Fast symbolic computation of the worst-case delay in tandem networks and applications

Computing deterministic performance guarantees is a defining issue for systems with hard real-time constraints, like reactive embedded systems. In this paper, we use burst-rate constrained arrivals and rate-latency servers to deduce tight worst-case delay bounds in tandem networks under arbitrary multiplexing. We present a constructive method for computing the exact worst-case delay, which we prove to be a linear function of the burstiness and latencies; our bounds are hence symbolic in these parameters. Our algorithm runs in quadratic time in the number of servers. We also present an application of our algorithm to the case of stochastic arrivals and server capacities. For a generalization of the exponentially bounded burstiness (EBB) model, we deduce a polynomial-time algorithm for stochastic delay bounds that strictly improve the state-of-the-art separated flow analysis (SFA) type bounds.

[1]  Mukesh Taneja.  A service curve approach for quality of service management in integrated services networks , 1998 .

[2]  Felix Poloczek,et al.  Scheduling analysis with martingales , 2014, Perform. Evaluation.

[3]  Cheng-Shang Chang,et al.  Load balanced Birkhoff-von Neumann switches, part II: multi-stage buffering , 2002, Comput. Commun..

[4]  Samarjit Chakraborty,et al.  Event count automata: a state-based model for stream processing systems , 2005, 26th IEEE International Real-Time Systems Symposium (RTSS'05).

[5]  Giovanni Stea,et al.  Exact worst-case delay for FIFO-multiplexing tandems , 2012, 6th International ICST Conference on Performance Evaluation Methodologies and Tools.

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

[7]  Pascale Minet,et al.  Worst case end-to-end response times of flows scheduled with FP/FIFO , 2006, International Conference on Networking, International Conference on Systems and International Conference on Mobile Communications and Learning Technologies (ICNICONSMCL'06).

[8]  Jens B. Schmitt,et al.  Delay Bounds under Arbitrary Multiplexing: When Network Calculus Leaves You in the Lurch... , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

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

[10]  Florin Ciucu,et al.  A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid , 2012, IEEE Journal on Selected Areas in Communications.

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

[12]  Eric Thierry,et al.  Tight performance bounds in the worst-case analysis of feed-forward networks , 2010, 2010 Proceedings IEEE INFOCOM.

[13]  Luciano Lenzini,et al.  Tight end-to-end per-flow delay bounds in FIFO multiplexing sink-tree networks , 2006, Perform. Evaluation.

[14]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks-the multiple node case , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[15]  Anne Bouillard,et al.  Worst-case delay bounds with fixed priorities using network calculus , 2011, VALUETOOLS.

[16]  PEGASE - A Robust and Efficient Tool for Worst-Case Network Traversal Time Evaluation on AFDX , 2011 .

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

[18]  Moshe Sidi,et al.  Performance and stability of communication networks via robust exponential bounds , 1993, TNET.

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

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

[21]  Yashar Ghiassi-Farrokhfal,et al.  On the Impact of Link Scheduling on End-to-End Delays in Large Networks , 2011, IEEE Journal on Selected Areas in Communications.

[22]  Keith W. Ross,et al.  Video on demand over ATM: constant-rate transmission and transport , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[23]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks-the single node case , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[24]  Cheng-Shang Chang,et al.  Load balanced Birkhoff-von Neumann switches , 2001, 2001 IEEE Workshop on High Performance Switching and Routing (IEEE Cat. No.01TH8552).

[25]  J. Schmitt,et al.  Perspectives on network calculus: no free lunch, but still good value , 2012, SIGCOMM '12.

[26]  Stability , 1973 .

[27]  Liliana Cucu-Grosjean,et al.  A component-based framework for modeling and analyzing probabilistic real-time systems , 2011, ETFA2011.

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

[29]  Eric Thierry,et al.  Comparison of different classes of service curves in network calculus , 2010, WODES.