# How to linearize such a constraint?

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

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

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?

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