On expressing networks with flow transformations in convolution-form

Convolution-form networks have the property that the end-to-end service of network flows can be expressed in terms of a (min,+)-convolution of the per-node services. This property is instrumental for deriving end-to-end queueing results which fundamentally improve upon alternative results derived by a node-by-node analysis. This paper extends the class of convolution-form networks with stochastic settings to scenarios with flow transformations, e.g., by loss, dynamic routing or retransmissions. In these networks, it is shown that by using the tools developed in this paper end-to-end delays grow as O(n) in the number of nodes n; in contrast, by using the alternative node-by-node analysis, end-to-end delays grow as O(n2).

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

[2]  E. Gilbert.  Capacity of a burst-noise channel , 1960 .

[3]  Florin Ciucu,et al.  Scaling properties of statistical end-to-end bounds in the network calculus , 2006, IEEE Transactions on Information Theory.

[4]  E. O. Elliott.  Estimates of error rates for codes on burst-noise channels , 1963 .

[5]  Insup Lee,et al.  Compositional Analysis Framework Using EDP Resource Models , 2007, RTSS 2007.

[6]  Yong Liu,et al.  Stochastic Network Calculus , 2008 .

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

[8]  Weijia Jia,et al.  Performance of Acyclic Stochastic Networks with Network Coding , 2011, IEEE Transactions on Parallel and Distributed Systems.

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

[10]  Florin Ciucu,et al.  Non-asymptotic Delay Bounds for Networks with Heavy-Tailed Traffic , 2010, 2010 Proceedings IEEE INFOCOM.

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

[12]  Lothar Thiele,et al.  Real-time calculus for scheduling hard real-time systems , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[13]  Jennifer C. Hou,et al.  Network calculus based simulation for TCP congestion control: theorems, implementation and evaluation , 2004, IEEE INFOCOM 2004.

[14]  Jens B. Schmitt,et al.  On the way to a distributed systems calculus: an end-to-end network calculus with data scaling , 2006, SIGMETRICS '06/Performance '06.

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

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

[17]  Guoqiang Hu,et al.  A calculus for information-driven networks , 2009, 2009 17th International Workshop on Quality of Service.

[18]  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).

[19]  Hong Shen Wang,et al.  Finite-state Markov channel-a useful model for radio communication channels , 1995 .

[20]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

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

[22]  Lothar Thiele,et al.  A Comprehensive Worst-Case Calculus for Wireless Sensor Networks with In-Network Processing , 2007, RTSS 2007.

[23]  Florin Ciucu,et al.  Network Calculus Delay Bounds in Queueing Networks with Exact Solutions , 2007, ITC.

[24]  Florin Ciucu,et al.  On Q(H log H) Scaling of Network Delays , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

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

[26]  Lothar Thiele,et al.  Quantitative Characterization of Event Streams in Analysis of Hard Real-Time Applications , 2004, Proceedings. RTAS 2004. 10th IEEE Real-Time and Embedded Technology and Applications Symposium, 2004..