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Issue No.04 - April (2013 vol.62)
pp: 644-661
Haibo Zeng , Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, QC, Canada
Marco Di Natale , Scuola Superiore S. Anna, TECIP Inst., Pisa, Italy
In the design of time-critical applications, schedulability analysis is used to define the feasibility region of tasks with deadlines, so that optimization techniques can find the best design solution within the timing constraints. The formulation of the feasibility region based on the response time calculation requires many integer variables and is too complex for solvers. Approximation techniques have been used to define a convex subset of the feasibility region, used in conjunction with a branch and bound approach to compute suboptimal solutions for optimal task period selection, priority assignment, or placement of tasks onto CPUs. In this paper, we provide an improved and simpler real-time schedulability test that allows an exact and efficient definition of the feasibility region in Mixed Integer Linear Programming (MILP) optimization. Our method requires a significantly smaller number of binary variables and is viable for the treatment of industrial-size problem, as shown by the experiments.
tree searching, approximation theory, design engineering, integer programming, linear programming, processor scheduling, industrial-size problem, real-time feasibility region, design optimization, time-critical applications, schedulability analysis, timing constraints, response time calculation, integer variables, approximation techniques, branch and bound approach, optimal task period selection, priority assignment, task placement, real-time schedulability test, mixed integer linear programming optimization, MILP, binary variables, Optimization, Silicon, Time factors, Redundancy, Algorithm design and analysis, Real time systems, Indexes, mixed integer linear programming, Real-time systems, schedulability analysis
Haibo Zeng, Marco Di Natale, "An Efficient Formulation of the Real-Time Feasibility Region for Design Optimization", IEEE Transactions on Computers, vol.62, no. 4, pp. 644-661, April 2013, doi:10.1109/TC.2012.21
[1] N. Audsley, A. Burns, M. Richardson, K. Tindell, and A.J. Wellings, "Applying New Scheduling Theory to Static Priority Pre-Emptive Scheduling," Software Eng. J., vol. 8, no. 5, pp. 284-292, Sept. 1993.
[2] E. Bini and G.C. Buttazzo, "Schedulability Analysis of Periodic Fixed Priority Systems," IEEE Trans. Computers, vol. 53, no. 11, pp. 1462-1473, Nov. 2004.
[3] E. Bini and G.C. Buttazzo, "Measuring the Performance of Schedulability Tests," Real-Time Systems, vol. 30, nos. 1/2, pp. 129-154, May 2005.
[4] E. Bini, T.H. Châu Nguyen, P. Richard, and S.K. Baruah, "A Response-Time Bound in Fixed-Priority Scheduling with Arbitrary Deadlines," IEEE Trans. Computers, vol. 58, no. 2, pp. 279-286, Feb. 2009.
[5] A. Cervin, D. Henriksson, B. Lincoln, J. Eker, and K.E. Arzen, "How Does Control Timing Affect Performance? Analysis and Simulation of Timing Using Jitterbug and TrueTime," IEEE Control Systems Magazine, vol. 23, no. 3, pp. 16-30, June 2003.
[6] A. Davare, Q. Zhu, M.D. Natale, C. Pinello, S. Kanajan, and A. Sangiovanni-Vincentelli, "Period Optimization for Hard Real-Time Distributed Automotive Systems," Proc. 44th Design Automation Conf., pp. 278-283, 2007.
[7] L. George, N. Riviere, and M. Spuri, "Preemptive and Non-Preemptive Real-Time Uniprocessor Scheduling," technical report, INRIA, 1996.
[8] R. Ghattas and A.C. Dean, "Preemption Threshold Scheduling: Stack Optimality, Enhancements and Analysis," Proc. 13th Real-Time and Embedded Technology and Applications Symp., pp. 147-157, 2007.
[9] B. Grünbaum, Convex Polytopes, second ed., p. 52a. Springer, 2003.
[10] A. Hamann, R. Racu, and R. Ernst, "Multi-Dimensional Robustness Optimization in Heterogeneous Distributed Embedded Systems," Proc. 13th Real-Time and Embedded Technology and Applications Symp., pp. 269-280, 2007.
