Drift rate control of a Brownian processing system
| dc.creator | Ata, Bar | |
| dc.creator | Harrison, J. M. | |
| dc.creator | Shepp, L. A. | |
| dc.date | 2005-05-11 | |
| dc.date.accessioned | 2026-07-07T05:19:47Z | |
| dc.date.available | 2026-07-07T05:19:47Z | |
| dc.description | A system manager dynamically controls a diffusion process Z that lives in a finite interval [0,b]. Control takes the form of a negative drift rate θthat is chosen from a fixed set A of available values. The controlled process evolves according to the differential relationship dZ=dX-θ(Z) dt+dL-dU, where X is a (0,σ) Brownian motion, and L and U are increasing processes that enforce a lower reflecting barrier at Z=0 and an upper reflecting barrier at Z=b, respectively. The cumulative cost process increases according to the differential relationship dξ=c(θ(Z)) dt+p dU, where c(\cdot) is a nondecreasing cost of control and p>0 is a penalty rate associated with displacement at the upper boundary. The objective is to minimize long-run average cost. This problem is solved explicitly, which allows one to also solve the following, essentially equivalent formulation: minimize the long-run average cost of control subject to an upper bound constraint on the average rate at which U increases. The two special problem features that allow an explicit solution are the use of a long-run average cost criterion, as opposed to a discounted cost criterion, and the lack of state-related costs other than boundary displacement penalties. The application of this theory to power control in wireless communication is discussed. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051604000000855 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0505210 | |
| dc.identifier | http://arxiv.org/abs/math/0505210 | |
| dc.identifier | Annals of Applied Probability 2005, Vol. 15, No. 2, 1145-1160 | |
| dc.identifier | doi:10.1214/105051604000000855 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75149 | |
| dc.subject | Probability | |
| dc.subject | 60K25, 60J70, 90B22, 90B35 (Primary) | |
| dc.title | Drift rate control of a Brownian processing system | |
| dc.type | text |