Journal article
ADMISSION CONTROL FOR MULTIDIMENSIONAL WORKLOAD INPUT WITH HEAVY TAILS AND FRACTIONAL ORNSTEIN-UHLENBECK PROCESS
Advances in applied probability, v 47(2), pp 476-505
01 Jun 2015
Abstract
The infinite source Poisson arrival model with heavy-tailed workload distributions has attracted much attention, especially in the modeling of data packet traffic in communication networks. In particular, it is well known that under suitable assumptions on the source arrival rate, the centered and scaled cumulative workload input process for the underlying processing system can be approximated by fractional Brownian motion. In many applications one is interested in the stabilization of the work inflow to the system by modifying the net input rate, using an appropriate admission control policy. In this paper we study a natural family of admission control policies which keep the associated scaled cumulative workload input asymptotically close to a prespecified linear trajectory, uniformly over time. Under such admission control policies and with natural assumptions on arrival distributions, suitably scaled and centered cumulative workload input processes are shown to converge weakly in the path space to the solution of a d-dimensional stochastic differential equation driven by a Gaussian process. It is shown that the admission control policy achieves moment stabilization in that the second moment of the solution to the stochastic differential equation (averaged over the d-stations) is bounded uniformly for all times. In one special case of control policies, as time approaches infinity, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H > 1/2.
Metrics
9 Record Views
Details
- Title
- ADMISSION CONTROL FOR MULTIDIMENSIONAL WORKLOAD INPUT WITH HEAVY TAILS AND FRACTIONAL ORNSTEIN-UHLENBECK PROCESS
- Creators
- Amarjit Budhiraja - Univ N Carolina, Chapel Hill, NC 27599 USAVladas Pipiras - Univ N Carolina, Chapel Hill, NC 27599 USAXiaoming Song - Univ N Carolina, Chapel Hill, NC 27599 USA
- Publication Details
- Advances in applied probability, v 47(2), pp 476-505
- Publisher
- Applied Probability Trust
- Number of pages
- 30
- Grant note
- DMS-1004418; DMS-1016441 / National Science Foundation; National Science Foundation (NSF) H98230-13-1-0220 / NSA; National Security Agency W911NF-10-1-0158 / Army Research Office 2008466 / US-Israel Binational Science Foundation
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000357549600008
- Scopus ID
- 2-s2.0-84940387680
- Other Identifier
- 991021864453404721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Statistics & Probability