Multifractal Processes and Burst Assembly Algorithms

In this paper, we introduce a probabilistic lower bound for the amount of work arrived for a multifractal process. The obtained bound is accurate and tight. In the optical burst switching context, using the developed lower bound we obtained an analytical expression for the minimum burst length generated by a timer-based burst assembly algorithm, the maximum delay imposed by a burstlength-based burst assembly algorithm and project constraints of a mixed timer/burstlength-based burst assembly algorithm when the incoming traffic is multifractal. Our results are very useful when designing optical burst switching networks and analyzing the performance of burst assembly algorithms at the presence of multifractality.

[1]  Richard G. Baraniuk,et al.  Multiscale nature of network traffic , 2002, IEEE Signal Process. Mag..

[2]  H.H. Takada,et al.  A Lower Bound for Cumulative Self-Similar Processes and Burst Assembly Algorithms , 2006, 2006 First International Conference on Communications and Networking in China.

[3]  Chunming Qiao,et al.  Optical burst switching: a new area in optical networking research , 2004, IEEE Netw..

[4]  Nelson Luis Saldanha da Fonseca,et al.  An envelope process for multifractal traffic modeling , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[5]  R. Peltier,et al.  Multifractional Brownian Motion : Definition and Preliminary Results , 1995 .

[6]  Walter Willinger,et al.  Is Network Traffic Self-Similar or Multifractal? , 1997 .

[7]  Nelson Luis Saldanha da Fonseca,et al.  Statistical multiplexing of multifractal flows , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[8]  Richard G. Baraniuk,et al.  A Multifractal Wavelet Model with Application to Network Traffic , 1999, IEEE Trans. Inf. Theory.

[9]  Iraj Saniee,et al.  Performance impacts of multi-scaling in wide area TCP/IP traffic , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[10]  An Ge,et al.  On optical burst switching and self-similar traffic , 2000, IEEE Communications Letters.

[11]  Anja Feldmann,et al.  Data networks as cascades: investigating the multifractal nature of Internet WAN traffic , 1998, SIGCOMM '98.

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

[13]  Chunming Qiao,et al.  Study of traffic statistics of assembled burst traffic in optical burst-switched networks , 2002, SPIE ITCom.