Depends on the queue... I've seen SQS queues holding millions of messages, and think I've heard of a billion plus somewhere - not sure other systems handle that kind of pressure.
In terms of monitoring, yeah, most systems will offer that... On AWS for example we setup cloudwatch alarms that post in our team chat / email when the number of messages waiting in certain queues reaches N, and we go see what's up. AWS also has autoscaling options with cloudwatch alarms, so some consumer services are configured to automatically add more capacity when there are more then N messages in the queue.
In terms of monitoring, yeah, most systems will offer that... On AWS for example we setup cloudwatch alarms that post in our team chat / email when the number of messages waiting in certain queues reaches N, and we go see what's up. AWS also has autoscaling options with cloudwatch alarms, so some consumer services are configured to automatically add more capacity when there are more then N messages in the queue.