You don’t want to overburden the system by checking this every couple of seconds. Honestly, the difference between 5 and 15 is huge from the customer’s perspective, but remember that, at 15, the average wait time is going to be about 8 seconds. Anything less than 5 is probably too much.
One more thing - while the phone is ringing, it isn’t in the queue any more. It’s been allocated to a phone. The “joining” of the call to the phones happens once at the beginning. I think there’s a setting for the ringing to expire and drop back into the queue (to allow the phones to be checked for busy), but that gives the customer the experience of “ringing, wait in queue, ringing, back to queue, ringing, back to queue”. I don’t think there’s a perfect solution using either a queue or a ring group.
Perhaps it’s time to explore a different model.
Set up all three phones in a call pickup group and put them into a ring-group. When the phones start to ring, the one person that’s actually doing their job can get off the phone and press “call pickup” and answer the ringing phone.
This solution is just as bad as the other, but easier for you to implement.
From a customer satisfaction perspective, the best solution is to implement the method you are using right now, but add a button the phone to log them into and out of the queue. This way, you allow the customer to do things like divert themselves to voicemail, or press a “special code” that drops them onto a high priority queue. The problem, though, seems to be that your customer wants their key-system back. There are some things that Asterisk can’t do, but there are lots of things it can do that your customer hasn’t explored.
Another approach is to not have them sign in and out, but use time-conditions instead. At 09:00 (or when the second one arrives) you can press “Day Mode” and the phones just ring. If all the phones are in the same pickup group, a simple star-code (programmed into the buttons on the phone) can be used to pick up whatever phone is ringing anywhere in the network.
Most of the places that I’ve set up phones for that weren’t call centers use this model. The only thing that’s the least bit tricky is the call pickup code, and that can be easily handled either through a configuration in EPM or by you managing the phone configs by hand (for less than 5 phones, by hand should work