# Optimal time for scheduling the tasks

• MHB
• mathmari
In summary, The conversation discusses the execution times and prerequisites of tasks $T_1$ through $T_{10}$ and creating a schedule for them using three processors. The goal is to have the execution time $\omega$ be no more than $5/3$ of the optimal time for the tasks. The conversation ends with a question about the definition of the optimal time for the execution of the tasks.
mathmari
Gold Member
MHB
Hey!

We have the following tasks with the respective times of execution:
\begin{equation*}\begin{matrix}T_1/5 & T_2/4 & T_3/8 & T_4/3 & T_5/4 & T_6/6 & T_7/8 & T_8/3 & T_9/5 & T_{10}/3\end{matrix}\end{equation*} The tasks $T_3,T_4$ have as prerequisite the task $T_2$, the tasks $T_5, T_6, T_7$ have as prerequisite the task $T_4$ and the tasks $T_8, T_9$ have as prerequisite the task $T_7$. Make the schedule of these tasks using three processors so that the time of execution of the tasks $\omega$ is not more than $5/3$ of the optimal time for the execution of the tasks. First I made a diagramm of the tasks in respect of the prerequisites:

Then using 3 processors I got the following:

Is this correct? This means that the time needed for the execution of the tasks is $\omega=20$, right?

But which is the optimal time for the execution of the tasks, since $\omega$ has to less or equal to $5/3$ of that optimal time?

Or is the way I did the above wrong? :unsure:

mathmari said:
This means that the time needed for the execution of the tasks is $\omega=20$, right?
Hey mathmari!

Looks correct to me. (Nod)

mathmari said:
But which is the optimal time for the execution of the tasks, since $\omega$ has to less or equal to $5/3$ of that optimal time?
That depends on how the 'optimal time for the execution of the tasks' is defined.
Is that somewhere in your texts? I can't seem to easily find it. (Wondering)

If I had to guess given the context, I'd guess that it is the time needed if all CPU's run at 100% without wasting any time waiting.
Alternatively it might be the time needed if we had an infinite number of processors.

## 1. What is the optimal time for scheduling tasks?

The optimal time for scheduling tasks varies depending on the individual, their workload, and their personal preferences. It is important to find a time that works best for you and allows you to be productive.

## 2. How can I determine the optimal time for scheduling tasks?

To determine the optimal time for scheduling tasks, you can try different times and see when you are most productive. You can also consider your energy levels, peak work hours, and any external factors that may impact your schedule.

## 3. Is there a specific time of day that is considered the most optimal for scheduling tasks?

There is no one specific time of day that is considered the most optimal for scheduling tasks. It ultimately depends on the individual and their unique circumstances. Some people may find early mornings to be the most productive, while others may prefer late evenings.

## 4. How can I prioritize tasks within my optimal scheduling time?

To prioritize tasks within your optimal scheduling time, you can use techniques such as the Eisenhower Matrix or the ABCDE method. These methods help you categorize tasks based on urgency and importance, allowing you to focus on the most critical tasks first.

## 5. Can the optimal time for scheduling tasks change over time?

Yes, the optimal time for scheduling tasks can change over time. It is important to regularly reassess and adjust your schedule as needed to accommodate any changes in your workload, energy levels, or personal circumstances.

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