The Burstiness Behavior of Regulated Flows in Networks

In this paper we study the impact of statistical multiplexing on leaky-bucket regulated traffic streams as they pass through the network. In particular we show that the burstiness of a flow is randomized as it transits through the nodes with mean equal to its initial burstiness value at the ingress. We then show that the random burstiness for a single flow converges to a constant equal to the initial value at the ingress when the flow is multiplexed with a large number of sources. The results do not depend on independence or homogeniety between flows. We conclude by providing some simulation results that confirm the theory.

[1]  D. Mitra,et al.  Stochastic theory of a data-handling system with multiple sources , 1982, The Bell System Technical Journal.

[2]  Thomas L. Saaty,et al.  Elements of queueing theory , 2003 .

[3]  Jean-Yves Le Boudec,et al.  Stochastic analysis of some Expedited Forwarding networks , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[4]  Jean-Yves Le Boudec,et al.  Worst case burstiness increase due to FIFO multiplexing , 2002, Perform. Evaluation.

[5]  Ness B. Shroff,et al.  Simplification of network analysis in large-bandwidth systems , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[6]  Damon Wischik.  The output of a switch, or, effective bandwidths for networks , 1999, Queueing Syst. Theory Appl..

[7]  Takis Konstantopoulos,et al.  On the dynamics and performance of stochastic fluid systems , 2000, Journal of Applied Probability.

[8]  Rene L. Cruz,et al.  A calculus for network delay, Part I: Network elements in isolation , 1991, IEEE Trans. Inf. Theory.

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

[10]  Moshe Sidi,et al.  Performance and stability of communication networks via robust exponential bounds , 1993, TNET.

[11]  J. W. Roberts.  Traffic theory and the Internet , 2001 .

[12]  San-qi Li,et al.  Traffic distortion and inter-source cross-correlation in high-speed integrated networks , 1997, Comput. Networks ISDN Syst..

[13]  Wilton R. Abbott,et al.  Network Calculus , 1970 .

[14]  Rene L. Cruz,et al.  A calculus for network delay, Part II: Network analysis , 1991, IEEE Trans. Inf. Theory.

[15]  Jean-Yves Le Boudec,et al.  Network Calculus , 2001, Lecture Notes in Computer Science.

[16]  Dirk Abendroth,et al.  Intelligent shaping: well shaped throughout the entire network? , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[17]  Don Towsley,et al.  Theories and models for Internet quality of service , 2002, Proc. IEEE.

[18]  Walter Willinger,et al.  On the Self-Similar Nature of Ethernet Traffic ( extended version ) , 1995 .

[19]  Moshe Sidi,et al.  Stochastically bounded burstiness for communication networks , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

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

[21]  Catherine Rosenberg,et al.  Extremal traffic and bounds for the mean delay of multiplexed regulated traffic streams , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[22]  Catherine Rosenberg,et al.  Buffer overflow bounds for multiplexed regulated traffic streams , 2003 .

[23]  Anthony Busson,et al.  Stochastic Majorization of Aggregates of Leaky Bucket-Constrained Traffic Streams , 1998 .