Question

a grocery store estimates that customer arrive at the rate of 15 per hour. the cashier can servce customers at a rate of 20 per hour calculate the average number of customers in a line

Answer 1

2.25

Explanation:

let: Mean arrival rate
`\alpha=15` and mean service rate
`s=20`

#First we need to calculate the average number of customers in the system
`N` and average time a customer spends in the system,
`W` as:

`N=(\alpha)/(s-\alpha)=15/(20-15)=3\\\\\\W=(N)/(\alpha)=3/15=12\ mins`

The average time spend in the line is:

`N_l=\alpha W_l=\alpha^2/s(s-\alpha)\\=15^2/(20*5)\\\\=2.25`

Hence the average number of customers in a line is 2.25