feat: To add health status check for remote VLLM (#2303)

# What does this PR do?
<!-- Provide a short summary of what this PR does and why. Link to
relevant issues if applicable. -->
To add health status check for remote VLLM
<!-- If resolving an issue, uncomment and update the line below -->
<!-- Closes #[issue-number] -->

## Test Plan
<!-- Describe the tests you ran to verify your changes with result
summaries. *Provide clear instructions so the plan can be easily
re-executed.* -->
PR includes the unit test to test the added health check implementation
feature.

llama_stack/distribution/routers/inference.py

@@ -602,7 +602,7 @@ class InferenceRouter(Inference):
 
     async def health(self) -> dict[str, HealthResponse]:
         health_statuses = {}
-        timeout = 0.5
+        timeout = 1  # increasing the timeout to 1 second for health checks
         for provider_id, impl in self.routing_table.impls_by_provider_id.items():
             try:
                 # check if the provider has a health method

llama_stack/providers/remote/inference/vllm/vllm.py

@@ -56,7 +56,11 @@ from llama_stack.apis.inference.inference import (
 from llama_stack.apis.models import Model, ModelType
 from llama_stack.models.llama.datatypes import BuiltinTool, StopReason, ToolCall
 from llama_stack.models.llama.sku_list import all_registered_models
-from llama_stack.providers.datatypes import ModelsProtocolPrivate
+from llama_stack.providers.datatypes import (
+    HealthResponse,
+    HealthStatus,
+    ModelsProtocolPrivate,
+)
 from llama_stack.providers.utils.inference.model_registry import (
     ModelRegistryHelper,
     build_hf_repo_model_entry,
@@ -298,6 +302,22 @@ class VLLMInferenceAdapter(Inference, ModelsProtocolPrivate):
     async def unregister_model(self, model_id: str) -> None:
         pass
 
+    async def health(self) -> HealthResponse:
+        """
+        Performs a health check by verifying connectivity to the remote vLLM server.
+        This method is used by the Provider API to verify
+        that the service is running correctly.
+        Returns:
+
+            HealthResponse: A dictionary containing the health status.
+        """
+        try:
+            client = self._create_client() if self.client is None else self.client
+            _ = [m async for m in client.models.list()]  # Ensure the client is initialized
+            return HealthResponse(status=HealthStatus.OK)
+        except Exception as e:
+            return HealthResponse(status=HealthStatus.ERROR, message=f"Health check failed: {str(e)}")
+
     async def _get_model(self, model_id: str) -> Model:
         if not self.model_store:
             raise ValueError("Model store not set")