I know I've seen the formulas that help you figure out how many registers a grocery store should have open, or how many analysts a call center should have, in order to service the number of requests you receive. I don't remember what they were called (Poisson?) or what they looked like.

We are trying to figure out the optimum number of threads our broker should have running to service the number of messages we get.

We get a request about every 2 seconds. Usually a request can be serviced in less than 4 seconds, leaving the thread ready to handle the next request. But on occasion (network latency, slow client processing) the response time may be 20 seconds.

Currently we have 5 threads, and know that is not enough. Just thinking in a linear fashion, we need 10 threads.

Anyone have any formulas, documents, or ideas than can help us fine tune that number?