You could literally just store a .CSV file in S3 with a table that has the on-call schedule in it and run SQL queries against Athena that would be cheap... you'd be querying a few KB, but DynamoDB is probably better for this use case, honestly. Athena is great for scanning huge datasets very quickly.
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Note: instead of dynamodb for the lookup mentioned at the bottom, maybe consider https://aws.amazon.com/athena/ for an s3 query
You could literally just store a .CSV file in S3 with a table that has the on-call schedule in it and run SQL queries against Athena that would be cheap... you'd be querying a few KB, but DynamoDB is probably better for this use case, honestly. Athena is great for scanning huge datasets very quickly.