A Work-Demand Analysis Compatible with Preemption-Aware Scheduling for Power-Aware Real-Time Tasks

Algorithm 3

CalcLowerPriorityWork(additional slack 𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}).

Input: a reference task 𝜏_𝛽 and current time 𝑡

Output: the amount of lower-priority work needed to be done before 𝑢𝑑_𝛽

(17) if   𝜏_𝛽 is identical to 𝜏_𝑛  then return 0;

(18) Identify the task 𝜏_𝑟 that has the earliest upcoming deadline among the tasks

   whose priorities are lower than that of 𝜏_𝛽;

(19) 𝐿_𝑟(𝑡)∶= CalcLowerPriorityWork(𝜏_𝑟, t, 𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾});

(20) 𝑙𝑜𝑎𝑑_𝑟(𝑡)∶=𝑤^rem_𝛽(𝑡)+𝐻_𝑟(𝑡)+𝐿_𝑟(𝑡);

(21)  ∗∗∗ if   𝑢𝑑_𝑟 is multiple of 𝑝_𝑛  then  𝑢𝑑_𝑟∶=𝑢𝑑_𝑟+𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾};

(22) 𝐿_𝛽(𝑡)∶= max0,𝑙𝑜𝑎𝑑_𝑟(𝑡)−𝑤_𝛽(𝑡)−𝐻_𝛽(𝑡)−𝑢𝑑_𝑟+𝑢𝑑_𝛽;

(23)  return  𝐿_𝛽(𝑡);