It's actually a somewhat difficult thing to predict spikes. Say you have n clients, d timeslices. When does the probability exceed 0.5 that you get more than k

It's actually a somewhat difficult thing to predict spikes. Say you have n clients, d timeslices. When does the probability exceed 0.5 that you get more than k requests concurrently? Unfortunately the solution is exponential in k. People might recognise the birthday problem here; for d=365, k=2 (days a year, single share) the well known answer is 23. Wikipedia gives a formula for a rough approximation for n for p=0.5 and k < 20.