[brudgers]

To me, the interesting part is the "why?" with an implied "do you think the system won't fall over?" In the real world, the system design should provide capacity based on a statistical analysis of the independent events.

Fortunately, it is unlikely that all users will have three consecutive five minute conversations each starting at the same time. However, it is equally unlikely that the conversations will be evenly distributed. It is unlikely but less so that over time the worst case will be close to equally distributed because text conversations often spike around external events...the interesting answers to the question describe engineering judgments.

From the perspective of taking the question seriously, it is worth pointing out that it is slightly underspecified. Are conversations only between two parties or is group text possible?

Anyway, to me the question is interesting as a scheduling problem. The way I would search for an answer is by modeling it rather than intuition because scheduling problems are in NP.

Good luck.