Add docs on serving with Llama Stack

[terrytangyuan]

See guide in https://github.com/meta-llama/llama-stack/blob/main/docs/source/getting_started/distributions/self_hosted_distro/remote_vllm.md

[github-actions]

👋 Hi! Thank you for contributing to the vLLM project.
Just a reminder: PRs would not trigger full CI run by default. Instead, it would only run fastcheck CI which starts running only a small and essential subset of CI tests to quickly catch errors. You can run other CI tests on top of those by going to your fastcheck build on Buildkite UI (linked in the PR checks section) and unblock them. If you do not have permission to unblock, ping simon-mo or khluu to add you in our Buildkite org.

Once the PR is approved and ready to go, your PR reviewer(s) can run CI to test the changes comprehensively before merging.

To run CI, PR reviewers can do one of these:

• Add ready label to the PR
• Enable auto-merge.

🚀

[russellb]

want to mention the inline integration, as well?

https://github.com/meta-llama/llama-stack/tree/main/llama_stack/providers/inline/inference/vllm

[terrytangyuan]

Definitely! I'll update this in a bit. Let me see if I can find the relevant guide. I wasn't sure if that's available yet.

[terrytangyuan]

@russellb I couldn't find a guide yet but I have added a reference to the inline implementation.

[russellb]

Suggested an addition of sample config

[terrytangyuan]

Thanks! Looking good.

[russellb]

Other than adding Signed-off-by to the commits so DCO will pass, this lgtm now. Thanks!

Feel free to add my Signed-off-by to the co-authored commit with my addition.

[russellb]

Actually, I think you need one more change. Right now you'll get an error that this page is not listed anywhere:

checking consistency... /Users/rbryant/src/vllm/docs/source/serving/serving_with_llamastack.rst: WARNING: document isn't included in any toctree

I would add this to docs/source/serving/integrations.rst

[terrytangyuan]

Should be fixed now!

[terrytangyuan]

Build failures seem unrelated.

[russellb]

thanks!

[youkaichao]

thanks for the integration!