Static Scheduling of Periodic Hardware Tasks with Precedence and Deadline Constraints on Reconfigurable Hardware Devices

Algorithm 4

Total and partial migration or addition of RZs.

(1) Comb // Combination of overlapping execution intervals

(2) Non-overload-comb // Boolean controlling after migration whether RZ is no longer overloaded by Comb

(3) RZ-Load// Load of the RZ corresponding to Comb

(4) RZ-migration // The set of RZs helpful for partial migration

(5) Task-migration // The set of tasks that might perform partial migration

(6) for  all  Comb giving overloaded RZ  do

(7)   Non-overload-comb= False

(8)   while  (Non-overload-comb = False) and (Comb≠⊘)  do

(9)    // Total migration of tasks

(10)    Select the interval from Comb that gives the most heavy occupation rate and discard it from Comb.

(11)    Check whether the iteration, corresponding to the execution interval of the selected task, is studied on another

       non-overload RZ and update the load of the overloaded RZ after the elimination of the selected task.

(12)    if  RZ-Load≤1  then

(13)     Non-overload-comb= True

(14)    end  if

(15)   end  while

(16)  if  Non-overload-comb=False  then

(17)   Reinitialize RZ-Load and Comb with its tasks

(18)   Task-migration=⊘

(19)   RZ-migration=⊘

(20)   // Partial migration of tasks

(21)   Omit the tasks from the overloaded RZ, corresponding to Comb, that are also acceptable by another RZs (𝐷≠∞) and

    reduce their occupation rates from the loads of these RZs. These latter RZs with the overloaded RZ corresponding to

     Comb are included in the set RZ-migration. The omitted tasks are included in Task-migration

(22)   while  Task-migration≠⊘  do

(23)    In Task-migration set, start by the task that gives the best trade-off between least number of RZs in RZ-migration

     where it could migrate and heaviest occupation rate in the overloaded RZ.

(24)    During Comb, within the selected task, choose the biggest execution sections that could be placed in RZs from the

     set RZ-migration without overloading them.

(25)    Update the load of RZs receiving execution sections from the selected task

(26)    if  Some execution sections of the selected task are not placed  then

(27)     Reinitialize the loads of RZs in RZ-migration to values before processing Comb

(28)     Increment the number of RZ corresponding to Comb up to ⌈RZ-Load⌉, go to 6

(29)    else

(30)     Discard the selected task from Task-migration.

(31)    end  if

(32)   end  while

(33)   // All the execution sections of tasks are placed

(34)   Non-overload-comb=True

(35)  end  if

(36) end  for