2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61126A certain functional-difference equation that Runyon encountered when analyzing a queuing system was solved in a combined effort of Morrison, Carlitz, and Riordan. We simplify that analysis by exclusively using generating functions, in particular the kernel method, and the Lagrange inversion formula.Avoid recursions, use generating functionsCombinatorics04A15text