Waiting Line Analysis
A small bookstore is located next to a large college campus. The bookstore is open 24 hours a day and students arrive around the clock. The store manager believes that customers arrive on average at the rate of 18 per hour regardless of the time of day-morning or night. The bookstore has only one checkout line staffed by one worker at a time. The time required to checkout a customer is independent of the time of day and averages 2.5 minutes per customer.
a. Assume that every customer who enters the bookstore buys something (a newspaper, a book, a cup of coffee, etc.) and must go through the checkout. What is the probability that a customer must wait in line to checkout?
b. Assume that every customer who enters the bookstore buys something (a newspaper, a book, a cup of coffee, etc.) and must go through the checkout. What is the average time that a customer must wait in line before being checked out? Calculate the time spent in the checkout line only; do not include the service (processing) time. Please state your answer in minutes.
c. What is the average number of customers who are either waiting in line or being checked out at the counter? That is, the total number in the system?
d. Again, when answering this question assume that all customers who enter the bookstore buy something. As a special service to its customers the bookstore offers free snacks and treats to all customers waiting in the checkout line. (The customer at the checkout counter being served is too busy paying to enjoy the snacks). The store owner estimates that every minute spent by a customer waiting in line costs the bookstore $1.25 in consumed snacks. Calculate the hourly cost of providing the snacks for waiting customers.