On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory
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, there...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/896342 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |