Schedule Table Generation for Time-Triggered Mixed Criticality Systems
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1 Schedule Table Generation for Time-Triggered Mixed Criticality Systems Jens Theis and Gerhard Fohler Technische Universität Kaiserslautern, Germany Sanjoy Baruah The University of North Carolina, Chapel Hill, NC, USA
2 Introduction System mixed criticality Challenges efficient resource usage safety critical deterministic behavior certification simple certification 2
3 Job Model Vestal-model for dual criticality jobs r i d i release time deadline χ i LO, HI criticality levels C i LO, C i HI worst case execution time (WCET) for LO and HI C i LO = C i HI, if χ i = LO C i LO C i HI, if χ i = HI 3 under certification authorities' (CAs) assumptions under designers' assumptions
4 Time-Triggered (TT) Mode Changes approach by Baruah and Fohler proof of concept TT schedule tables: J1 χ 1 =LO J2 χ 2 =HI J4 χ 4 =LO J3 χ 3 =HI HI-table J1 χ 1 =LO J2 χ 2 =HI J4 χ 4 =LO J3 χ 3 =HI 4
5 TT Mode Changes approach by Baruah and Fohler proof of concept mode switch at runtime: J1 χ 1 =LO J2 χ 2 =HI J4 χ 4 =LO J3 χ 3 =HI HI-table J1 χ 1 =LO J2 χ 2 =HI J4 χ 4 =LO J3 χ 3 =HI switch-through property 5 switch-through obtained by inserting LO-criticality jobs in HI-table at cost of utilization
6 Basic Idea! designers CAs separate designers' and CAs' WCET-assumptions J1 1 2 J2 2 3 J2 3 4 J1 4 5 J1 1 2 J4 5 6 J2 2 3 J3 6 7 J2 3 4 J3 7 8 J1 4 5 J4 5 6 J3 6 7 J3 7 8 J3 8 9 J1 1 2 J2 2 3 J2 3 4 J3 8 9 J1 4 5 J1 1 2 J4 5 6 J2 2 3 J2 3 4 J1 4 5 J4 5 6 use heuristic tree search to generate two time-triggered (TT) schedule tables 6
7 Separate WCET Assumptions separate demand based on designer assumptions from additional demand by CAs' pessimism split HI-criticality jobs C 1 LO J1 χ 1 =HI C 1 HI J1 χ 1 =HI 7
8 Separate WCET Assumptions separate demand based on designer assumptions from additional demand by CAs' pessimism split HI-criticality jobs C 1 LO J1 LO χ 1 =HI job with designer assumptions C 1 HI C 1 LO J1 Δ χ 1 =HI job representing CAs' pessimism 8
9 Parameter Derivation of Split Jobs add a precedence constraint derive new parameters for the split jobs designer assumptions CAs' pessimism J1 LO χ 1 =HI J1 Δ χ 1 =HI r 1 LO d 1 LO r 1 d 1 t 9
10 Parameter Derivation of Split Jobs add a precedence constraint derive new parameters for the split jobs designer assumptions CAs' pessimism J1 LO χ 1 =HI J1 Δ χ 1 =HI r 1 Δ d 1 Δ r 1 d 1 t 10
11 Job Parameters Overview job parameters for scheduling: for all jobs with χ i = LO: J i = r i, d i, C i LO for all jobs with χ i = HI: J LO i = r LO i, d LO i, C LO i LO J Δ i = r Δ i, d Δ i, C Δ i HI 11
12 Job Allocation to Modes job allocation to modes: HI-table J i χ i =LO J i LO χ i =HI J i LO χ i =HI J i Δ χ i =HI 12
13 TT Mode Changes after Splitting precedence constraints used to reduce utilization in HI-table HI-table J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO J3 LO χ 3 =HI J4 χ 4 =LO J2 LO χ 2 =HI J2 Δ χ J3 LO χ 2 =HI 3 =HI J3 Δ χ 3 =HI switch-through property switch-through obtained by splitting HI-criticality jobs 13
14 Basic Idea! designers CAs separate designers' and CAs' WCET-assumptions J1 1 2 J2 2 3 J2 3 4 J1 4 5 J1 1 2 J4 5 6 J2 2 3 J3 6 7 J2 3 4 J3 7 8 J1 4 5 J4 5 6 J3 6 7 J3 7 8 J3 8 9 J1 1 2 J2 2 3 J2 3 4 J3 8 9 J1 4 5 J1 1 2 J4 5 6 J2 2 3 J2 3 4 J1 4 5 J4 5 6 use heuristic tree search to generate two time-triggered (TT) schedule tables 14
15 General Tree Search Example with 2 jobs start J1 J2 slot 0 J2 J1 slot 1 J1 J2 J2 J1 15
16 Schedule Tables Construction start slot 0 slot 1 slot 2 partial schedule infeasible schedule path to infeasible schedule feasible schedule 16
17 Guiding the Search Heuristic function: The leeway δ s of a slot s in determines how many we can delay the job scheduled in that slot. Backtracking 17
18 Leeway leeway δ s of jobs with χ i = LO: δ s c = 5 J1 s c s c +1 s c +2 s c +3 s c +4 s c +5 18
