Mok & friends. Resource partition for real-time systems (RTAS 2001)

1. Mok & friends. Resource partition for real-time systems (RTAS 2001)

2. Feasibility analysis: the processor demand criterion methodology dbf(T,t): the maximum execution requirement by jobs of task T over any interval of length t Feasibility For all to yes  system is feasible no  system is infeasible

3. Open systems • Share one processor among many applications • Develop each application in isolation • a task group  = {T1,, T2, ..., Tn}; Ti = (ci, di, pi) a sporadic task • assume, executes on a virtual processor • Two-level scheduler • top (“second”) level -- chooses which application to execute • application level -- schedules each application (task group)

4. Real-time virtual resources • Earlier models -- the resource (processor) is available at a uniform rate • Not valid when open systems are being designed • The abstraction introduced in this paper • processor is available at a uniform rate in the virtual-time domain • If events e and e’ occur x time units apart in the virtual-time domain, then they occur at most (x + D) time units apart in the real-time domain for some constantD

5. Vi(t) = t (= 1) Vi(t) t Virtual time The ith task group is analyzed assuming a virtual processor of rate  Thus far...

6. Vi(t) = t (= 1) Vi(t) =  Vi(t) t Virtual time The ith task group is analyzed assuming a virtual processor of rate  Just a slower processor...

7. Vi(t) = t Vi(t) t Virtual time The ith task group is analyzed assuming a virtual processor of rate  The generalization...

8. Vi(t) e’ e t Virtual time The ith task group is analyzed assuming a virtual processor of rate  • Real-time virtual resources: If events e and e’ occur x time units apart in the virtual-time domain, then they occur at most (x + D) time units apart in the real-time domain for some constantD The generalization... Vi(t) = 

9. Not static-priority!! System model • Periodic task T = (c,d,p) • A task group  = {T1, T2,...,Tn}, Ti = (ci, di, pi) • The processor is partitioned into real-time virtual processors, and each task group executes on its own virtual processor • How to partition the processor? • [Sec 2] The static resource partition model • [Sec 3] The bounded-delay resource partition model

10. How to partition the processor? • The static resource partition model • partition specified by a look-up table (a list) (like table-driven scheduling) • E.g. {(1,2), (4,6), (7,8), (10,12), ....} • The bounded-delay resource partition model • partition specified by • utilization, and • delay bound (the D parameter in the definition of real-time virtual resources)

11. Static resource partitioning: definitions • A resource partition  = (, P) • P is the partition period •  = {(S1, E1), (S2, E2), ..., (SN, EN)} is the partition list with 0  S1<E1 <S2 < E2 < ... < SN < EN  P • The resource is available during time-slots [Si, Ei) • The intervals [Ei, Si+1) are called blocking times slots • Availability factor of resource partition  • () = [(E1 - S1) + (E2 - S2) + ... + (EN - SN)]/P • Supply function S(t)of resource partition  is the total amount of execution that is available to  over [0,t) • (formula? properties[p7])

12. Vi(t) t Static resource partitioning: virtual time The ith task group is analyzed assuming a virtual processor of rate  Executing at rate 1, or not executing at all

13. Static resource partitioning: fixed-pri scheduling • Identify critical instance of job arrivals • An idea -- start of largest blocking time slot? • Theorem: A fixed priority assignment on a task group with deadlines  periods meets all deadlines iff it meets the first deadline of each task when a job of each task arrives at the start of blocking time slot [Ei, Si+1), for all blocking time slots • Theorem:Rate-monotonic/ deadline monotonic priority assignment is optimal • Corollary: Static-priority feasibility assignment in pseudo-polynomial time • (N simulations, where N is the number of slots in the partition list)

14. Theorem: A task group is feasible in a partition  iff • for all positive to and t Static resource partitioning: dynamic-pri scheduling • Theorem: EDF is an optimal scheduling algorithm • Approach: facilitate the computation of rhs. Define • least supply function [S*(t)] (analogous to dbf) and • critical partition [*] • contains (N  N) time slots in its partition lists • represents (perhaps not achievable in static-pri) worst-case behaviour