fix(router.py): calculate max_parallel_requests from given tpm limits

use the azure formula to calculate rpm -> max_parallel_requests based on a deployment's tpm limits

litellm/utils.py

@@ -5395,6 +5395,46 @@ def get_optional_params(
     return optional_params
 
 
+def calculate_max_parallel_requests(
+    max_parallel_requests: Optional[int],
+    rpm: Optional[int],
+    tpm: Optional[int],
+    default_max_parallel_requests: Optional[int],
+) -> Optional[int]:
+    """
+    Returns the max parallel requests to send to a deployment.
+
+    Used in semaphore for async requests on router.
+
+    Parameters:
+    - max_parallel_requests - Optional[int] - max_parallel_requests allowed for that deployment
+    - rpm - Optional[int] - requests per minute allowed for that deployment
+    - tpm - Optional[int] - tokens per minute allowed for that deployment
+    - default_max_parallel_requests - Optional[int] - default_max_parallel_requests allowed for any deployment
+
+    Returns:
+    - int or None (if all params are None)
+
+    Order:
+    max_parallel_requests > rpm > tpm / 6 (azure formula) > default max_parallel_requests
+
+    Azure RPM formula:
+    6 rpm per 1000 TPM
+    https://learn.microsoft.com/en-us/azure/ai-services/openai/quotas-limits
+
+
+    """
+    if max_parallel_requests is not None:
+        return max_parallel_requests
+    elif rpm is not None:
+        return rpm
+    elif tpm is not None:
+        return int(tpm / 1000 / 6)
+    elif default_max_parallel_requests is not None:
+        return default_max_parallel_requests
+    return None
+
+
 def get_api_base(model: str, optional_params: dict) -> Optional[str]:
     """
     Returns the api base used for calling the model.