On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory

Abstract EN

We describe the point spectrum of the generator of a C0-semigroup associated with the M/M/1 queueing model that is governed by an infinite system of partial differential equations with integral boundary conditions.

Our results imply that the essential growth bound of the C0-semigroup is 0 and, therefore, that the semigroup is not quasi-compact.

Moreover, our result also shows that it is impossible that the time-dependent solution of the M/M/1 queueing model exponentially converges to its steady-state solution.