Question

Imagine a simple process in which 5 ticket booths are selling tickets for an opera. If customers are coming at a rate of 15 / hour, and the utilization of the 5 booths is 50%, then how long does a customer spend at a booth (each customer goes to only one booth)?

Answer 1

Answer: The customer spends 10 minutes at a booth.

Explanation:

Let n= number of booths,
`\rho` = utilization,
`\lambda` = arrival rate,
`\mu=`Service rate

We know that

`\rho=(\lambda)/(\mu* n)`

As per given,

`0.5=(15)/(\mu*5)\\\\\Rightarrow\ \mu=(15)/(5*0.5)\\\\\Rightarrow\ \mu=6`

Service rate = 6 customers per hour.

Time taken by each customer =
`(1)/(\mu)`

`=(1)/(6) \ hours \ or\ (60)/(6)\ minutes\\\\=10 \ minutes`

Hence, the customer spends 10 minutes at a booth.