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 |
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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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| _version_ | 1832565908375076864 |
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| author | Geni Gupur |
| author_facet | Geni Gupur |
| author_sort | Geni Gupur |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-196cb0e1632744f1beaf1be0854fa5bc |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-196cb0e1632744f1beaf1be0854fa5bc2025-02-03T01:05:32ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/896342896342On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing TheoryGeni Gupur0College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, ChinaWe 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.http://dx.doi.org/10.1155/2014/896342 |
| spellingShingle | Geni Gupur On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory Abstract and Applied Analysis |
| title | On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory |
| title_full | On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory |
| title_fullStr | On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory |
| title_full_unstemmed | On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory |
| title_short | On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory |
| title_sort | on eigenvalues of the generator of a c0 semigroup appearing in queueing theory |
| url | http://dx.doi.org/10.1155/2014/896342 |
| work_keys_str_mv | AT genigupur oneigenvaluesofthegeneratorofac0semigroupappearinginqueueingtheory |