Utilization Bound Scheduling Analysis for Nonpreemptive Uniprocessor Architecture Using UML-RT

Algorithm 1

Step  1. Computation times are randomly generated and arranged according to shortest job first

   priority scheme.

𝐶₁≤𝐶₂≤𝐶₃≤⋯≤𝐶_𝑘≤⋯≤𝐶_𝑚

Initialize 𝑎=1;

Step  2. hec(𝑚−𝑎)=𝐶(1)+𝐶(2)+⋯+𝐶(𝑚−𝑎)

     hec(𝑚)=𝐶(1)+𝐶(2)+⋯+𝐶(𝑚)

Step  3.  𝑙_𝛿=hec(𝑚−𝑎),𝑙_𝛿<hec(𝑚)

Step  4. assign 𝑇₁=𝑙_𝛿;

     for 𝑖=2 to 𝑚

        do 𝑇_𝑖=𝑇_𝑖−1+𝐶_𝑖−1

     end for

Step  5. Find 𝑈(𝜏)=∑_{𝜏𝑖∈𝜏}𝑈_𝑖 where 𝑈_𝑖=𝐶_𝑖/𝑇_𝑖

Step  6. if 0.9<𝑈(𝜏)≤1;

   Step  6.1. Vary 𝑇_𝑖, such that processor is effectively utilized to schedule “𝑚” tasks in 𝑈(𝜏).

   Therefore 𝑈(𝜏) is work conserving utilization bound.

   Step  6.2. exit;

Step  7. if 𝑈(𝜏)<0.9; 𝑙_𝛿−−; go to Step  4.

Step  8. if 𝑈(𝜏)>1; 𝑙_𝛿++; go to Step  4.