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My original content was like this:

Assuming that server $k$ can only allocate corresponding computing functions to MU $i$ after receiving their tasks. Let

$$ y_{i,k,t} = \begin{cases} 1 & \text{if MU $i$ has sent a task to server $k$ at time slot $t$} \\ 0 &\text{otherwise} \end{cases} $$

Therefore, we have

\begin{eqnarray} y_{i,k,t} \leq s_{i, k,t}, \quad \forall i,k,t. \end{eqnarray} \begin{eqnarray} y_{i,k,t} \geq x_{i,k,t}, \quad \forall i,k,t. \end{eqnarray} \begin{equation} x_{i,k,t} \geq y_{i,k,t} + s_{i,k,t} - 1. \quad \forall i,k,t. \label{3_start} \end{equation}

where

  • $s_{i, k, t}$ denotes whether the user $i$ is transferring tasks to the server $k$ at time slot $t$

  • $x_{i, k, t}$ denotes whether the server $k$ is allocating resources to the user $i$ at time slot $t$.

I want to constrain the server to only start allocating resources to users after receiving their task requests. However, now I want to change this constraint to that users may need more than one time slot to send tasks. How should I change this constraint?

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  • $\begingroup$ Would you please, what conditional expressions you have tried to write? (e.g. if x=1 then y=1), etc. $\endgroup$
    – A.Omidi
    May 28, 2023 at 8:56
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    $\begingroup$ Original content of what? What does MU stand for? $\endgroup$ May 28, 2023 at 9:52

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