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

Algorithm 2

CalcSlackTime(additional slack 𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}).

Input: the active task 𝜏_𝛼, readyQ and current time 𝑡

Output: the slack time 𝑠𝑙𝑎𝑐𝑘_𝛼(𝑡) for 𝜏_𝛼

(12) Identify the task 𝜏_𝛽 that has the earliest upcoming deadline among tasks whose

   priorities are not higher than that of 𝜏_𝑎;

(13) 𝐿_𝛽(𝑡)∶= CalcLowerPriorityWork(τ _β, 𝑡, 𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾});

(14) 𝑙𝑜𝑎𝑑_𝛽(𝑡)∶=𝑤^rem_𝛽(𝑡)+𝐻_𝛽(𝑡)+𝐿_𝛽(𝑡);

(15) 𝑠𝑙𝑎𝑐𝑘_𝛼(𝑡)∶= max0,𝑢𝑑_𝛽−𝑡−𝑙𝑜𝑎𝑑_𝛽;

(16)  return 𝑠𝑙𝑎𝑐𝑘_𝛼(𝑡);