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2014 On Eigenvalues of the Generator of a C 0 -Semigroup Appearing in Queueing Theory
Geni Gupur
Abstr. Appl. Anal. 2014(SI62): 1-9 (2014). DOI: 10.1155/2014/896342

Abstract

We describe the point spectrum of the generator of a C 0 -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 C 0 -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.

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Geni Gupur. "On Eigenvalues of the Generator of a C 0 -Semigroup Appearing in Queueing Theory." Abstr. Appl. Anal. 2014 (SI62) 1 - 9, 2014. https://doi.org/10.1155/2014/896342

Information

Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07023264
MathSciNet: MR3272224
Digital Object Identifier: 10.1155/2014/896342

Rights: Copyright © 2014 Hindawi

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Vol.2014 • No. SI62 • 2014
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