# Queueing server with exponential+deterministic stages

1. Dec 20, 2012

Hi, does anyone know how to model probability density function, b(x), of a system that has two parallel servers:

-The first is selected by the customer with probability $p$, it has an exponential rate of $\mu$.
-The second server is selected by the customer with probability $1-p$, it has a deterministic rate of $k$.
-When a customer chooses a server, another servers waits until the customer being served leaves.

If the second server were an exponential rate server, it would simply be an M/Er=2/1 system but now I don't know how to model this. Can anyone help me, plz?

2. Dec 22, 2012

### chiro

Are you allowed to use Monte-Carlo simulation to simulate the process so that you get a PDF (by stipulating a large enough number of simulations)?

3. Dec 22, 2012

### chiro

Are you allowed to use Monte-Carlo simulation to simulate the process so that you get a PDF (by stipulating a large enough number of simulations)?

4. Dec 22, 2012