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Queues with Delays in Two-State Strategies and Lévy Input
| Content Provider | Scilit |
|---|---|
| Author | Bekker, R. Boxma, O. J. Kella, O. |
| Copyright Year | 2008 |
| Description | We consider a reflected Lévy process without negative jumps, starting at the origin. When the reflected process first upcrosses level K, a timer is activated. After D time units, the timer expires and the Lévy exponent of the Lévy process is changed. As soon as the process hits zero again, the Lévy exponent reverses to the original function. If the process has reached the origin before the timer expires then the Lévy exponent does not change. Using martingale techniques, we analyze the steady-state distribution of the resulting process, reflected at the origin. We pay special attention to the cases of deterministic and exponential timers, and to the following three special Lévy processes: (i) a compound Poisson process plus negative drift (corresponding to an M/G/1 queue), (ii) Brownian motion, and (iii) a Lévy process that is a subordinator until the timer expires. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4B7C2A6EB98A789B85331CC77A9BFD08/S0021900200004253a.pdf/div-class-title-queues-with-delays-in-two-state-strategies-and-levy-input-div.pdf |
| Ending Page | 332 |
| Page Count | 19 |
| Starting Page | 314 |
| ISSN | 00219002 |
| e-ISSN | 14756072 |
| DOI | 10.1017/s0021900200004253 |
| Journal | Journal of applied probability |
| Issue Number | 02 |
| Volume Number | 45 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2008-06-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of applied probability Mathematical Physics 1 Queue Workload Process Storage Process Reflected Lévy Process Lévy Exponent state Strategy Delayed Feedback Control |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability Statistics, Probability and Uncertainty |
