A Local Hamburger Chain Is Considering Adding a Drive-Through Window

question 9

Essay

A local hamburger chain is considering adding a drive-through window. They estimate that during the dinner hour, customer arrival rate will average 18 per hour and follow a Poisson distribution. Service times during this same period are estimated to follow an exponential distribution with a mean of 24 customers per hour.
a. Determine the probability that the service facility (drive-through window) is idle.
b. Determine the probability of four vehicles in the system.
c. Determine the average number of vehicles waiting for service.
d. Determine the average number of vehicles in the system.
e. Determine the average time a vehicle spends waiting for service.
f. Determine the average time a vehicle spends in the system.
g. Determine the probability that an arriving vehicle has to wait for service.

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Definitions:

Architect

A professional who designs buildings and in many cases also supervises their construction.

Style

A distinctive artistic manner. Period style is the characteristic style of a specific time. Regional style is the style of a particular geographical area. Personal style is an individual artist’s unique manner.

Interior Support Frame

A structural element within objects or buildings that provides stability and support to the overall form.

Truthful

Corresponding to fact or reality; honest and accurate representation without deceit or falsification.