Abstract and Applied Analysis

On Eigenvalues of the Generator of a C 0 -Semigroup Appearing in Queueing Theory

Geni Gupur

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 896342, 9 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425047823

Digital Object Identifier
doi:10.1155/2014/896342

Mathematical Reviews number (MathSciNet)
MR3272224

Zentralblatt MATH identifier
07023264

Citation

Gupur, Geni. On Eigenvalues of the Generator of a ${C}_{0}$ -Semigroup Appearing in Queueing Theory. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 896342, 9 pages. doi:10.1155/2014/896342. https://projecteuclid.org/euclid.aaa/1425047823


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