Two-parameter sample path large deviations for infinite-server queues
Let Q<sub>λ</sub>(t,y) be the number of people present at time t with y units of remaining service time in an infinite server system with arrival rate equal to λ>0. In the presence of a non-lattice renewal arrival process and assuming that the service times have a continuous distribut...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute for Operations Research and the Management Sciences (INFORMS)
2014-09-01
|
| Series: | Stochastic Systems |
| Subjects: | |
| Online Access: | http://www.i-journals.org/ssy/viewarticle.php?id=80&layout=abstract |
| Summary: | Let Q<sub>λ</sub>(t,y) be the number of people present at time t with y units of remaining service time in an infinite server system with arrival rate equal to λ>0. In the presence of a non-lattice renewal arrival process and assuming that the service times have a continuous distribution, we obtain a large deviations principle for Qλ( · )/λ under the topology of uniform convergence on [0,T]×[0,∞). We illustrate our results by obtaining the most likely path, represented as a surface, to ruin in life insurance portfolios, and also we obtain the most likely surfaces to overflow in the setting of loss queues. |
|---|---|
| ISSN: | 1946-5238 1946-5238 |