docs: add vLLM Semantic Router integration

assets/agw-docs/pages/agentgateway/llm/providers/multiple-endpoints.md

@@ -4,7 +4,7 @@ Configure access to multiple OpenAI API endpoints such as for chat completions,
 
 To set up multiple LLM endpoints, use the `ai.routes` field in the `policies` section of the {{< reuse "agw-docs/snippets/backend.md" >}} resource. This field maps the API paths to supported route types. The keys are URL suffix matches, like `/v1/models`. The values are the route types, like `Completions` or `Passthrough`.
 
-Alternatively, you can define the routes in a separate {{< reuse "agw-docs/snippets/policy.md" >}} resource attached to an {{< reuse "agw-docs/snippets/agentgateway.md" >}} {{< reuse "agw-docs/snippets/gateway-api.md" >}}. This approach decouples routing configuration from the backend definition, which can simplify management when you have multiple routes pointing to the same backend.
+Alternatively, you can define the routes in a separate {{< reuse "agw-docs/snippets/policy.md" >}} resource attached to an {{< reuse "agw-docs/snippets/agentgateway.md" >}} `HTTPRoute`. This approach decouples routing configuration from the backend definition, which can simplify management when you have multiple routes pointing to the same backend.
 
 - `Completions`: Parses the request, translates it to the LLM provider format, and fully processes it as an LLM request. This route type unlocks the full set of {{< reuse "agw-docs/snippets/agentgateway.md" >}} LLM features, such as tokenization and token-based rate limiting, prompt guards, prompt enrichment, model aliasing, transformations, cost tracking, and detailed observability.
 - `Detect`: Forwards the request as-is, but makes a best effort to extract the model and token counts so that a subset of policies still applies, specifically token-based rate limiting and telemetry. Guardrails and other request-shaping policies do not apply. Use this route type for endpoints with a format that cannot be automatically parsed by {{< reuse "agw-docs/snippets/agentgateway.md" >}}, but where you still want metrics and rate limiting.

assets/agw-docs/pages/integrations/vllm-semantic-router.md

@@ -0,0 +1,44 @@
+[vLLM Semantic Router (vSR)](https://vllm-sr.ai/) classifies OpenAI-compatible LLM requests and selects a model based on prompt content. With agentgateway, you can make this semantic decision before routing while continuing to apply gateway policies and record model, token, latency, and cost telemetry.
+
+This integration is distinct from using [vLLM as an inference provider]({{< link-hextra path="/llm/providers/vllm/" >}}). vSR provides the model-selection policy. Your configured provider, Kubernetes Service, or InferencePool serves the selected model.
+
+## How the integration works
+
+The following diagram shows the cost-based routing example. A coding agent requests the stable `auto` model, vSR selects a lower-cost or higher-capability model, and agentgateway forwards the request and records the result.
+
+{{< reuse-image-light src="img/integrations/vllm-semantic-router-cost-routing.svg" alt="A coding agent sends model auto to agentgateway. Agentgateway asks vLLM Semantic Router to select a model, routes the request to a lower-cost or higher-capability model, and records catalog-priced telemetry." >}}
+{{< reuse-image-dark srcDark="img/integrations/vllm-semantic-router-cost-routing.svg" alt="A coding agent sends model auto to agentgateway. Agentgateway asks vLLM Semantic Router to select a model, routes the request to a lower-cost or higher-capability model, and records catalog-priced telemetry." >}}
+
+The request follows these component boundaries:
+
+1. A client sends an OpenAI-compatible request to agentgateway.
+2. An AgentgatewayPolicy calls vSR as an external processor during the `PreRouting` phase.
+3. vSR evaluates its semantic, complexity, keyword, context, and structure signals. It returns the selected model in its processing response.
+4. Agentgateway applies the routing decision and forwards the request to the configured provider or inference workload.
+5. Agentgateway records the requested and selected models alongside usage, latency, and optional catalog-priced cost data.
+
+`PreRouting` is important when the vSR decision changes the model or adds a header that an HTTPRoute uses for matching. It makes the result available before agentgateway evaluates the route.
+
+## Choose an integration path
+
+The vSR and agentgateway projects provide complementary guides. Choose the one that matches the models and outcome that you want to evaluate.
+
+{{< cards >}}
+{{< card link="https://vllm-sr.ai/docs/installation/k8s/agentgateway/" title="Deploy vSR with agentgateway" icon="external-link" description="Follow the vSR project guide to deploy the components on Kubernetes and route to vLLM-compatible inference workloads.">}}
+{{< card link="https://github.com/agentgateway/agentgateway/tree/main/examples/llm-semantic-routing" title="Evaluate cost-based routing" icon="external-link" description="Use the agentgateway example to select between hosted model tiers and measure the result with a model cost catalog and OpenTelemetry.">}}
+{{< /cards >}}
+
+The vSR deployment guide owns the installation, Helm values, and semantic-router configuration. The agentgateway example owns the cost-routing policy and runnable gateway resources. Keeping those details with their projects avoids version drift in this integration overview.
+
+{{< callout type="info" >}}
+Current vSR examples require agentgateway 1.3.0 or later for the external-processing options that control request streaming and mode overrides.
+{{< /callout >}}
+
+## Integration considerations
+
+- **Client model selection:** The cost-based example uses `model: "auto"` to opt in to semantic selection. This value is an example policy convention, not a reserved agentgateway model. You can let clients request model tiers directly or [validate the request body]({{< link-hextra path="/traffic-management/transformations/validate/" >}}) to require the automatic path.
+- **Backend choice:** vSR can select models served by hosted providers or Kubernetes inference workloads. Configure the corresponding [LLM provider]({{< link-hextra path="/llm/providers/" >}}) or routing backend in agentgateway.
+- **Model names:** Keep the names returned by vSR aligned with the models in your agentgateway routes, provider configuration, and cost catalog. You can expose stable client-facing names with [model aliases]({{< link-hextra path="/llm/alias/" >}}).
+- **Cost and observability:** vSR makes the semantic decision. Agentgateway remains the source for completed-request telemetry and can calculate realized cost when you configure a [model cost catalog]({{< link-hextra path="/llm/cost-controls/costs/" >}}). Use [LLM metrics and logs]({{< link-hextra path="/llm/observability/" >}}) or the [OpenTelemetry stack]({{< link-hextra path="/observability/otel-stack/" >}}) to evaluate the result.
+
+Before a broad rollout, compare routed traffic with a fixed higher-capability-model baseline. Confirm that the policy uses both tiers, then evaluate task completion, user feedback, retries, and escalation rates alongside cost and latency.

content/docs/kubernetes/latest/integrations/vllm-semantic-router.md

@@ -0,0 +1,9 @@
+---
+title: vLLM Semantic Router
+weight: 10
+description: Route OpenAI-compatible requests by prompt semantics with vLLM Semantic Router and agentgateway.
+aliases:
+  - vllm
+---
+
+{{< reuse "agw-docs/pages/integrations/vllm-semantic-router.md" >}}

content/docs/kubernetes/main/integrations/vllm-semantic-router.md

@@ -0,0 +1,9 @@
+---
+title: vLLM Semantic Router
+weight: 10
+description: Route OpenAI-compatible requests by prompt semantics with vLLM Semantic Router and agentgateway.
+aliases:
+  - vllm
+---
+
+{{< reuse "agw-docs/pages/integrations/vllm-semantic-router.md" >}}