A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic

Stochastic Processes and their Applications

Volumn 117, Issue 2, 2007, Pages 188-201

  Delgado, Rosario ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Fluid model; Heavy traffic; On off sources; Queueing network; Reflected fractional Brownian motion; Workload process

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FLOW OF FLUIDS; FUNCTION EVALUATION; QUEUEING NETWORKS; TELECOMMUNICATION TRAFFIC; THEOREM PROVING;

FLUID MODEL; HEAVY TRAFFICS; ON OFF SOURCES; REFLECTED FRACTIONAL BROWNIAN MOTION; WORKLOAD PROCESS;

BROWNIAN MOVEMENT;

EID: 33947151983     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2006.07.001     Document Type: Article

References (8)

1. n. Stochastics and Stochastics Reports 34 (1991) 149-167
2. Billingsley P. Convergence of Probability Measures (1968), Wiley
3. Debicki K., and Mandjes M. Traffic with an fBm limit: Convergence of the stationary workload process. Queueing Systems 46 (2004) 113-127
4. El Karoui N., and 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 (1978) 117-144
5. Harrison J.M. Balanced fluid models of multiclass queueing networks: A heavy traffic conjecture. In: Kelly F.P., and Williams R.J. (Eds). Stochastic Networks. IMA Volumes in Mathematics and its Applications vol. 71 (1995), Springer-Verlag, New York 1-20
6. Mandelbrot B.B., and Van Ness J.W. Fractional brownian motions, fractional noises and applications. SIAM Review 10 4 (1968) 422-437
7. Taqqu M.S., Willinger W., and Sherman R. Proof of a fundamental result in self-similar traffic modeling. Computer Communication Review 27 (1997) 5-23
8. Williams R.J. An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Systems 30 (1998) 5-25