It's a bit difficult to cover as it is highly dependent on the queue system you use.

You'd usually want your queue system to fail the enqueue if it is full, and you'd want monitoring to ensure the queue isn't growing at an unsustainable rate.

It also forces you to think a bit about your message payload (rich data or foreign keys the worker loads).

RabbitMQ, Redis-based queues (ex: ActiveJob or sidekiq), Gearman, and others will all offer different mechanisms to tackle full queues.