Buffer overflow asymptotics for multiplexed regulated traffic

By characterizing the worst-case profile, which maximizes the content of a buffer fed with leaky bucket regulated flows in packet telecommunication networks, we derive a tight upper bound in the many-sources regime for the tail distribution of the workload generated by these flows in a FIFO queue with constant service rate. Furthermore, we compare this workload distribution with an M/G/1 queue and get insights on the better-than-Poisson property of regulated flows. We conclude that the superposition of independent regulated flows generates an asymptotically smaller workload than a marked Poisson process whose service times and intensity depend on the parameters of regulated sources.

[1]  Jin Cao,et al.  A Poisson limit for buffer overflow probabilities , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[2]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[3]  R. R. Bahadur,et al.  On Deviations of the Sample Mean , 1960 .

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

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

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

[7]  Nick G. Duffield,et al.  Large deviations, the shape of the loss curve, and economies of scale in large multiplexers , 1995, Queueing Syst. Theory Appl..

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

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

[10]  R. Mazumdar,et al.  Cell loss asymptotics for buffers fed with a large number of independent stationary sources , 1999 .

[11]  Leonard Kleinrock,et al.  Theory, Volume 1, Queueing Systems , 1975 .

[12]  S. Varadhan,et al.  Large deviations , 2019, Graduate Studies in Mathematics.

[13]  Jacky Guibert,et al.  Large Deviations Approximations for Fluid Queues Fed by a Large Number of On/Off Sources , 1995, IEEE J. Sel. Areas Commun..

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

[15]  Leonard Kleinrock,et al.  Queueing Systems - Vol. 1: Theory , 1975 .

[16]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[17]  Atm Switches,et al.  BUFFER OVERFLOW ASYMPTOTICS FOR A BUFFER HANDLING MANY TRAFFIC SOURCES , 1996 .

[18]  Jean-Yves Le Boudec,et al.  Application of Network Calculus to Guaranteed Service Networks , 1998, IEEE Trans. Inf. Theory.

[19]  Laurent Massoulié.  Large deviations ordering of point processes in some queueing networks , 1998, Queueing Syst. Theory Appl..

[20]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[21]  W. R. Buckland,et al.  Introduction to congestion theory in telephone systems , 1962 .

[22]  Michel Mandjes,et al.  Large Deviations for Small Buffers: An Insensitivity Result , 2001, Queueing Syst. Theory Appl..

[23]  Alexandre Proutière,et al.  Statistical performance guarantees for streaming flows using expedited forwarding , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[24]  Catherine Rosenberg,et al.  The Burstiness Behavior of Regulated Flows in Networks , 2005, NETWORKING.

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

[26]  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.

[27]  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).

[28]  George Kesidis,et al.  Worst-case performance of a buffer with independent shaped arrival processes , 2000, IEEE Communications Letters.

[29]  Jean-Yves Le Boudec,et al.  Bounds for independent regulated inputs multiplexed in a service curve network element , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[30]  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.

[31]  Florin Ciucu,et al.  A network service curve approach for the stochastic analysis of networks , 2005, SIGMETRICS '05.

[32]  George Kesidis,et al.  Extremal Traffic and Worst-Case Performance for Queues with Shaped Arrivals , 1998 .

[33]  Cheng-Shang Chang,et al.  On the performance of multiplexing independent regulated inputs , 2001, SIGMETRICS '01.

[34]  R. A. Acton.  Introduction to Congestion Theory in Telephone Systems , 1961 .

[35]  S. Wittevrongel,et al.  Queueing Systems , 2019, Introduction to Stochastic Processes and Simulation.