Delay Bounds under Arbitrary Multiplexing

Network calculus has proven as a valuable and versatile methodology for worstcase analysis of communication networks. One issue in which it is still lacking is the treatment of aggregate multiplexing, in particular if the FIFO property cannot be assumed when ows are merged. In this report, we address the problem of bounding the delay of individual tra c ows in feed-forward networks under arbitrary multiplexing. Somewhat surprisingly, we nd that direct application of network calculus results in loose bounds even in seemingly simple scenarios. The reasons for this failure of network calculus are discussed in detail and a method to arrive at tight delay bounds for arbitrary (aggregate) multiplexing is presented. This method is based on the solution of an optimization problem. For the special case of sink-tree networks this optimization problem is solved explicitly, thus arriving at a closed-form expression for the delay bound. Numerical experiments illustrate that in sink-tree networks the improvement over bounds based on direct application of network calculus can be considerable.

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

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

[3]  Jean-Yves Le Boudec,et al.  Delay Bounds in a Network with Aggregate Scheduling , 2000, QofIS.

[4]  Vicent Cholvi,et al.  Worst case burstiness increase due to arbitrary aggregate multiplexing , 2006, valuetools '06.

[5]  Tor Skeie,et al.  Timeliness of real-time IP communication in switched industrial Ethernet networks , 2006, IEEE Transactions on Industrial Informatics.

[6]  George C. Polyzos,et al.  Scheduling for quality of service guarantees via service curves , 1995, Proceedings of Fourth International Conference on Computer Communications and Networks - IC3N'95.

[7]  Jens B. Schmitt,et al.  The DISCO network calculator: a toolbox for worst case analysis , 2006, valuetools '06.

[8]  Geert Jan Olsder,et al.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[9]  Jean-Yves Le Boudec,et al.  Packet scale rate guarantee for non-FIFO nodes , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

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

[11]  Markus Fidler,et al.  An End-to-End Probabilistic Network Calculus with Moment Generating Functions , 2005, 200614th IEEE International Workshop on Quality of Service.

[12]  Rene L. Cruz,et al.  Quality of Service Guarantees in Virtual Circuit Switched Networks , 1995, IEEE J. Sel. Areas Commun..

[13]  Yiwei Thomas Hou,et al.  Fundamental trade-offs in aggregate packet scheduling , 2005, IEEE Transactions on Parallel and Distributed Systems.

[14]  Matthew Andrews,et al.  Instability of FIFO in session-oriented networks , 2000, SODA '00.

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

[16]  Mark G. Karpovsky,et al.  Application of network calculus to general topologies using turn-prohibition , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[17]  Cheng-Shang Chang,et al.  Stability, queue length, and delay of deterministic and stochastic queueing networks , 1994, IEEE Trans. Autom. Control..

[18]  Guillaume Urvoy-Keller,et al.  Traffic engineering in a multipoint-to-point network , 2002, IEEE J. Sel. Areas Commun..

[19]  Utz Roedig,et al.  Sensor Network Calculus - A Framework for Worst Case Analysis , 2005, DCOSS.

[20]  Jean-Yves Le Boudec,et al.  Network Calculus: A Theory of Deterministic Queuing Systems for the Internet , 2001 .

[21]  Eric Thierry,et al.  An Algorithmic Toolbox for Network Calculus , 2008, Discret. Event Dyn. Syst..

[22]  Yuming Jiang.  Delay bounds for a network of guaranteed rate servers with FIFO aggregation , 2002, Comput. Networks.

[23]  Yuming Jiang,et al.  A basic stochastic network calculus , 2006, SIGCOMM.

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

[25]  Volker Sander,et al.  A parameter based admission control for differentiated services networks , 2004, Comput. Networks.

[26]  Eduardo Tovar,et al.  Modeling and Worst-Case Dimensioning of Cluster-Tree Wireless Sensor Networks , 2006, 2006 27th IEEE International Real-Time Systems Symposium (RTSS'06).

[27]  Yuming Jiang,et al.  Delay bounds for a network of guaranteed rate servers with FIFO aggregation , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[28]  Jean-Yves Le Boudec,et al.  "Pay bursts only once" does not hold for non-FIFO guaranteed rate nodes , 2005, Perform. Evaluation.

[29]  Lothar Thiele,et al.  Performance evaluation of network processor architectures: combining simulation with analytical estimation , 2003, Comput. Networks.