Question

A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what proportion of the time is the server busy (utilized)?

a. 0.25b. 0.50c. 0.75d. 2.25e. 3.00

Answer 1

Option c is right

Explanation:

Given that a suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution.

service rate per customer =
`(15)/(2) =7.5`

Average number of arrivals per hour = 6

Service time for 6 customers =
`7.5*6=45` minutes

i.e. on an average per hour the server is buy in 45 minutes

Proportion =
`(45)/(60) =0.75`

Option c is right