Inputs & Outputs in a simple PDQ Example

M/M/1 Formula

It is more convenient to think in terms of inputs and outputs. In other words, which parameters do we need to provide to the formulae versus those values we will calculate as the result of applying the formulae? We list them here:

Inputs:

* The average Arrival Rate into the queue: λ.
* The average Service Time at the server: S.


With these input parameters we can calculate all other performance quantities (outputs) of interest.

Outputs:

* The average Residence Time a customer spends getting through the queueing system: R = S / (1 − λS).
* The Utilization of the server: U = λS.
* The average Queue Length of the system: Q = λR.
* The average Waiting Time a customer can expect to spend before getting service: W = R − U.

To apply these relationships, we need to choose some values for λ and S. We choose the following values so as to keep the arithmetic simple.

Reference