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

Geni Gupur

Abstract and Applied Analysis, 2014, vol. 2014, 1-9

Abstract:

We describe the point spectrum of the generator of a -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 -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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:896342

DOI: 10.1155/2014/896342

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