Consider a distributed computing system with 5 physical processors, running a workload of 6 SPMD jobs:

J1: has 4 VPs J2: has 3 VPs J3: has 4 VPs J4: has 1 VPs J5: has 7 VPs J6: has 2 VPs

1. Using the framework for spatial and temporal scheduling presented in class, find an allocation (spatial schedule) that leads to a temporal fair schedule with a 0% idling ratio.

2. Suppose that after a number of temporal schedule time periods processor number 3 fails completely.

(a) Provide a NEW allocation (spatial schedule) on the remaining 4 physical proces- sors, namely 1, 2, 4, and 5, such that a new temporal schedule is obtained with as small an idling ratio as possible.

(b) Attempt to provide a new allocation (spatial schedule) that uses the original 0% idling ratio as a basis and re-assigns the VPs originally allocated to physical processor number 3 among the other surviving processors. By only re-assigning VPs of the failing processor, migration delays are minimized.

3. Compare the cost in number of "migrating VPs" between the two options of item 2 above.