1亿文档 免费下载

免费下载此文档侵权投诉# AROBUSTIDENTIFICATIONALGORITHMFORTRAFFICMODELSIN TELECOMMUNICATIONS

### Word文档免费下载：AROBUSTIDENTIFICATIONALGORITHMFORTRAFFICMODELSIN TELECOMMUNICATIONS

（下载1-6页，共6页）

*Thegoalofthispaperistopresentarobustidenti-cationalgorithmfortheparametersofARstochastic processes,andemploythisinanalyzingtelecommu-nicationtracdata,mainlyvideotrac(VBR)in TherehasbeengrowinginterestinMA,ARandAR-MAmodelsoftracintelecommunicationsnetworks*

A ROBUST IDENTIFICATION ALGORITHM FOR TRAFFIC MODELS IN TELECOMMUNICATIONS Omar Ait-Hellal1, Eitan Altman1 INRIA, 2004 Route des Lucioles, 06902 Sophia Antipolis Cedex, France. Tel: (+33) 04 92 38 77 86 Email: foaithel,altmang@sophia.inria.fr The goal of this paper is to present a robust identi cation algorithm for the parameters of AR stochastic processes, and employ this in analyzing telecommunication tra c data, mainly video tra c (VBR) in ATM networks. Coordinated Science Laboratory, University of Illinois, 1308 West Main Street, Urbana, IL 61801-2307, USA. Tel: (217) 333-3607; Fax: (217) 244-1653; Email: tbasar@decision.csl.uiuc.edu.

Tamer Ba ar2

ABSTRACT

2. The model We consider in this paper the estimation of the parameters`1;:::;`d of the AR process n= d X i=1

1. Introduction There has been growing interest in MA, AR and ARMA models of tra c in telecommunications networks in recent years. Such models allow not only for the identi cation of the characteristics and understanding of the behavior of tra c, but also for queueing performance analysis (e.g. 1]) as well as optimization and control issues. ARMA models have been used for characterizing LAN tra c 5], video codec sources in ATM networks 7, 14], and ATM tra c 9]. In the latter, the ARMA tra c model has been shown to perform better than a two-state MMPP (Markov Modulated Poisson Process). Comparisons with other tra c models can be found in 13]. An important feature of ARMA models is that they can easily be used in control design. We cite in this context 15], which uses an auto-regressive approach for designing a predictive congestion control in the presence of other real time tra c. Two other references, 2] and 3], have analyzed the stability of rate based ow control of ABR (Available Bit Rate) tra c in ATM in the presence of exogenous VBR tra c. In 4], a robust control approach has been used for the design of rate-based ow controls for ABR tra c, in the presence of exogenous tra c modeled by ARMA processes. The goal of this paper is to present a robust identication algorithm for the parameters of AR stochastic processes, and employ this in analyzing telecommunication tra c data. 1. The work by the rst two authors was supported by the France-Telecom C.N.E.T. through research grant CTI 97 1B 206 2. Research supported by Grants ANI 9813710 and INT9804950 from the National Science Foundation.

`i n?i+ k n;

(1)

Here`0 is some initial estimate for`, Q0> 0 is a xed weighting matrix, and Qn 0; n= 0; 1;::: is

where k is taken to be a constant, and equal to 1 without any loss of generality. For the special case when the driving noise n is i.i.d. Gaussian, the least squares approach can be used to obtain an optimal estimator for both its variance (in case it is unknown) as well as the coe cients`; see e.g. 10, 12, 16]. We shall adopt here, instead, a robust identi cation approach. This technique often leads to better performance when the noise is correlated and/or nonst

ationary, and it is more robust to modeling imprecisions. These advantages were already observed in the design of optimal controllers with noisy information and dynamics driven by some noise, see 4] for examples of dynamic ow control in high speed telecommunications networks. Our derivation here will follow closely the methodology introduced in 6] where the robust identi cation problem was addressed in a continuous-time setting. We use the following vector notation of the dynamics (1): 0 (2) n+1= n`+ n where?=` def`d;:::;`1 0 and n def ( n?d+1; n?d+2; n )0:= n is an unknown noise sequence (satisfying some persistency of excitation conditions, to be made precise later). We wish to obtain a sequence of (progressively im^ proving) estimates for`, to be denoted`n at step n,^n would depend on all the past and present so that`^^ values of ( ), i.e.`n=`( n; n?1;:::; 0 ). The criterion to be used (which is to be minimized) is of the H1 type, which is the gain from the energy of the unknowns to a weighted quadratic identi cation error:^ n=0 J (f`ng1 ):= P1 (^ 0^ (3) sup P1 n=02`?`n ) Qn(0`?`n ) f n g1=0;` n=0 j n j+ (`?`0 ) Q0 (`?`0 ) n

## 猜你喜欢