[11] J.P. Lehoczky, L. Sha, and Y. Ding, "The Rate Monotonic Scheduling Algorithm: Exact Characterization and Average Case Behavior," Proc. 10th Real-Time Systems Symp., pp. 166-171, 1989.
[12] M. Di Natale, "Optimizing the Multitask Implementation of Multirate Simulink Models," Proc. 12th Real-Time and Embedded Technology and Applications Symp., pp. 335-346, 2006.
[13] M. Di Natale and V. Pappalardo, "Buffer Optimization in Multitask Implementations of Simulink Models," ACM Trans. Embedded Computing Systems, vol. 7, no. 3, pp. 1-32, May 2008.
[14] M. Di Natale, L. Guo, H. Zeng, and A. Sangiovanni-Vincentelli, "Synthesis of Multi-Task Implementations of Simulink Models with Minimum Delays," IEEE Trans. Industrial Informatics, vol. 6, no. 4, pp. 637-651, Nov. 2010.
[15] A. Metzner and C. Herde, "RTSAT—An Optimal and Efficient Approach to the Task Allocation Problem in Distributed Architectures," Proc. 27th Real-Time Systems Symp., pp. 147-158, 2006.
[16] A.K. Mok, "Fundamental Design Problems of Distributed Systems for the Hard-Real-Time Environment," PhD thesis, MIT, 1983.
[17] M. Oral and O. Kettani, "Linearization Procedure for Quadratic and Cubic Mixed-Integer Problems," Operations Research, vol. 40, no. S1, pp. 109-116, Jan./Feb. 1992.
[18] "OSEK/VDX Operating System Specification Version 2.2.3," http:/, Feb. 2005.
[19] J. Regehr, "Scheduling Tasks with Mixed Preemption Relations for Robustness to Timing Faults," Proc. 23rd Real-Time Systems Symp., pp. 315-326, 2002.
[20] L. Sha, R. Rajkumar, and J.P. Lehoczky, "Priority Inheritance Protocols: An Approach to Real-Time Synchronization," IEEE Trans. Computers, vol. 39, no. 9, pp. 1175-1185, Sept. 1990.
[21] M. Sjödin and H. Hansson, "Improved Response Time Analysis Calculations," Proc. 19th Real-Time Systems Symp., pp. 399-408, 1998.
[22] W. Lamie, "Preemption-Threshold," White Paper, Express Logic, Inc.,, 2012.
[23] M. Velasco, P. Marti, and E. Bini, "Control-Driven Tasks: Modeling and Analysis," Proc. 29th Real-Time Systems Symp., pp. 280-290, 2008.
[24] Y. Wang and M. Saksena, "Scheduling Fixed-Priority Tasks with Preemption Threshold," Proc. Sixth Real-Time Computing Systems and Applications, pp. 328-335, 1999.
[25] H. Zeng and M.D. Natale, "An Efficient Formulation of the Real-Time Feasibility Region for Design Optimization," TECIP technical report, Scuola Superiore S. Anna, Pisa, Aug. 2011.
[26] W. Zheng, M.D. Natale, C. Pinello, P. Giusto, and A. Sangiovanni-Vincentelli, "Synthesis of Task and Message Activation Models in Real-Time Distributed Automotive Systems," Proc. Conf. Design, Automation & Test in Europe, pp. 93-98, 2007.
[27] W. Zheng, Q. Zhu, M. Di Natale, and A. Sangiovanni-Vincentelli, "Definition of Task Allocation and Priority Assignment in Hard Real-Time Distributed System," Proc. Real-Time System Symp., pp. 161-170, 2007.
[28] Q. Zhu, Y. Yang, E. Scholte, M. Di Natale, and A. Sangiovanni-Vincentelli, "Optimizing Extensibility in Hard Real-Time Distributed Systems," Proc. 15th Real-Time and Embedded Technology and Applications Symp., pp. 275-284, 2009.
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