On the Elasticity of Marking Functions: Scheduling, Stability, and Quality-of-Service in the Internet

Much of the research on Internet modeling and analysis has focused on the design of end controllers and network algorithms with the objective of stability and convergence of the transmission rate. However, the Internet is composed of a mix- ture of both (controlled) elastic flows and (uncontrolled) real-time flows. Uncontrolled real-time flows do not react to network con- gestion as well as they require a certain level of QoS guarantees. In this paper, we study the effects of marking elasticity (which characterizes how quickly the marking level changes during tran- sients) on the QoS for uncontrolled real-time flows, at a router accessed by both uncontrolled real-time and controlled flows. First, we derive lower and upper bounds on the queue over- flow probability at a router of a single bottleneck system. Using this, we quantify the trade-off between stability for controlled flows and QoS guarantee for uncontrolled real-time flows as a function of marking elasticity. The results indicate that some marking functions may be "uniformly" better than others. In particular, among the marking functions that we have compared, our bounds indicate that a rate based version of REM seems to provide the largest local-stability region for any given QoS re- quirement. Next, as a function of the marking function elasticity, we quan- tify the excess capacity required at the router with FIFO schedul- ing that results in the same queue overflow probability if priority scheduling was used instead. We show that the difference in the required capacities with FIFO and priority queueing decreases with more elastic marking functions. In other words, the gains due to scheduling decreases with increasing marking elasticity.

[1]  Rayadurgam Srikant,et al.  Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management , 2001, SIGCOMM.

[2]  R. Srikant,et al.  How good are deterministic fluid models of Internet congestion control? , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[3]  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..

[4]  R. Srikant,et al.  Many-Sources Delay Asymptotics with Applications to Priority Queues , 2001, Queueing Syst. Theory Appl..

[5]  R. Weber,et al.  Buffer overflow asymptotics for a buffer handling many traffic sources , 1996, Journal of Applied Probability.

[6]  Zheng Wang,et al.  An Architecture for Differentiated Services , 1998, RFC.

[7]  Glenn Vinnicombe,et al.  On the stability of end-to-end congestion control for the internet , 2001 .

[8]  Frank Kelly,et al.  Models for a self–managed Internet , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  G. Dullerud,et al.  Global stability of Internet congestion controllers with heterogeneous delays , 2004 .

[10]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[11]  David L. Black,et al.  An Architecture for Differentiated Service , 1998 .

[12]  Adam Shwartz,et al.  Large Deviations For Performance Analysis , 2019 .

[13]  R. Srikant,et al.  End-to-end congestion control schemes: utility functions, random losses and ECN marks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[14]  Laurent Massoulié,et al.  Bandwidth sharing: objectives and algorithms , 2002, TNET.

[15]  D. Wischik.  Sample path large deviations for queues with many inputs , 2001 .

[16]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[17]  Jean C. Walrand,et al.  Effective bandwidths for multiclass Markov fluids and other ATM sources , 1993, TNET.

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

[19]  Frank Kelly,et al.  Mathematical Modelling of the Internet , 2001 .

[20]  Jean C. Walrand,et al.  Effective bandwidths: Call admission, traffic policing and filtering for ATM networks , 1995, Queueing Syst. Theory Appl..

[21]  R. Srikant,et al.  Mean FDE models for Internet congestion control under a many-flows regime , 2004, IEEE Transactions on Information Theory.

[22]  Geir E. Dullerud,et al.  Global stability of Internet congestion controllers with heterogeneous delays , 2006, IEEE/ACM Transactions on Networking.

[23]  R. Srikant,et al.  Stability and convergence of TCP-like congestion controllers in a many-flows regime , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[24]  Ramesh Johari,et al.  End-to-end congestion control for the internet: delays and stability , 2001, TNET.

[25]  R. Srikant,et al.  Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management , 2001, SIGCOMM '01.