A mom and pop car wash with 1 drive through lane gets an average of 4 cars per hour, with a Poisson distribution. The washing and drying process has a mean of 12 minutes, exponentially distributed, and a car cannot enter the lane until the car in front of it is finished drying (there can only be one car in the lane at one time). Due to the location, there is only space enough to hold 5 cars in line waiting to get washed. However, they rent space from the empty lot next door that is large enough to hold as many cars as needed. They decided to rent a section that will hold only 3 cars. a) If they decide to rent a section that will hold 3 cars, what will you solve for to determine the probability that they will still turn cars away? b) They promise each customer their money back ($10) if it takes longer than 30 minutes to get their car washed (from the time they enter). They are open 8 hours per day. How much money can they expect to give away per day?
A mom and pop car wash with 1 drive through lane gets an average of 4 cars per hour, with a Poisson distribution. The washing and drying process has a mean of 12 minutes, exponentially distributed, and a car cannot enter the lane until the car in front of it is finished drying (there can only be one car in the lane at one time). Due to the location, there is only space enough to hold 5 cars in line waiting to get washed. However, they rent space from the empty lot next door that is large enough to hold as many cars as needed. They decided to rent a section that will hold only 3 cars. a) If they decide to rent a section that will hold 3 cars, what will you solve for to determine the probability that they will still turn cars away? b) They promise each customer their money back ($10) if it takes longer than 30 minutes to get their car washed (from the time they enter). They are open 8 hours per day. How much money can they expect to give away per day?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 18P
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Transcribed Image Text:A mom and pop car wash with 1 drive through lane gets an average of 4 cars per hour,
with a Poisson distribution. The washing and drying process has a mean of 12 minutes, M=
exponentially distributed, and a car cannot enter the lane until the car in front of it is
finished drying (there can only be one car in the lane at one time). Due to the location,
there is only space enough to hold 5 cars in line waiting to get washed. However, they
rent space from the empty lot next door that is large enough to hold as many cars as
needed. They decided to rent a section that will hold only 3 cars.
a) If they decide to rent a section that will hold 3 cars, what will you solve for to
determine the probability that they will still turn cars away?
b) They promise each customer their money back ($10) if it takes longer than 30
minutes to get their car washed (from the time they enter). They are open 8
hours per day. How much money can they expect to give away per day?
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