Max-Min and Min-Min algorithms implementation

I'm trying to simulate the Max-Min and Min-Min scheduling algorithms and code them myself in a simulation. But don't really understand how to implement the way they work in code.

For example, in FCFS algorithm i use 3 servers(vms),each server is faster than the other and 5 tasks with different arrival times. So the first task will check the first server and will be scheduled there, the second if arrive while the first is't completed yet, will check the availability and scheduled to the second server. If all 3 servers are occupied the next task will be scheduled to the one with the min remain executing time.

Now for the Min-Min and Min-Max this is the theoretical background:

Min-Min: Phase 1: First computes the completion time of every task on each machine and then for every task select the machine which processes the tasks in minimum possible time. Phase 2: Among all the tasks in Meta task the task with minimum completion time is selected and is assigned to machine on which minimum execution time is expected. The task is removed from the list of Meta Task and the procedure continues until Meta Task list is empty.

Max-Min: Phase 1: First computes the completion time of every task on each machine and then for every task chooses the machine which processes the tasks in minimum possible time Phase 2: Among all the tasks in Meta Task the task with maximum completion time is selected and is assigned to machine. The task is removed from the list of Meta Task and the procedure continues until Meta Task list is empty.

I get the phase 1 for both algorithms, I need to check the task's burst time and server's speedup -> burst/speedup = execution time. I will find the best server for each task. But I can't understand the phase 2. For Min-Min i have to choose every time the fastest task and when i find it I will have to schedule it to the faster server. But the workload will be imbalanced, as I said 3 servers and at least one is the faster, lets say server with ID 1, so every time the tasks will scheduled to this one, I also need the other 2 to work.

Same problem with Max-Min, find the worst task, schedule it to the worst server, but only one server is the worst so the other 2 will not work. How am I suppose to do the balancing and also take in consideration that the tasks arrive in different times?

If you need anything more just let me know and thanks in advance!

Solution

You can find nice description of both algorithms in:

I paste here pseudocode for Min-Min. ET_ij is execution time for task t_i on resource R_j. And r_j is ready time of R_j.

That's true that you can have imbalanced load, because all small task will get executed first. Max-Min algorithm overcomes this drawback.

Max-Min algorithm performs the same steps as the Min-Min algorithm but the main difference comes in the second phase, where a task t_i is selected which has the maximum completion time instead of minimum completion time as in min-min and assigned to resource R_j, which gives the minimum completion time.