifications, viz., (1) a system with persistent customers, (2) a system with nonpersistent customers, (3) a system with server vacations, are studied. For each modification, recurrent formulas for the stationary distribution of the multidimensional retrial queue and expressions for the generating functions are derived.