Matrix Product-Form Solutions of Stationary Probabilities in Tandem Queues

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

“…He showed that the stationary solution is a linear combination of Kronecker productforms which can be expressed in terms of roots of the associated characteristic polynomial. Luh [9] used a similar approach to derive stationary probabilities in terms of linear combinations of product-forms in studying a system of two stations in tandem. In short, we concentrate on what will be called the Kronecker vector approach.…”

“…However, there was no theoretic discussion of such a case in [1,3,4,9]. They all presented that the transforms of interarrival and service times distributions satisfy an equation of a simple form, and used the roots of the equation to express the stationary solution under the assumption all the roots are distinct.…”