Documentation: Create Gateway API Inference Extension installation guide

[Xunzhuo]

Description

Create a new installation guide for deploying vLLM Semantic Router with Gateway API Inference Extension on Kubernetes.

Requirements

1. Create new documentation file:

   • Path: website/docs/installation/k8s/gateway-api-inference-extension.md
   • Follow the same structure and format as ai-gateway.md

2. Content Requirements:

   • Architecture overview section
   • Prerequisites (kind, kubectl, Helm)
   • Step-by-step installation using Helm
   • Use GHCR OCI registry for semantic router: oci://ghcr.io/vllm-project/charts/semantic-router
   • All resource paths must use remote GitHub URLs: https://raw.githubusercontent.com/vllm-project/semantic-router/refs/heads/main/...
   • Testing section with example curl commands
   • Troubleshooting section
   • Cleanup section using helm uninstall commands

3. Integration with Gateway API Inference Extension:

   • Document how to install Gateway API CRDs
   • Document how to install Inference Extension
   • Show how to configure semantic router to work with the extension
   • Include example Gateway API resources

Reference Documentation

• Follow the same structure as: website/docs/installation/k8s/ai-gateway.md
• Gateway API Inference Extension docs: https://gateway-api-inference-extension.sigs.k8s.io/guides/
• Existing Istio guide mentions the extension: website/docs/installation/k8s/istio.md (line 87)

Files to Create

• website/docs/installation/k8s/gateway-api-inference-extension.md

Acceptance Criteria

• New documentation file created with complete installation guide
• Uses Helm-based installation for semantic router
• All resource references use remote GitHub URLs
• Includes architecture overview and benefits
• Includes testing and troubleshooting sections
• Cleanup section uses helm uninstall commands
• Documentation follows the same pattern as ai-gateway.md
• All commands are tested and working

[samzong]

/assign @samzong