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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Hindawi Limited
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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doaj-196cb0e1632744f1beaf1be0854fa5bc2020-11-25T01:02:11ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Geni Gupur |
| spellingShingle |
Geni Gupur On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory Abstract and Applied Analysis |
| author_facet |
Geni Gupur |
| author_sort |
Geni Gupur |
| title |
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_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_sort |
on eigenvalues of the generator of a c0-semigroup appearing in queueing theory |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2014/896342 |
| work_keys_str_mv |
AT genigupur oneigenvaluesofthegeneratorofac0semigroupappearinginqueueingtheory |
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