316_F07_HW4_Sol - IOE 316 Fall 2007 – Homework 4...

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Unformatted text preview: IOE 316 Fall 2007 – Homework 4 Solutions Due November 20, 2007 1. (10 points) As you arrive to a single-server fast-food restaurant you notice that there are three customers waiting in line and one additional customer is currently being serviced. You join the end of the line. If the service times are all exponential with mean μ , what is the expected amount of time you will spend waiting to get your food? (We are not interested in the time it actually takes you to eat your burgers. SOLUTION: (10 points) Each of the three customers in line will spend an amount of time in service that is exponential with mean μ , as will you. As for the customer already being serviced, by the memoryless property of the exponential distribution, her remaining service time is also exponentially distributed with mean μ . Since the expected value of the sum of n random variables is equal to the sum of their expected values, the expected amount of time you spend waiting to get your food is 5 μ ....
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This homework help was uploaded on 04/02/2008 for the course IOE 316 taught by Professor Dolinskaya during the Spring '08 term at University of Michigan.

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316_F07_HW4_Sol - IOE 316 Fall 2007 – Homework 4...

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