M/m/1 queuing theory Help with homework

[joscieja]

Homework Statement

Single employee. Customers arrive at a rate of 4 pr hr. Customers are served at an average rate of 5 per hour. Assume that arrival are random and independent and services times are exponentially distributed

What is the prob that exact 4 people arrive during a given one hour period
what is the average time per customer?
What is the prob that the cashier is idle?

Homework Equations

m/m/1

The Attempt at a Solution

po (4) 0 e-4 =e-4=0.183

 

[Mark44]

Homework Statement

Single employee. Customers arrive at a rate of 4 pr hr. Customers are served at an average rate of 5 per hour. Assume that arrival are random and independent and services times are exponentially distributed

What is the prob that exact 4 people arrive during a given one hour period
what is the average time per customer?
What is the prob that the cashier is idle?

Homework Equations

m/m/1

The Attempt at a Solution

po (4) 0 e-4 =e-4=0.183

I can't tell what this is supposed to mean. For this problem, I'm assuming you need to use Poisson distributions for the customer arrivals and serving times. Since four customers arrive per hour, then a customer arrives every 15 minutes. Since the system can serve 5 per hour, it takes 12 minutes, on average, to serve a customer.