A note on simple eigenvalues of matrix polynomials in queueing models with Erlang distributions

Abstract

In this note, we study anEk/Em/1 queueing model where interarrival and service times are Erlang distributions with parametersk andm respectively. We prove that the roots of the characteristic polynomial associated with Erlang distributions are simple if the arrival and service rates are real. Based on this result, a general solution space of vectors for stationary probabilities is easily constructed.