Sample Path Bounds for Long Memory FBM Traffic

Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent Internet traffic. Asymptotic, respectively, approximate performance measures are known from large deviations theory for single queuing systems with fBm traffic. In this paper we prove a rigorous sample path envelope for fBm that complements previous results. We find that both approaches agree in their outcome that overflow probabilities for fBm traffic have a Weibull tail. We show numerical results on the impact of the variability and the correlation of fBm traffic on the queuing performance.

[1]  Richard G. Baraniuk,et al.  Multiscale queueing analysis , 2006, TNET.

[2]  Amr Rizk,et al.  Statistical end-to-end performance bounds for networks under long memory FBM cross traffic , 2010, 2010 IEEE 18th International Workshop on Quality of Service (IWQoS).

[3]  Yuming Jiang,et al.  Analysis on generalized stochastically bounded bursty traffic for communication networks , 2002, 27th Annual IEEE Conference on Local Computer Networks, 2002. Proceedings. LCN 2002..

[4]  John A. Silvester,et al.  Time scale analysis of an ATM queueing system with long-range dependent traffic , 1997, Proceedings of INFOCOM '97.

[5]  Nick Duffield,et al.  Large deviations and overflow probabilities for the general single-server queue, with applications , 1995 .

[6]  Frank Kelly,et al.  Notes on effective bandwidths , 1994 .

[7]  Nelson Luis Saldanha da Fonseca,et al.  On the equivalent bandwidth of self-similar sources , 2000, TOMC.

[8]  Sally Floyd,et al.  Wide area traffic: the failure of Poisson modeling , 1995, TNET.

[9]  Walter Willinger,et al.  Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level , 1997, TNET.

[10]  Anja Feldmann,et al.  Dynamics of IP traffic: a study of the role of variability and the impact of control , 1999, SIGCOMM '99.

[11]  Chengzhi Li,et al.  A Network Calculus With Effective Bandwidth , 2007, IEEE/ACM Transactions on Networking.

[12]  Richard G. Baraniuk,et al.  Multiscale Queuing Analysis , 2004 .

[13]  Chaiwat Oottamakorn,et al.  Statistical service assurances for traffic scheduling algorithms , 2000, IEEE Journal on Selected Areas in Communications.

[14]  Walter Willinger,et al.  Proof of a fundamental result in self-similar traffic modeling , 1997, CCRV.

[15]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.

[16]  Florin Ciucu,et al.  Delay Bounds for Networks with Heavy-Tailed and Self-Similar Traffic , 2009, ArXiv.

[17]  Cheng-Shang Chang,et al.  Performance guarantees in communication networks , 2000, Eur. Trans. Telecommun..

[18]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[19]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[20]  Mukesh Taneja.  A service curve approach for quality of service management in integrated services networks , 1998 .

[21]  Laurent Massoulié,et al.  Large buffer asymptotics for the queue with fractional brownian input , 1999 .

[22]  Ilkka Nomos.  On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks , 1995 .

[23]  Florin Ciucu,et al.  Delay Bounds in Communication Networks With Heavy-Tailed and Self-Similar Traffic , 2009, IEEE Transactions on Information Theory.

[24]  Florin Ciucu,et al.  Scaling properties of statistical end-to-end bounds in the network calculus , 2006, IEEE Transactions on Information Theory.

[25]  Alain Simonian,et al.  Large Buffer Asymptotics For The Queue With FBM Input , 1998 .

[26]  Yong Liu,et al.  Stochastic Network Calculus , 2008 .