J.M. Lopez: Minimum and maximum utilization bounds for Multiprocessor RM

allocation algorithm: FF, WF, BF

scheduling algorithm: RM, EDF

 

两个参数

α: maximum reachable utilization factor of any task

β: maximum number of tasks when α

U: mutilprocessor utilization bound, associated with any reasonable allocation algorithm

 

1. 两个参数的函数关系，β <= f(α) && β >= f(α)， 所以β = f(α)

 

2. 在不指定分配算法的前提下，计算U上下界

　　a. 下界证明方法-不等式层层递减

　　b. 上界证明方法-

• • the task set is presented
  • task set is made up of m tasks, and processor utilization is U_max+ ε
  • the utilization factors of the task set are proven to be valid, that is, 0 < u_i < α
  • the task set does not fit into the multiprocessor

3. 采用WF时，计算U。WF allocation has no practical value, but is interesting from a theoretical perspective.

　方法同上界证明方法

　U for any reasonable allocation algorithm under dynamic allcation coincides with U for static WF allocation. More complex schedulability conditions are required to deal with transient states(after the task set changes)

 

4. 采用RAD（FFD, BFD）时，计算U

   方法同下届证明方法，该下届恰好等于不指定分配算法的U的上界。