Clarifications on AWS Batch Queue Operation and Lifecycle for Workflow Integration

I currently have no experience working with the service, but I am in the process of designing a workflow. The goal is to monitor updates in a database and, upon detecting changes in specific tables, trigger our applications to send a message to the AWS Batch queue. I have some questions about the AWS Batch queue functionality. Firstly, is the AWS Batch queue always operational? If it receives a message, does it automatically initiate the compute environment? Additionally, once a job is completed, does the infrastructure shut down based on a predetermined time or is it dependent on the queue messages?