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

Procedure 1

PRA (time 𝑡, task set 𝑇).

Input  t: current time, 𝑇^𝑏=𝑇−𝜏_𝑛

(1)  set 𝑏=𝑛−1,𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_𝚖𝚒𝚗←∞,𝑘=(𝑡+𝜀)/𝑝_𝑛,ℓ←0, 𝑇^𝖻𝗇={𝜏_𝑖∣𝑖<𝑛 and 𝑝_𝑖 spans astride the bn};

(2) if  𝑆𝑦𝑛𝑇^𝑏,𝑘∶==0

(3)  for  𝑖∶=1  to  𝑛−1

(4)   if 𝑆𝑦𝑛𝑇^𝑏−𝜏_𝑖,𝑘∶==0

(5)     then continue;

(6)     𝜏_{𝚊𝚜𝚢𝚗}∶=𝜏_𝑖;

(7)  if  ℓ≤0  then  𝜏_{𝚊𝚜𝚢𝚗}∶=∅;

(8)  Compute the value of 𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_{𝚊𝚜𝚢𝚗};

(9) else if  𝑆𝑦𝑛𝑇^𝑏,𝑘>0  or  𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_{𝚊𝚜𝚢𝚗}≤0

(10)  then Compute the values of 𝑒^𝚋𝚗 and 𝑒^{𝑠𝑙𝑎𝑐𝑘};

(11)  if  𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_{𝚊𝚜𝚢𝚗}≤0  then  𝑒^{𝙴𝚡𝚌𝚑𝚊𝚗𝚐𝚎}_𝚖𝚒𝚗∶= min𝑒^𝖻𝗇,𝑒^{𝑠𝑙𝑎𝑐𝑘};

(12)  else  𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_𝚖𝚒𝚗∶= min𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_{𝚊𝚜𝚢𝚗},𝑒^𝖻𝗇,𝑒^{𝑠𝑙𝑎𝑐𝑘};

(13) Choose a job 𝜏_𝛿∈𝑇^𝖻𝗇 with ℓ_𝛿^{𝚛𝚒𝚐𝚑𝚝}≥𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_𝚖𝚒𝚗 and 𝑤𝑐_𝛿≥𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_𝚖𝚒𝚗;

(14) When 𝜏_𝛿∈𝑟𝑒𝑎𝑑𝑦𝑄, change the priority of job 𝜏_𝛿 lower than that of job 𝜏_𝑛 in 𝑟𝑒𝑎𝑑𝑦𝑄;

(15) Return  𝑒^{𝖤𝗑𝖼𝗁𝖺𝗇𝗀𝖾}_𝚖𝚒𝚗;