9/13/2017

Example 17.4.4 Discrete simulation of a queue

Customers arrive at a checkout to pay for their items
Poisson process is used to model the arrival of customers at the checkout. We assume that customers arrive randomly at a constant rate lamda.
We also assume that the time to serve a single customer has an exponential distribution with mean mu. (This is not a very realistic assumption, but it gives us a reasonable starting point for a simulation.)
With exponential service times, the times when people depart the queue is a Poisson process with mean mu.
What happens if mu < lamda? Open discrete_queue.r and try it out.

Recall that the sum of two independent normal random variables is normally distribution. This is a remarkable result that we can check with simulation.
Check out normalsums.r
Do you think this result holds for other distibributions? Use simulation to check it out.

Create an R notebook that applies each of the six probability distributions above to one pratical problem. Ideally, your solution will have a theoretical and a simulated solution.
17.16 (c), 17.17