This paper considers importance sampling as a tool for rare-event simulation. The system at hand is a so-called tandem queue with slow-down, which essentially means that the server of the first queue (or: upstreanm queue) switches to a lower speed when the second queue (downstream queue) exceeds some threshold. The goal is to assess to what extent such a policy succeeds in protecting the first queue, and therefore we focus on estimating the probability of overflow in the downstream queue. It is known that in this setting importance sampling with traditional state-independent distributions performs poorly. More sophisticated state-dependent schemes can be shown to be asymptotically efficient, but their implementation may be problematic, as for each state the new measure has to be computed. This paper presents an algorithm that is considerably simpler than the fully state-dependent scheme; it requires low computational effort, but still has high efficiency.
|Title of host publication||Proceedings of the 7th Internationals Workshop on Rare Event Simulation, RESIM 2008|
|Place of Publication||Rennes, France|
|Number of pages||12|
|ISBN (Print)||not assigned|
|Publication status||Published - 2008|
|Event||7th International Workshop on Rare Event Simulation, RESIM 2008 - Rennes, France|
Duration: 24 Sep 2008 → 26 Sep 2008
Conference number: 7
|Workshop||7th International Workshop on Rare Event Simulation, RESIM 2008|
|Period||24/09/08 → 26/09/08|
Miretskiy, D. I., Scheinhardt, W. R. W., & Mandjes, M. R. H. (2008). Simple and efficient importance sampling scheme for a tandem queue with server slow-down. In Proceedings of the 7th Internationals Workshop on Rare Event Simulation, RESIM 2008 (pp. 38-49). Rennes, France: INRIA.