1. 6. Application mapping 6.1 Problem definition
6.2 Scheduling in real-time systems
6.3 Hardware/software partitioning
6.4 Mapping to heterogeneous multi-processors

2. 6.1 Problem definition Find: Objectives:
A mapping of applications to processors,
Appropriate scheduling techniques (if not fixed), and
A target architecture (if not fixed)
Objectives:
Keeping deadlines and/or maximizing performance, as well as
Minimizing cost, energy consumption, and possibly other objectives.
The application mapping problem is a very difficult one and currently only approximated for an automated mapping are available.
Standard scheduling techniques,
Hardware/software partitioning, and
Advanced techniques for mapping sets of applications onto multi-processor systems.
6. Application Mapping

3. 6.2 Scheduling in real-time systems
Scheduling is one of the key issues in implementing embedded systems.
Scheduling defines start times for each task and therefore defines a mapping  from nodes of a task graph G=(V, E) to time domain Dt:
: V  Dt (6.1)
6.2.1 Classification of scheduling algorithms
Classes of scheduling algorithms
real-time scheduling
hard deadlines
soft deadlines
periodic
aperiodic
preemptive
Non-preemptive
static
dynamic
6. Application Mapping

4. 6.2.2 Aperiodic scheduling without precedence constraints
Definitions
{Ti}, a set of tasks
ci be the execution time of Ti,
di be the deadline-interval,
li be the laxity or slack, defined as
Earliest Due Date (EDD) – Algorithm
Jackson’s rule:
Given a set of a independent tasks, any algorithm that executes the tasks in order of non-decreasing deadlines is optimal with respect to minimizing the maximum lateness.
Availability of Task di ci li t
6. Application Mapping

5. 6.2.2.3 Earliest Deadline First (EDF) – Algorithm
The Earliest Deadline First (EDF) algorithm is optimal with respect to minimizing the maximum lateness.
Given a set of n independent tasks with arbitrary arrival times, any algorithm that at any instant executes the task with the earliest absolute deadline among all the ready tasks is optimal with respect to minimizing the maximum lateness.
EDF is a dynamic scheduling algorithm.
Fig. 6.6 shows a schedule derived with the EDF algorithm. Vertical arrows indicate the arrival of tasks.
6. Application Mapping

6. 6.2.2.4 Least Laxity (LL) algorithm
Priorities = decreasing function of the laxity (lower laxity  higher priority); changing priority; preemptive.
Fig. 6.6 shows an example of an LL schedule, together with the computations of the laxity.
6. Application Mapping

7. 6.2.2.5 Scheduling without preemption
T1: periodic, c1 = 2, p1 = 4, d1 = 4
T2: occasionally available at times 4*n+1, c2= 1, d2= 1
T1 has to start at t =0
 deadline missed, but schedule is possible (start T2 first)
 scheduler is not optimal  contradiction! q.e.d.
6. Application Mapping

8. 6.2.3 Aperiodic scheduling with precedence constraints
Latest Deadline First (LDF) algorithm
In a task graph reflecting tasks dependences (Fig. 6.11). Task T3 can be executed only after tasks T1 and T2 have completed and sent message to T1.
As-soon-as-possible (ASAP) scheduling
Consider a 33 matrix.
6. Application Mapping

9. The determinant det(A) of this matrix can be computed as
ASAP schedule for the example of det(A) e i a f h b g d c  - +
=1
=3
=4
=6
=7
6. Application Mapping

10. 6.2.4 Periodic scheduling without precedence constraints
Notation
Let {Ti } be a set of tasks. Let:
pi be the period of task Ti,
ci be the execution time of Ti ,
di be the deadline interval, that is, the time between Ti becoming available and the time until which Ti has to finish execution.
li be the laxity or slack, defined as li = di - ci
fi be the finishing time.
Let  denote the utilization for a set of n processes, that is, the accumulated execution times of these processes divided by their period:
6. Application Mapping li pi ci di t i

11. 6.2.4.2 Rate monotonic scheduling
Necessary condition for schedulability (with m=number of processors):
Rate monotonic scheduling
RM policy: The priority of a task is a monotonically decreasing function of its period.
At any time, a highest priority task among all those that are ready for execution is allocated.
6. Application Mapping
T1 preempts T2 and T3.
T2 and T3 do not preempt each other.

12. 6.2.4.3 Earliest deadline first scheduling
EDF can also be applied to periodic scheduling.
EDF optimal for every hyper-period (= least common multiple of all periods)
Optimal for periodic scheduling
EDF must be able to schedule the example in which RMS failed.
At time 5, T2 not preempted, due to its earlier deadline.
6. Application Mapping