I have a real-life situation that can be solved using Queueing Theory.
This should be easy for someone in the field. Any pointers would be appreciated.

There is a single Queue and N Servers.
When a server becomes free, the Task at the front of the queue gets serviced.
The mean service time is T seconds.
The mean inter-Task arrival time is K * T (where K > 1)
(assume Poisson or Gaussian distributions, whichever is easier to analyze.)

At steady state, what is the length of the queue? (in terms of N, K).

Related Question:
What is the expected delay for a Task to be completed?

Here is the real-life situation I am trying to model:
I have an Apache web server with 25 worker processes.
At steady-state there are 125 requests in the queue.
I want to have a theoretical basis to help me optimize resources and understand quantitatively how adding more worker processes affects the queue length and delay.

I know the single queue, single server, Poisson distribution is well analyzed.
I don't know the more general solution for N servers.

thanks in advance,
-- David Jones


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