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June 2015 Admission control for multidimensional workload input with heavy tails and fractional Ornstein-Uhlenbeck process
Amarjit Budhiraja, Vladas Pipiras, Xiaoming Song
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Adv. in Appl. Probab. 47(2): 476-505 (June 2015). DOI: 10.1239/aap/1435236984


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 ∞, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H > ½.


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Amarjit Budhiraja. Vladas Pipiras. Xiaoming Song. "Admission control for multidimensional workload input with heavy tails and fractional Ornstein-Uhlenbeck process." Adv. in Appl. Probab. 47 (2) 476 - 505, June 2015.


Published: June 2015
First available in Project Euclid: 25 June 2015

zbMATH: 1321.60196
MathSciNet: MR3360386
Digital Object Identifier: 10.1239/aap/1435236984

Primary: 60G18 , 60G57
Secondary: 60G15 , 90B15

Keywords: admission control , fractional Brownian motion , fractional Ornstein-Uhlenbeck process , Gaussian random measure , heavy-tailed distribution , Poisson random measure , self-similarity

Rights: Copyright © 2015 Applied Probability Trust


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Vol.47 • No. 2 • June 2015
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