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A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic. (English) Zbl 1108.60074
Summary: We consider a family of non-deterministic fluid models that can be approximated under heavy traffic conditions by a multidimensional reflected fractional Brownian motion (rfBm). Specifically, we prove a heavy traffic limit theorem for multi-station fluid models with feedback and non-deterministic arrival process generated by a large enough number of heavy tailed ON/OFF sources, say $N$. Scaling in time by a factor $r$ and in state space conveniently, and letting $N$ and $r$ approach infinity (in this order) we prove that the scaled immediate workload process converges in some sense to an rfBm.

MSC:
60K25Queueing theory
60G15Gaussian processes
90B22Queues and service (optimization)
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References:
[1] Bernard, A.; El Kharroubi, A.: Régulations déterministes et stochastiques dans le premier orthant de rn. Stochastics and stochastics reports 34, 149-167 (1991) · Zbl 0727.60109
[2] Billingsley, P.: Convergence of probability measures. (1968) · Zbl 0172.21201
[3] Debicki, K.; Mandjes, M.: Traffic with an fBm limit: convergence of the stationary workload process. Queueing systems 46, 113-127 (2004) · Zbl 1061.90019
[4] El Karoui, N.; Chaleyat-Maurel, M.: Un problème de réflexion et ses aplications au temps local et aux équations différentielles stochastiques sur R. Cas continu. Société mathématique de France, astérisque 52--53, 117-144 (1978)
[5] Harrison, J. M.: Balanced fluid models of multiclass queueing networks: A heavy traffic conjecture. IMA volumes in mathematics and its applications 71, 1-20 (1995) · Zbl 0838.90045
[6] Mandelbrot, B. B.; Van Ness, J. W.: Fractional Brownian motions, fractional noises and applications. SIAM review 10, No. 4, 422-437 (1968) · Zbl 0179.47801
[7] Taqqu, M. S.; Willinger, W.; Sherman, R.: Proof of a fundamental result in self-similar traffic modeling. Computer communication review 27, 5-23 (1997)
[8] Williams, R. J.: An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing systems 30, 5-25 (1998) · Zbl 0911.90170