# HW6: Queueing Theory

Hi all,

Hope you all have a great spring break so far! I am thinking that some of you may want to have a couple more exercise for the queueing stuff. So here is one.

Consider a store with only two cashiers, one of them is hardworking and is always serving customers. And another one is lazy and will only work when the number of people waiting in the queue of the first cashier is larger than 10 (exclude the customer currently served). Both cashiers are equally efficient and can handle on average 2 customers per minute. And the service time is exponentially distributed. Assume that the arrival statistics of customers that came in to buy something are Poisson distributed with an average 3 customers per minute.

1. Draw a state transition diagram to describe the problem.

2. What is the steady state probability of having 12 customers in the store?

3. On average how many customers are in the store?

4. What is the average time spent of a customer to checkout?

Cheers,

Sam

N.B. Please see here for solution.