Static Scheduling of Jobs in Frames

1
Static Scheduling of Jobs in Frames

• Layout of task schedule for cyclic executive can
  be formulated as a schedule for jobs in a
  hyperperiod.
• This can be formulated as a network flow problem.

J1
F1
J2
F2
...
...
Fj
Ji
ei
f
Sink
Source
...
...
Jn-1
Fm-1
Fm
Jn
2
Preemptive Scheduling of Jobs with Arbitrary
Release Times, Deadlines, Execution Times

• Instead of frame boundaries, use release times
  and deadlines to partition timeline.

J1
I1
J2
I2
...
...
Ij
Ji
ei
Ij
Sink
Source
...
...
Jn-1
Im-1
Im
Jn
I1
Im
t
r3
r2
r4
d1
d2
d4
d3
r1
3
NP Completeness of Non-Preemptive Deadline
Scheduling

• Theorem The problem of scheduling a
  non-preemptable set of jobs J1, ..., Ji, ...
  Jn, each with release time ri, deadline di,
  and execution time ei is NP-complete.
• Proof Transformation from PARTITION
  Garey/Johnson,1979
• Given finite set A1, ..., Ai, ..., Am, each
  element of size ai. Let B Smi1ai
• Define a job set J1, ..., Jm1, as follows

B/2
B/2
Jm1
B/2
B/21
0
B1