Pooling
Elasticsearch communication occurs over HTTP. Hackney is, for better or worse, the most supported HTTP client for Elixir right now. It comes with pooling built-in. By using a specific pool for your Elasticsearch HTTP requests, your connections will automatically be reused until they are closed.
Asynchronous Worker Queue
For an asynchronous worker queue, I would recommend using a library like Verk. Verk is based on Sidekiq and stores its queues in Redis. This makes it tolerant of restarts and failures in your own application.
