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. F1F1 F2F2 FjFj F m-1 FmFm Sink J1J1 J2J2 JiJi J n-1 JnJn Source... eiei f

2. Preemptive Scheduling of Jobs with Arbitrary Release Times, Deadlines, Execution Times Instead of frame boundaries, use release times and deadlines to partition timeline. I1I1 I2I2 IjIj I m-1 ImIm Sink J1J1 J2J2 JiJi J n-1 JnJn Source... eiei IjIj t r1r1 r3r3 r2r2 r4r4 d1d1 d2d2 d4d4 d3d3 I1I1 ImIm

3. NP Completeness of Non-Preemptive Deadline Scheduling Theorem: The problem of scheduling a non-preemptable set of jobs J 1,..., J i,... J n, each with release time r i, deadline d i, and execution time e i is NP-complete. Proof: Transformation from PARTITION [Garey/Johnson,1979] Given: finite set A 1,..., A i,..., A m, each element of size a i. Let B =  m i=1 a i Define a job set J 1,..., J m+1, as follows: B/2 J m+1 B/2B/2+10B+1 B/2                         1 2/)1( 2/, 1 0 define,1for 1 1 1 1 m m m m ii i i i e Bd Br J ae Bd r Jmi