Constraint Programming with External Worst-Case Traversal Time Analysis

Authors Pierre Talbot , Tingting Hu, Nicolas Navet

Thumbnail PDF


  • Filesize: 2.74 MB
  • 20 pages

Document Identifiers

Author Details

Pierre Talbot
  • University of Luxembourg, Luxembourg
  • Interdisciplinary Centre for Security, Reliability and Trust (SnT), Luxembourg
Tingting Hu
  • University of Luxembourg, Luxembourg
Nicolas Navet
  • University of Luxembourg, Luxembourg


We are grateful to the reviewers for their detailed comments.

Cite AsGet BibTex

Pierre Talbot, Tingting Hu, and Nicolas Navet. Constraint Programming with External Worst-Case Traversal Time Analysis. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The allocation of software functions to processors under compute capacity and network links constraints is an important optimization problem in the field of embedded distributed systems. We present a hybrid approach to solve the allocation problem combining a constraint solver and a worst-case traversal time (WCTT) analysis that verifies the network timing constraints. The WCTT analysis is implemented as an industrial black-box program, which makes a tight integration with constraint solving challenging. We contribute to a new multi-objective constraint solving algorithm for integrating external under-approximating functions, such as the WCTT analysis, with constraint solving, and prove its correctness. We apply this new algorithm to the allocation problem in the context of automotive service-oriented architectures based on Ethernet networks, and provide a new dataset of realistic instances to evaluate our approach.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Computer systems organization → Real-time systems
  • Networks → Network performance evaluation
  • Constraint programming
  • external function
  • multi-objective optimization
  • network analysis
  • worst-case traversal time analysis
  • abstract interpretation


