End-to-end delay analysis for networked systems

End-to-end delay measurement has been an essential element in the deployment of real-time services in networked systems. Traditional methods of delay measurement based on time domain analysis, however, are not efficient as the network scale and the complexity increase. We propose a novel theoretical framework to analyze the end-to-end delay distributions of networked systems from the frequency domain. We use a signal flow graph to model the delay distribution of a networked system and prove that the end-to-end delay distribution is indeed the inverse Laplace transform of the transfer function of the signal flow graph. Two efficient methods, Cramer’s rule-based method and the Mason gain rule-based method, are adopted to obtain the transfer function. By analyzing the time responses of the transfer function, we obtain the end-to-end delay distribution. Based on our framework, we propose an efficient method using the dominant poles of the transfer function to work out the bottleneck links of the network. Moreover, we use the framework to study the network protocol performance. Theoretical analysis and extensive evaluations show the effectiveness of the proposed approach.

[1]  P. D. Roberts,et al.  Linear Control System Analysis and Design , 1982 .

[2]  Jon Crowcroft,et al.  Flow aggregation for enhanced TCP over wide-area wireless , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[3]  Xue Liu,et al.  Minimizing Electricity Cost: Optimization of Distributed Internet Data Centers in a Multi-Electricity-Market Environment , 2010, 2010 Proceedings IEEE INFOCOM.

[4]  Thilo Sauter,et al.  Asymmetry Mitigation in IEEE 802.3 Ethernet for High-Accuracy Clock Synchronization , 2014, IEEE Transactions on Instrumentation and Measurement.

[5]  Ness B. Shroff,et al.  Delay Analysis for Multi-Hop Wireless Networks , 2009, IEEE INFOCOM 2009.

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

[7]  Chaiwat Oottamakorn,et al.  Statistical service assurances for traffic scheduling algorithms , 2000, IEEE Journal on Selected Areas in Communications.

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

[9]  Lui Sha,et al.  NetSimplex: Controller Fault Tolerance Architecture in Networked Control Systems , 2013, IEEE Transactions on Industrial Informatics.

[10]  Keith W. Ross,et al.  A framework for guaranteeing statistical QoS , 2002, TNET.

[11]  Markus Fidler,et al.  Survey of deterministic and stochastic service curve models in the network calculus , 2009, IEEE Communications Surveys & Tutorials.

[12]  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).

[13]  Ali El-Hajj,et al.  A transfer function computational algorithm for linear control systems , 1995 .

[14]  Almut Burchard,et al.  A Min-Plus Calculus for End-to-End Statistical Service Guarantees , 2006, IEEE Transactions on Information Theory.

[15]  Yeqiong Song,et al.  Combining Analytical and Simulation Approaches for Estimating End-to-End Delay in Multi-hop Wireless Networks , 2012, 2012 IEEE 8th International Conference on Distributed Computing in Sensor Systems.

[16]  Xue Liu,et al.  Reliability Calculus: A Theoretical Framework to Analyze Communication Reliability , 2010, 2010 IEEE 30th International Conference on Distributed Computing Systems.

[17]  Vern Paxson,et al.  End-to-end Internet packet dynamics , 1997, SIGCOMM '97.

[18]  Alhussein A. Abouzeid,et al.  Queuing network models for delay analysis of multihop wireless ad hoc networks , 2006, IWCMC '06.

[19]  Feng Xia,et al.  Evaluating IEEE 802.15.4 for Cyber-Physical Systems , 2011, EURASIP J. Wirel. Commun. Netw..

[20]  Edward W. Knightly,et al.  Inter-class resource sharing using statistical service envelopes , 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).

[21]  Ness B. Shroff,et al.  A central-limit-theorem-based approach for analyzing queue behavior in high-speed networks , 1998, TNET.

[22]  Jean-Chrysostome Bolot,et al.  End-to-end packet delay and loss behavior in the internet , 1993, SIGCOMM '93.

[23]  Hairong Qi,et al.  Achieving k-Barrier Coverage in Hybrid Directional Sensor Networks , 2014, IEEE Transactions on Mobile Computing.

[24]  John D'Azzo,et al.  Linear Control System Analysis and Design: Conventional and Modern , 1977 .

[25]  Christian Fraboul,et al.  Improving the Worst-Case Delay Analysis of an AFDX Network Using an Optimized Trajectory Approach , 2010, IEEE Transactions on Industrial Informatics.

[26]  Martin Haenggi,et al.  Towards an end-to-end delay analysis of wireless multihop networks , 2009, Ad Hoc Networks.

[27]  Youxian Sun,et al.  Enhancing Real-Time Delivery in Wireless Sensor Networks With Two-Hop Information , 2009, IEEE Transactions on Industrial Informatics.

[28]  Lothar Thiele,et al.  A Comprehensive Worst-Case Calculus for Wireless Sensor Networks with In-Network Processing , 2007, 28th IEEE International Real-Time Systems Symposium (RTSS 2007).

[29]  Martin May,et al.  End-to-end vs. hop-by-hop transport , 2007, PERV.

[30]  Tarek F. Abdelzaher,et al.  On real-time capacity limits of multihop wireless sensor networks , 2004, 25th IEEE International Real-Time Systems Symposium.

[31]  Dhiraj K. Pradhan,et al.  Improving performance of TCP over wireless networks , 1997, Proceedings of 17th International Conference on Distributed Computing Systems.