> For the complete documentation index, see [llms.txt](https://blendr-network.gitbook.io/blendr-network-technical-plan/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://blendr-network.gitbook.io/blendr-network-technical-plan/blendrs-decentralized-architecture/task-scheduler-optimization-active-gpus.md).

# 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.