[ECS] ALB slow start on ECS deployments

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**Tell us about your request**
In 2018, AWS [announced](https://aws.amazon.com/about-aws/whats-new/2018/05/application-load-balancer-announces-slow-start-support/) slow start load balancing algorithm for ALB. Unfortunately, this feature is ignored by ECS.

The problem is that on a new deployment, when the new (and cold) tasks enter the "healthy" state on the target group, the old ones are shut down automatically, forcing the new tasks to exit "slow start" mode and receive 100% of requests all of sudden, leading to undesirable latency spikes.

ECS needs to shut down older tasks only after the slow start period.

**Which service(s) is this request for?**
ECS.

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
I have low latency requirements, and my application takes about ten requests to warm up and respond with full performance. ALB's slow start feature would fit like a glove, but it's incompatible with ECS.

**Are you currently working around this issue?**
No, but I'm open to suggestions.

**Attachments**
- [Related Stack Overflow question](https://stackoverflow.com/questions/75207918/how-to-make-alb-slow-start-work-during-ecs-update-service)

Start with the AWS ALB slow-start announcement and the linked Stack Overflow question, then examine how ECS deployments replace healthy tasks. Done means ECS keeps older tasks serving until the ALB slow-start period has elapsed, avoiding an immediate shift of all requests to cold tasks.

Written by the indexing model from the issue text.