Task Scheduler Optimization active GPUs

Incorporating the concept of Quality of Service (QoS) parameters, the task allocation problem can be reformulated to optimize both computation time and resource allocation efficiency, introducing a multi-objective optimization problem:

Minimize: $Z = \alpha \sum_{j=1}^{m} \sum_{i=1}^{n} X_{ij} \cdot T_{ij} + \beta \sum_{i=1}^{n} (1 - U_i)$

Subject to:

$$\sum_{j=1}^{m} X_{ij} \cdot D_j \leq C_i, \ \forall i$$

$$\sum_{i=1}^{n} X_{ij} = 1, \ \forall j$$

$$U_i = \frac{\sum_{j=1}^{m} X_{ij} \cdot D_j}{C_i}, \ \forall i$$

Where:

• $U_i$represents the utilization rate of node $i$,

• $\alpha$ and $\beta$ are coefficients balancing the importance between minimizing computation time and maximizing resource utilization.