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© COPYRIGHT IKERLAN 2014 Adding Precedence Relations to the Response-Time Analysis of EDF Distributed Real-Time Systems Unai Díaz de Cerio (IK4-Ikerlan) Michael González Harbour (Univ. Cantabria) J. Carlos Palencia (Univ. Cantabria) Juan P. Uribe (IK4-Ikerlan) 22nd International Conference on Real-Time Networks and Systems Versailles, France, October 8-10, 2014
© COPYRIGHT IKERLAN 2014 Motivation Context Distributed real-time systems Response-time schedulability analysis EDF scheduling: GC-EDF (Global-Clock EDF) Global clock or clock synchronization available LC-EDF (Local-Clock EDF) One clock per processor and no clock synchronization available Problem No exact solution for schedulability analysis in distributed systems More techniques to reduce the pessimism in the analysis for FP (fixed- priorities) than for EDF 2
© COPYRIGHT IKERLAN 2014 Motivation Analysis techniqueFPGC-EDFLC-EDF 3 Tindell and Clark, 94Spuri, 96Rivas et al., 10Holistic WCDO Palencia and González Harbour, 98 Palencia and González Harbour, 03 Palencia and González Harbour, 99 WCDOPS XX X WCDO : Worst Case Dynamic Offsets WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
© COPYRIGHT IKERLAN 2014 Objectives Reduce the pessimism of the response time analysis for EDF scheduled systems Extending dynamic offsets technique (WCDO) to LC-EDF scheduled systems Extending precedence relations technique (WCDOPS) to LC-EDF and GC-EDF scheduled systems 4
© COPYRIGHT IKERLAN 2014 System model Distributed system of n task/messages statically allocated in m processors/networks Tasks/messages ( τ ij ) linked making up end-to-end flows ( Γ i ) Periodic end-to-end flows with minimum time between instances: T i Task offset: Task release jitter: Task release time interval: t = external event arrival time 5
© COPYRIGHT IKERLAN 2014 System model Task worst case execution time (WCET): C ij Relative global deadline (related to external event arrival): D ij Relative local deadline (related to task release in its processor): d ij Global response time (related to external event arrival): R ij Local response time (related to task release in its processor): r ij 6 d i3 D i3
© COPYRIGHT IKERLAN 2014 WCDO-EDF (LC-EDF) Analysis techniqueFPGC-EDFLC-EDF 7 Tindell and Clark, 94Spuri, 96Rivas et al., 10Holistic WCDO Palencia and González Harbour, 98 Palencia and González Harbour, 03 Palencia and González Harbour, 99 WCDOPS XX X WCDO : Worst Case Dynamic Offsets WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
© COPYRIGHT IKERLAN 2014 WCDO-EDF (LC-EDF) Find worst case busy period ( length t and deadline D, created with the task τ ik ) and calculate the contribution of the tasks to this busy period. Jobs categorized in 3 sets: Set 0: Activations that occur before the busy period and that, even applying its maximum jitter, cannot be delayed until the busy period. Set 1: Activations that occur before the busy period and can be delayed with an amount of jitter such that they coincide with the beginning of the busy period. Set 2: Activations that occur inside the busy period. 8
© COPYRIGHT IKERLAN 2014 Jobs with deadline previous to D Number of jobs in Set2 Only jobs with deadline previous to D can contribute Number of jobs in Set1 WCDO-EDF (LC-EDF) Maximum contribution when jobs in Set 1 suffer an amount of jitter that they are release at the beginning of the busy period and job in Set 2 suffer an amount of jitter equal to zero: 9
© COPYRIGHT IKERLAN 2014 WCDOPS-EDF (LC-EDF) Analysis techniqueFPGC-EDFLC-EDF 10 Tindell and Clark, 94Spuri, 96Rivas et al., 10Holistic WCDO Palencia and González Harbour, 98 Palencia and González Harbour, 03 Palencia and González Harbour, 99 WCDOPS XX WCDO : Worst Case Dynamic Offsets WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
© COPYRIGHT IKERLAN 2014 Precedence relation and activation conflicts 11
© COPYRIGHT IKERLAN 2014 Precedence relation and activation conflicts 12
© COPYRIGHT IKERLAN 2014 Precedence relation and activation conflicts 13 Activation conflicts: Two tasks are in conﬂict when their executions are incompatible in the same busy period for the purpose of analyzing task τ ab. H-section: Two tasks τ ij and τ ik are in the same H-section, for the analysis of τ ab, if both execute in the same processor as τ ab with priority equal to or higher than τ ab and there are no intermediate tasks between them in the same processor and with priority lower than τ ab. H ij ( τ ab ) identiﬁes the H-section to which τ ij belongs.