19 Leeway leeway δ s of jobs with χ i = HI: (more details considering several HI-criticality jobs in the paper) δ s c = 3 J2 LO s c s c +1 s c +2 s c +3 s c +4 s c +5 HI-table J2 Δ s c s c +1 s c +2 s c +3 s c +4 s c +5 19
20 Schedule Tables Generation search tree : according to EDF HI-table: depending on criticality level in LO: Δ-fraction job by EDF HI: same job as in leeway HI-table 20
21 Schedule Tables Generation search tree : select job by EDF J1 HI-table: select Δ-fraction job by EDF idle slot slot 0 leeway δ 0 = 1 J1 χ 1 =LO HI-table idle 21
22 Schedule Tables Generation search tree : select job by EDF J2 LO slot 0 slot 1 HI-table: schedule same job as in J2 LO leeway δ 0 = 1 δ 1 = 1 HI-table J1 χ 1 =LO idle J2 LO χ 2 =HI J2 LO χ 2 =HI TODO J2 Δ χ 2 =HI 22
23 Schedule Tables Generation search tree : select job by EDF J4 HI-table: select Δ-fraction job by EDF slot 0 slot 1 slot 2 J2 Δ leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO HI-table idle J2 LO χ 2 =HI J2 Δ χ 2 =HI 23
24 Schedule Tables Generation search tree : select job by EDF J4 HI-table: select Δ-fraction job by EDF idle slot slot 0 slot 1 slot 2 slot 3 leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 δ 3 = 1 J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO J4 χ 4 =LO HI-table idle J2 LO χ 2 =HI J2 Δ χ 2 =HI idle 24
25 Schedule Tables Generation search tree : select job by EDF J3 LO negative leeway backtracking slot 0 slot 1 slot 2 slot 3 slot 4 leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 δ 3 = 1 δ 4 = 1 HI-table J1 χ 1 =LO idle J2 LO χ 2 =HI J2 LO χ 2 =HI J4 χ 4 =LO J2 Δ χ 2 =HI J4 χ 4 =LO idle J3 LO χ 3 =HI TODO J3 Δ χ 3 =HI 25
26 Schedule Tables Generation search tree : select job by EDF J3 LO negative leeway backtracking slot 0 slot 1 slot 2 slot 3 slot 4 leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 δ 3 = 1 δ 4 = 1 J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO J3 LO χ 3 =HI J4 χ 4 =LO HI-table idle J2 LO χ 2 =HI J2 Δ χ 2 =HI idle 26
27 Schedule Tables Generation search tree : select job by EDF J3 LO negative leeway backtracking slot 0 slot 1 slot 2 slot 3 slot 4 leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 δ 3 = 0 δ 4 = 0 J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO J3 LO χ 3 =HI J4 χ 4 =LO HI-table idle J2 LO χ 2 =HI J2 Δ χ 2 =HI idle 27
28 Schedule Tables Generation search tree : select job by EDF J3 LO HI-table: schedule same job as in J3 LO slot 0 slot 1 slot 2 slot 3 slot 4 leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 δ 3 = 0 δ 4 = 0 J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO J3 LO χ 3 =HI J4 χ 4 =LO HI-table idle J2 LO χ 2 =HI J2 Δ χ 2 =HI J3 LO χ 3 =HI idle 28
29 Schedule Tables Generation search tree : swapped job has LO-criticality HI-table: select Δ-fraction job by EDF J3 Δ slot 0 slot 1 slot 2 slot 3 slot 4 leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 δ 3 = 0 δ 4 = 0 J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO J3 LO χ 3 =HI J4 χ 4 =LO HI-table idle J2 LO χ 2 =HI J2 Δ χ 2 =HI J3 LO χ 3 =HI J3 Δ idle χ 3 =HI 29
30 Schedule Tables Generation search tree : swapped job has LO-criticality HI-table: select Δ-fraction job by EDF J3 Δ slot 0 slot 1 slot 2 slot 3 slot 4 leeway δ 0 = 1 δ 1 = 1 δ 2 = 2 δ 3 = 0 δ 4 = 0 J1 χ 1 =LO J2 LO χ 2 =HI J4 χ 4 =LO J3 LO χ 3 =HI J4 χ 4 =LO HI-table idle J2 LO χ 2 =HI J2 Δ χ 2 =HI J3 LO χ 3 =HI J3 Δ idle χ 3 =HI 30
31 Conclusion System mixed criticality safety critical certification 31
32 Conclusion created two TT schedule tables (one for each criticality level) constructive proof by TT execution job splitting separates designer and CAs assumptions added precedence constraints pessimistic CAs assumptions excluded from LO-criticality system behavior leeway and swapping used for backtracking 32
33 Thank You. Jens Theis and Gerhard Fohler Technische Universität Kaiserslautern, Germany Sanjoy Baruah The University of North Carolina, Chapel Hill, NC, USA
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