08 May WHAT IS THE AVERAGE WAIT TIME IN LINE WAITING FOR SERVICE?
You go to the library to study for the OM exam. You will do as many problems as you can in 3 hours of studying, taking no breaks and having no interruptions. You timed the first problem you did and found it took 14 minutes. You decide that there is a 90% learning rate here that will continue with the remaining problems. Assume that if there were no learning effect, each problem would take the same amount of time.
a. (10 points) How much time will it take to do the third problem?
b. (10 points) Approximately how many problems will you be able to complete in the 3 hours? Assume the learning effect will continue, and you take no breaks. You must show your work for full credit.
c. (10 points) At the conclusion of the 3 hour study session, you see a friend that has also been studying for the exam. Your friend has completed 25 problems in the same 3 hours, with the first problem taking 14 minutes. What was your friend’s approximate learning percentage? You must show your work for full credit.
d. (20 points) Give an example from our own life that illustrates the concept of the learning curve. Please do not use the example of studying for or taking this or any other education course. Present the situation, discuss why you believe it illustrates a learning effect, and discuss how this illustrates the key concepts of learning curves.
2)
a) (10 points) Rush Franken receives about 60,000 calls in a 3 hour period into his phone lines for his radio show, but he is only able to accept 15 per hour to go on the air. Discuss whether this would or would not fit into one of the 3 waiting line models discussed in the text. Why or why not?
3) A local radio call-in show has about 25 calls arrive each hour, and the radio host spends about 1.1 minutes per caller, exponentially distributed. Assume no commercials and callers are immediately taken on the air if there is one waiting; all other appropriate assumptions also hold. Also assume that there is an infinite line possible, that is, callers will not get a busy signal but will always be put into a line to go on the air.
a. (5 points) What is the average number of callers waiting to go on the air?
b. (5 points) What is the average time to wait before going on the air?
c. (5 points) What is the utilization?
4) An airline ticket counter has one line feeding into 2 ticket agents. The airline is considering adding a third agent. Arrivals are spaced at an average of 3.333 minutes, Poisson distribution. An agent spends about 6 minutes per customer, exponentially distributed. All other appropriate assumptions hold.
a. (10 points) What is the average number in line waiting for service?
b. (5 points) What is the average wait time in line waiting for service?
c. (10 points) If a third agent is added, what is the average number in line waiting for service?
d. (5 points) If a third agent is added, what is the average wait time in line waiting for service?
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