If there are remote members, I usually respond to them on IM and try to ignore everyone else. This is to prevent colocated team members from having an advantage as I allow them to walk to my cube. I've toyed with having a requirement from them that if remote team members IM me, then they have to pick up a headset and talk live (similar to being interrupted in person). I haven't tried it yet.
Email in 36 hours is excessive for me - I think by the end of day is good for me.
Clearly different people have different preferences. My focus is to relieve the burden of always checking/being available. It prevents deep focus. I think this aligns with the author of the submission.
[1] Note that this is for IM in general. I've never used Slack - I've heard Slack is more than just IM so perhaps I would find a good use for it.
Alert system (pagerduty): 5 minutes (NOT normally used)
“Instant” message (slack): 2 hours
Email: 36 hours
Maybe that’s too much for you. But knowing I can get both get a response from anyone within 2 hours, but don’t have to respond in less than 2 hours would make me very happy.