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# core.solver.MoERoutingModel { #mlsysim.core.solver.MoERoutingModel }
```python
core.solver.MoERoutingModel()
```
Models first-order Mixture-of-Experts routing imbalance and optional
expert-parallel all-to-all cost.
Sparse models decouple memory from compute: total parameters determine memory,
while active parameters determine the compute path. `MoERoutingModel` adds one
teachable knob, `routing_imbalance_factor`, for hot-expert effects.
## Methods
| Name | Description |
| --- | --- |
| [solve](#mlsysim.core.solver.MoERoutingModel.solve) | Estimate effective active parameters and optional EP all-to-all latency. |
### solve { #mlsysim.core.solver.MoERoutingModel.solve }
```python
core.solver.MoERoutingModel.solve(
model,
batch_size,
seq_len,
precision='fp16',
ep_size=1,
routing_imbalance_factor=1.0,
fleet=None,
)
```
#### Parameters
| Name | Type | Description | Default |
| --- | --- | --- | --- |
| model | SparseTransformerWorkload | Sparse Transformer / MoE workload. | _required_ |
| batch_size | int | Local routed batch size. | _required_ |
| seq_len | int | Sequence length. | _required_ |
| precision | str | Activation precision for routed bytes. | `'fp16'` |
| ep_size | int | Expert-parallel degree. | `1` |
| routing_imbalance_factor | float | Hot-expert multiplier, where `1.0` is balanced. | `1.0` |
| fleet | Fleet | Optional fabric used to compute all-to-all latency. | `None` |
#### Returns
`MoERoutingResult` with effective active experts, effective active parameters,
routed bytes, and optional all-to-all latency.