© COPYRIGHT IKERLAN 2014 Applicability for EDF Priority depends on absolute deadlines Absolute deadline change from one job to the next Contrary to ﬁxed priorities Activation conflicts between jobs, instead of between tasks H-sections composed by jobs, instead of tasks 14
© COPYRIGHT IKERLAN 2014 Applicability for GC-EDF 15 Not useful Task absolute deadlines are related to the external event arrival Task deadlines ordered D i1 < D i2 No activation conflicts
© COPYRIGHT IKERLAN 2014 Applicability for LC-EDF 16 Task absolute deadlines are related to the task release Task deadlines are not ordered There are activation conflicts Applicable
© COPYRIGHT IKERLAN 2014 WCDOPS-EDF (LC-EDF) 17 Contribution of each task: First job that can be delayed to the busy period: Last job in the busy period that have its deadline previous to the deadline of the task under analysis:
© COPYRIGHT IKERLAN 2014 WCDOPS-EDF (LC-EDF) 18 Construct an activation conflict table for the contribution of the end-to- end flow Γ i t1t2t3t4t5 p=-3C1C1 00C4C4 0 p=-2C1C1 C2C2 0C4C4 0 p=-1C1C1 C2C2 0C4C4 C5C5 p=0C1C1 C2C2 C3C3 C4C4 C5C5 p=1C1C1 0C3C3 C4C4 C5C5 p=2C1C1 0C3C3 00 W i (p=-3) = max(C 1, C 4 ) W i (p=-2) = max(C 1 +C 2, C 4 ) W i (p=-1) = max(C 1 +C 2, C 4 +C 5 ) W i (p=0) = C 1 +C 2 +C 3 +C 4 +C 5 W i (p=1) = max(C 1,C 3 +C 4 +C 5 ) W i (p=-3) = max(C 1, C 3 ) W i = W i (p=-3) + W i (p=-2) + W i (p=-1) + W i (p=0) + W i (p=1) + W i (p=2) = max(C 1, C 4 ) + max(C 1 +C 2, C 4 ) + max(C 1 +C 2, C 4 +C 5 ) + C 1 +C 2 +C 3 +C 4 +C 5 + max(C 1,C 3 +C 4 +C 5 ) + max(C 1, C 3 )
© COPYRIGHT IKERLAN 2014 Simulation results 19 Extensive simulations with random task sets generated with GEN4MAST [Rivas et al., 13] and analysed with MAST Compared holistic technique [Rivas et al., 10] with the new algorithms WCDO-EDF and WCDOPS-EDF for LC-EDF distributed systems
© COPYRIGHT IKERLAN 2014 Simulation results 20 Processor maximum utilization: Around 9% better utilization for WCDO-EDF Around 16% better utilization for WCDOPS-EDF
© COPYRIGHT IKERLAN 2014 Conclusions and future work Analysis techniqueFPGC-EDFLC-EDF 21 Tindell and Clark, 94Spuri, 96Rivas et al., 10Holistic WCDO Palencia and González Harbour, 98 Palencia and González Harbour, 03 Palencia and González Harbour, 99 WCDOPS Not useful WCDO : Worst Case Dynamic Offsets WCDOPS: Worst Case Dynamic Offset with Precedence Schemes
© COPYRIGHT IKERLAN 2014 Conclusions and future work Reduced significantly the pessimism of the response time analysis for systems scheduled by LC-EDF. Improvements come “for free”. Only affect the analysis, not the scheduling policy, nor the system’s architecture. Some works have slightly improved the WCDO and WCDOPS analysis for fixed-priorities (Mäki-Turja and Nolin, 08; Redell, 04). We have not taken into account for our analysis. Future work: Analyse previous improvements to try to reduce even more the pessimism. Analyse the possibility to develop an exact test that will allow us to quantify the pessimism of these analysis. 22
© COPYRIGHT IKERLAN 2014 Bibliography [Palencia and González Harbour, 98] J. C. Palencia and M. González Harbour. Schedulability analysis for tasks with static and dynamic oﬀsets. In Proc. 19th IEEE Real-time Systems Symp., pages 26–37, 1998. [Palencia and González Harbour, 99] J. C. Palencia and M. González Harbour. Exploiting precedence relations in the schedulability analysis of distributed real-time systems. In Proc. 20th IEEE Real-Time Systems Symp., pages 328–339, 1999. [Palencia and González Harbour, 05] J. C. Palencia and M. González Harbour. Response time analysis of EDF distributed real-time systems. J. Embedded Comput., 1(2):225–237, 2005. [Rivas et al., 10] J. M. Rivas, J. J. Gutiérrez García, J. C. Palencia, and M. González Harbour. Optimized deadline assignment and schedulability analysis for distributed real-time systems with local EDF scheduling. In Proc. 8th Int. Conf. on Embedded Systems and Applications, 2010. [Spuri, 96] M. Spuri. Holistic analysis for deadline scheduled real-time distributed systems. Technical report, INRIA, 1996. [Tindell and Clark, 94] K. Tindell and J. Clark. Holistic schedulability analysis for distributed hard real-time systems. Microprocessing and microprogramming, 40(2), 1994. [Rivas et al., 13] J. M. Rivas, J. J. Gutiérrez, and M. González Harbour. Fixed priorities or edf for distributed real- time systems? SIGBED Rev., 10(2):21–21, 2013. [Mäki-Turja and Nolin, 08] J. Mäki-Turja and M. Nolin. Eﬃcient implementation of tight response-times for tasks with oﬀsets. Real-Time Systems, 40(1):77–116, 2008. [Redell, 04] O. Redell. Analysis of tree-shaped transactions in distributed real time systems. In Proc. 16 th Euromicro Conf. on Real-Time Systems, 2004., pages 239–248. 23
© COPYRIGHT IKERLAN 2014 P.º J.M. Arizmendiarrieta, 2 20500 Arrasate-Mondragón (Gipuzkoa) Tel.: 943 71 24 00 Fax: 943 79 69 44 www.ikerlan.es 24
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