Kronecker product-forms of steady-state probabilities with \(C_k/C_m/1\) by matrix polynomial approaches (Q429005)

The authors consider a single server queue with unlimited waiting room, and inter-arrival times and service times of Coxian type. This allows to apply matrix-analytical methods for quasi-birth-death processes and needs the evaluation of a quadratic matrix equation. Using an inherent Kronecker product structure, the authors investigate the associated fundamental matrix polynomial in detail. The result is a structural simplification for obtaining the steady state probabilities of non-boundary states which may enhance the numerical procedures still to perform.