# Determining bandwidth exhaustion based on probability of events

During a normal 8 hour business day, each user has a 50/50 probability of uploading a single 20MB file to our servers. We have a 1 gigabit/second connection. Each user averages 2 megabit/second which means on average, it will take 90 seconds to upload the file to our servers. What is the max number of users we can have before expecting our 1gigabit/second connection to be completely saturated?

As far as figuring this out, I know that our max is 500 concurrent users uploading a file at the same time, but I'm not quite sure how to figure out the probability of X number of users resulting in 500 users uploading during the same 90 second window, which would max out our connection

• I guess you're supposed to assume that a customer is equally likely to do his upload at any time in the day, so the probability that he chooses a particular $90$-second window is ${3/2\over 480}={1\over320}$ and the probability that he uploads in a particular window is ${1\over640}$ – saulspatz Mar 29 at 13:47