问题
Suppose I have N M/M/1 queues in parallel where an arriving job is equally likely to join one of the N queues. We want to keep the probability for a job to wait less than 0.2. Given that we have an arrival rate of 400 jobs/second, and a processing times are exponentially distributed with mean 1 second, how many servers would be required?
So my take on the question so far is:
\lambda = 400 jobs/second
\mu = 1 second
\rho = (\lambda)/(k\mu)
since we want to keep the probability of waiting less than 0.2, we would need the utilization of the server to be 80% or 0.8.
0.8 = (400)/(k*1) -> k = 500 servers.
来源：https://stackoverflow.com/questions/58808038/capacity-provisioning-for-server-farms