In our Call manager (version 7.1.3, we have configured several hunt group in broadcast mode and all DN members have busy trigger parameter setup to 1.
We have observed the next behavior: We made a first call to hunt pilot number, all members of this hunt group ring together, meanwhile we made a second call (firrst call is still ringing), it gives us a busy tone. Is there any way to queue that second call?
There are two types of "hunt" configurations supported in CUCM. One is Attendant Console and the other is standard Hunt Groups. Based on context clues I believe you are using the latter. Which means, you have a Hunt Pilot (the number you are calling/testing). The Hunt Pilot points to a Hunt Group (which contains 1 or more line groups). The Line Group contains your directory numbers/lines.
Now, the issue you describe is directly related the max busy trigger values you have assigned. If you are using the new 69xx series phones then you don't have the option to update the busy trigger. If you are restricting the busy trigger due to a business or technical requirement, then you are in the same boat.
To avoid the fast busy situation, you can increase the busy trigger on the line group members. You could also create an additional line group and configure the Hunt Group to "hunt" to this secondary line group. You would then need to create another line appearance on these phones that would ring out and be members of the secondary line group. If you need 3x calls, you need to repeat the process. Of course, this isn't a very logical approach if you have the ability to increase the max busy triggers on the line group members. Meaning, I would increase the max busy triggers on the lines if possible before I start eating up buttons on the phone.
If your phones are the 69xx series, you have no choice but to eat the buttons. If you have a policy/requirement to consider than you may want to create a special line on the phone that doesn't conform to the policy and is used for this particular hunt pilot application only.
You should also note that this is not a case where the weakest link breaks the chain. Meaning, if 4 out of 5 phones have a max busy trigger value of 1 but that fifth phone has a max busy trigger >1 your second call would ring on the fifth phone only. So, there may be a solution to your issue in that subtle fact.
In regards to your question about "queuing" the callers. This is not possible with standard hunt groups. The AC hunt groups can queue (see this link: http://www.netcraftsmen.net/resources/blogs/basic-queuing-in-cucm-callmanager-without-using-uccx.html) but I haven't tested this with 7.1.3. There is a broadcast hunt option in the AC hunt group solution. You will want to look at configuring the CUCM attendant services as well.
One last item. If I was wrong on the context clues and you are using AC Hunt Groups then go to the link I reference above to see how to "queue" callers.