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 t o 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  = {T 1,, T 2,..., T n }; T i = (c i, d i, p i ) 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 constant D

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

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

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

8. Virtual time t V i (t) The ith task group is analyzed assuming a virtual processor of rate  The generalization... V i (t) =  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 constant D e’ e

9. System model Periodic task T = (c,d,p) A task group  = {T 1, T 2,...,T n }, T i = (c i, d i, p i ) 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 Not static-priority!!

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   = {(S 1, E 1 ), (S 2, E 2 ),..., (S N, E N )} is the partition list with 0  S 1 <E 1 <S 2 < E 2 <... < S N < E N  P The resource is available during time-slots [S i, E i ) The intervals [E i, S i+1 ) are called blocking times slots Availability factor of resource partition   (  ) = [(E 1 - S 1 ) + (E 2 - S 2 ) +... + (E N - S N )]/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. Static resource partitioning: virtual time t V i (t) 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: 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 [E i, S i+1 ), for all blocking time slots Theorem: Theorem: Rate-monotonic/ deadline monotonic priority assignment is optimal Corollary: Corollary: Static-priority feasibility assignment in pseudo- polynomial time (N simulations, where N is the number of slots in the partition list)

14. Theorem: Theorem: A task group is feasible in a partition  iff for all positive t o and t Static resource partitioning: dynamic-pri scheduling Theorem: Theorem: EDF is an optimal scheduling algorithm Approach: 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