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

Geni Gupur

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
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https://doi.org/10.1155/2014/896342

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:896342

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