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Krzysztof R. Apt. The essence of constraint propagation. Theoretical computer science, 221(1-2):179-210, 1999. URL:
  2. Anne Bouillard and Éric Thierry. An algorithmic toolbox for network calculus. Discrete Event Dynamic Systems, 18(1):3-49, 2008. URL:
  3. Marc Boyer and Hugo Daigmorte. Improved service curve for element with known transmission rate. IEEE Networking Letters, 5(1):46-49, 2023. URL:
  4. Marc Boyer, Jörn Migge, and Nicolas Navet. An efficient and simple class of functions to model arrival curve of packetised flows. In Proceedings of the 1st International Workshop on Worst-Case Traversal Time, WCTT '11, pages 43-50, New York, NY, USA, 2011. Association for Computing Machinery. URL:
  5. Gabriel Campeanu, Jan Carlson, and Severine Sentilles. Component Allocation Optimization for Heterogeneous CPU-GPU Embedded Systems. In 2014 40th EUROMICRO Conference on Software Engineering and Advanced Applications, pages 229-236, Verona, Italy, 2014. IEEE. URL:
  6. Patrick Cousot and Radhia Cousot. Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In Proceedings of the 4th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL '77, pages 238-252, New York, NY, USA, 1977. Association for Computing Machinery. URL:
  7. Robert I. Davis, Alan Burns, Reinder J. Bril, and Johan J. Lukkien. Controller Area Network (CAN) Schedulability Analysis: Refuted, Revisited and Revised. Real-Time Systems, 35(3):239-272, 2007. URL:
  8. Rina Dechter and Avi Dechter. Belief Maintenance in Dynamic Constraint Networks. In Proceedings of the Seventh AAAI National Conference on Artificial Intelligence, AAAI'88, pages 37-42. AAAI Press, 1988. Google Scholar
  9. Jip J. Dekker. MiniZinc Python, 2023. URL:
  10. Vijay D'Silva, Leopold Haller, and Daniel Kroening. Abstract satisfaction. In Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14, pages 139-150, San Diego, California, USA, 2014. ACM Press. URL:
  11. Johannes Eder, Sebastian Voss, Andreas Bayha, Alexandru Ipatiov, and Maged Khalil. Hardware architecture exploration: automatic exploration of distributed automotive hardware architectures. Software and Systems Modeling, 19(4):911-934, 2020. URL:
  12. Alexander Ek, Maria Garcia de la Banda, Andreas Schutt, Peter J. Stuckey, and Guido Tack. Modelling and Solving Online Optimisation Problems. Proceedings of the AAAI Conference on Artificial Intelligence, 34(02):1477-1485, 2020. URL:
  13. Marco Gavanelli. An algorithm for multi-criteria optimization in CSPs. In ECAI 2002: 15th European Conference on Artificial Intelligence, July 21-26, 2002, Lyon France: Including Prestigious Applications of Intelligent Systems (PAIS 2002): Proceedings, volume 77, page 136. IOS Press, 2002. Google Scholar
  14. Tias Guns, Peter J. Stuckey, and Guido Tack. Solution Dominance over Constraint Satisfaction Problems, 2018. arXiv:1812.09207 [cs]. URL:
  15. Pierre-Emmanuel Hladik, Hadrien Cambazard, Anne-Marie Déplanche, and Narendra Jussien. Solving a real-time allocation problem with constraint programming. Journal of Systems and Software, 81(1):132-149, 2008. URL:
  16. J.N. Hooker and G. Ottosson. Logic-based Benders decomposition. Mathematical Programming, 96(1):33-60, 2003. URL:
  17. Stefan Kugele, Philipp Obergfell, and Eric Sax. Model-based resource analysis and synthesis of service-oriented automotive software architectures. Software and Systems Modeling, 20(6):1945-1975, December 2021. URL:
  18. Jean-Yves Le Boudec and Patrick Thiran. Network Calculus. In Network Calculus: A Theory of Deterministic Queuing Systems for the Internet, pages 3-81. Springer Berlin Heidelberg, Berlin, Heidelberg, 2001. URL:
  19. Martin Lukasiewycz, Michael Glaß, Christian Haubelt, and Jürgen Teich. Solving Multi-objective Pseudo-Boolean Problems. In Theory and Applications of Satisfiability Testing – SAT 2007, pages 56-69. Springer Berlin Heidelberg, Berlin, Heidelberg, 2007. URL:
  20. Bjørnar Luteberget, Koen Claessen, Christian Johansen, and Martin Steffen. SAT modulo discrete event simulation applied to railway design capacity analysis. Formal Methods in System Design, 57(2):211-245, August 2021. URL:
  21. Irene Moser and Sanaz Mostaghim. The automotive deployment problem: A practical application for constrained multiobjective evolutionary optimisation. In IEEE Congress on Evolutionary Computation, pages 1-8, Barcelona, Spain, July 2010. IEEE. URL:
  22. Ahmed Nasrallah, Akhilesh S. Thyagaturu, Ziyad Alharbi, Cuixiang Wang, Xing Shao, Martin Reisslein, and Hesham ElBakoury. Ultra-Low Latency (ULL) Networks: The IEEE TSN and IETF DetNet Standards and Related 5G ULL Research. IEEE Communications Surveys & Tutorials, 21(1):88-145, 2019. URL:
  23. Mitra Nasri, Sanjoy Baruah, Gerhard Fohler, and Mehdi Kargahi. On the Optimality of RM and EDF for Non-Preemptive Real-Time Harmonic Tasks. In Proceedings of the 22nd International Conference on Real-Time Networks and Systems - RTNS '14, pages 331-340, Versaille, France, 2014. ACM Press. URL:
  24. Asef Nazari, Dhananjay Thiruvady, Aldeida Aleti, and Irene Moser. A mixed integer linear programming model for reliability optimisation in the component deployment problem. Journal of the Operational Research Society, 67(8):1050-1060, August 2016. URL:
  25. Nicholas Nethercote, Peter J. Stuckey, Ralph Becket, Sebastian Brand, Gregory J. Duck, and Guido Tack. MiniZinc: Towards a standard CP modelling language. In Principles and Practice of Constraint Programming - CP 2007, pages 529-543. Springer, 2007. Google Scholar
  26. Olga Ohrimenko, Peter J. Stuckey, and Michael Codish. Propagation via Lazy Clause Generation. Constraints, 14(3):357-391, September 2009. URL:
  27. Marie Pelleau, Antoine Miné, Charlotte Truchet, and Frédéric Benhamou. A Constraint Solver Based on Abstract Domains. In Verification, Model Checking, and Abstract Interpretation, pages 434-454. Springer, 2013. URL:
  28. R. Queck. Analysis of Ethernet AVB for automotive networks using Network Nalculus. In 2012 IEEE International Conference on Vehicular Electronics and Safety (ICVES 2012), pages 61-67, July 2012. URL:
  29. RealTime-at-Work. Rtaw-pegase, 2022. URL:
  30. Andrea Rendl, Tias Guns, Peter J. Stuckey, and Guido Tack. MiniSearch: a solver-independent meta-search language for MiniZinc. In Principles and Practice of Constraint Programming, pages 376-392. Springer, 2015. URL:
  31. Pierre Schaus and Renaud Hartert. Multi-Objective Large Neighborhood Search. In Principles and Practice of Constraint Programming, volume 8124, pages 611-627. Springer Berlin Heidelberg, Berlin, Heidelberg, 2013. URL:
  32. Christian Schulte, Guido Tack, and Mikael Lagerkvist. Modeling and Programming with Gecode, 2020. Google Scholar
  33. Joseph Scott. Other Things Besides Number: Abstraction, Constraint Propagation, and String Variable Types. PhD thesis, Acta Universitatis Upsaliensis, Uppsala, 2016. OCLC: 943721122. Google Scholar
  34. Seyed Mohammadhossein Tabatabaee, Marc Boyer, Jean-Yves Le Boudec, and Jörn Migge. Efficient and accurate handling of periodic flows in time-sensitive networks. In 2023 IEEE 29th Real-Time and Embedded Technology and Applications Symposium (RTAS), pages 303-315, 2023. URL:
  35. Pierre Talbot, Éric Monfroy, and Charlotte Truchet. Modular Constraint Solver Cooperation via Abstract Interpretation. Theory and Practice of Logic Programming, 20(6):848-863, 2020. URL:
  36. Dhananjay Thiruvady, I. Moser, Aldeida Aleti, and Asef Nazari. Constraint Programming and Ant Colony System for the Component Deployment Problem. Procedia Computer Science, 29:1937-1947, 2014. URL:
  37. Tindell, Hansson, and Wellings. Analysing real-time communications: controller area network (CAN). In Proceedings Real-Time Systems Symposium REAL-94, pages 259-263, San Juan, Puerto Rico, 1994. IEEE Comput. Soc. Press. URL:
  38. K. W. Tindell, A. Burns, and A. J. Wellings. Allocating hard real-time tasks: An NP-Hard problem made easy. Real-Time Systems, 4(2):145-165, June 1992. URL:
  39. P. M. Yomsi, D. Bertrand, N. Navet, and R. Davis. Controller Area Network (CAN): Response Time Analysis with Offsets. In 9th IEEE International Workshop on Factory Communication Systems, pages 43-52, United States, May 2012. IEEE. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail