Off-line (Optimal) Multiprocessor Scheduling of Dependent Periodic Tasks

Transcription

1 Off-line (Optimal) Multiprocessor Scheduling of Dependent Periodic Tasks Julie Barot, Frédéric Boniol, Mikel Cordovilla, Eric Noulard, Claire Pagetti ONERA, Toulouse, France SAC 2012 March, 27th

2 Context Critical embedded applications: Essentially control/command applications (for airplane, UAV, cars, satellites, nuclear power-plant,...) Multiperiodic applications Execution time should be fully controlled with formally verified properties Computer architecture used in this context: Nowadays: mono-core mature and widely used, but they may disappear from the market. Today or near future: multi-core already in the way (GR712RC Dual-Core LEON3FT, Power PC QorIQ, ARM MPCore), many-core are coming (Intel SCC, Tilera Gx, ) 2 EADS - Astrium Ex: navigation of a spatial vehicle functions - Partial precedences constraints + slots positioning (1553) - DM scheduling - monoprocessor

3 Prelude+SchedMcore framework Prelude specification Input: set of imported functions Output: dependent real-time task set Current talk Schedulability analysis Time accurate simulation 3

4 Outline 1. Reminder and notations 2. Fixed priority assignment 3. Off-line schedule 4. Conclusion and perspectives 4

5 System model Dependant periodic task set <S,R>: 5 S={τi = (Ti, Oi, Di, Ci)} finite periodic task set, where Ti is the period, Ci is the wcet, Di is the deadline and Oi is the offset. τik is the kth job of τi. H=lcm(Ti) is the hyper-period R is the periodic extended precedence relation. Finite set of jobs precedences. Ex: T Oi Ci Di Ti τ τ τ

6 Real-time scheduling Scheduling policy: Algorithm : give access to the CPUs to the tasks Global scheduling : global management (full migration) Preemptive : a job (instance of a task) can be interrupted and resumed later On-line vs off-line schedule : o On-line: decisions are taken at execution time o Off-line: scheduling parameters are statically computed before execution Embedded critical industrial designer s choices: 6 Off-line schedule o Minimal embedded mechanisms o Costs are assessable FP (fixed priority) policy o Simplest on-line policy

7 Execution encoding Encode the possible behaviours At [discrete] time t the state of the system is conf(t) = <conf(τ 1,t),, conf(τ n,t)> With conf(τ i,t) = (Ti (t), Ci (t), Di (t), Oi (t)) Precedence encoded as well with a set of active words 7 Ti Oi τ τ τ Di 10 τ1 τ2 Policy: FP τ 1< τ 2 < τ 3 τ1 τ3 2 processors τ2 τ3 Ci 5 (0,0) (0,0) (0,0)

8 Outline 1. Reminder and notations 2. Fixed priority assignment 3. Off-line schedule 4. Conclusion and perspectives 8

9 Fixed priority assignment For uniprocessor platform: RM is optimal for synchronous implicit deadline independent task sets DM is optimal for synchronous constrained deadline independent task sets Audsley s algorithm is optimal for asynchronous constrained deadline independent periodic tasks These policies have been extended for dependent task set For multiprocessor platform: No known simple assignment Audsley cannot be adapted: test if a task accepts the lowest priority by applying a schedulability analysis which does not require to assign a priority to the other tasks. Cucu & Goossens proposed a brute force solution (complexity n!xc) Contribution: 9 Implementation of the brute force method Efficient sub-optimal heuristic

10 Brute force method Algorithm Choose an assignment Test with an exhaustive simulation if the task set is schedulable Feasible window: [0,H] for synchronous independent task set [0,Sn+H] for asynchronous independent task set Test if a configuration has already been visited for dependent task set Two versions 10 C and UPPAAL C Uppaal

11 Sub optimal heuristic 1. the lowest priorities n, n 1..., n k+1 have been given to the tasks S S. 2. consider task τi S\S which accepts the priority n k, this means that the REFUSE condition is false. a) Choose a random complete assignment (except for the tasks which already temporary accept a low priority) b) Apply an exact schedulability test. 1. If the test succeeds, the assignment is correct and a solution has been found. 2. If one task τk S {τi} with a temporary low priority exceeds its deadline, the algorithm backtracks to the step where τk temporary accepts the lowest priority and chooses a next task. 3. Otherwise, the algorithm continues the search. It goes in step 1, assumes the priorities n, n 1..., n k have been assigned and tries to find a task in S \ (S {τi}) to tentatively accept the lowest priority. REFUSE condition: τ1 = (T1, D1, C1, O1) refuses the lowest priority if: 11

12 Experiment CPU load: 80% Hyper-period Variable number of tasks 2 processors gllf gedf heuristic Good acceptance ratio 12

13 Outline 1. Reminder and notations 2. Fixed priority assignment 3. Off-line schedule 4. Conclusion and perspectives 13

14 Off-line optimal schedule This feasible task set is not schedulable with gedf, gllf, LLREF or FP on 2 processors Principles: find a feasible schedule State of the art: branch and bound approach for synchronous task set Petri net for asynchronous task set on a uniprocessor Cost timed automata for jobs Contribution: encoding the problem as a reachability problem in a finite automaton 14

15 Encoding Input: Dependent periodic task set <S,R> Multiprocessors with p processors Output: Finite sequence A feasible sequence exists iff the state ok is reachable E<>ok 15

16 Experiments CPU load: 80% Hyper-period 1000 Variable number of tasks 2 processors optimal 16 gllf

17 Outline 1. Reminder and notations 2. Fixed priority assignment 3. Off-line schedule 4. Conclusion and perspectives 17

18 Conclusion Open end-to-end framework for the development of multi-periodic real-time systems Efficient off-line parameters computation Work in progress: 18 Theoretical complexity of the sub optimal heuristic Use of model checker which compacts more the states (Tina) Add a cost model on the preemptions and migrations