Ours seemed very busy, but we also had access to an assistant, and I think it was the hotel director's adm. asst. or secretary. We often laeft messages that were always responded to promtly with a return call and/or action.
It was our 1st expereience with a concierge, and memory tells me a tip was not part of a general tip. However, it seems I was also told that such staff is compensated pretty well, and tipping was not necessary. That said, we appreciated her service very much, as it saved us much grief resolving the two problems we had, so we tipped her pretty well, by putting cash in an envelope, and delivering it to her office, which was just behind the main service desk. I think a tip could be directed to the concierge staff, but it would be subject to splitting. I also tried to sniff out what might be appropriate, but the staff could not and would not make any suggestions.