The managers of the Grand Hotel are evaluating the possibility of setting up a computer area where conference attendees can check their e-mail on computers provided by the conference organizers. There will be one common queue for all computers, and only one person uses a computer at a time. On average there are 12 attendee arrivals per hour, and the standard deviation of the time between arrivals is 2.5 minutes. The average time that a person spends on the computer is 20 minutes, with a standard deviation of 10 minutes.
Suppose the organizers decide to install 5 computers. GH1. What is the average utilization of the 5 computers?
GH2. What is the expected time (in minutes) that an attendee will have to wait for a computer to become available?
GH3. How long (in minutes) will the average computer be empty during an 8-hour day?
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GH4. What is going to be the average number of attendees in the computer area (either waiting for a computer or using a computer)? (Your answer does NOT have to be an integer.)
GH5. The firm does not want the average waiting time to be higher than 0.1 minute. What is the minimum total number of computers that the firm will have to install to meet this goal?
There are 5 coin-operated massage chairs at Philadelphia's 30th Street train station. The length of time that each customer spends in a massage chair averages 12 minutes and has a standard deviation of 5 minutes. Customers pay $0.50 per minute for the massage. On average, every hour there are 15 potential customers interested in receiving a massage at one of these chairs. The inter-arrival times are assumed to be exponentially distributed. If no spot is available when the customer arrives, then the customer goes away.
TM1. What is the probability that an arriving customer will find all massage chairs occupied? TM2. On average, how much revenue does Train Massage collect over the course of one hour?
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TM3. How would that number change if the coefficient of variation of the massage time were reduced to zero?