I don't think so this is a good design consideration. Load balancing should be generally used when there are multiple backends.
However, in your case where we have only one backend (CDN endpoint), I do not think it would benefit us, rather add a extra latency.
As you said, "My website is hosted only in one region in Azure Static website, and I configure CDN to this website."
- CDN here, already provided your website a global presence via POP servers
- CDN has point-of-presence (POP) locations, that are distributed across the globe and the latency between CDN POPs and your storage account would be greatly optimized since they utilize Azure backbone.
I have not seen use cases where we place a CDN behind Azure Traffic Manager or any other load balancer for that matter.
Azure Load Balancer is a regional resource and CDN is a global resource.
- This means, keeping a CDN behid a regional resource would only lower the performance and increase the latency for other region users.
- And L4 Load balancer does not support adding a Public resource such as CDN as backend
CDN itself is perfectly capable of providing a low latency and a high-bandwidth service. Refer : What is a content delivery network on Azure?
If you have a different consideration that requires you to go with a load balancing solution, let us know please do elaborate why and I shall try my best to address it.
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