Hw6_ORIE3510_S10 - ORIE3510 Introduction to Engineering...

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Unformatted text preview: ORIE3510 Introduction to Engineering Stochastic Processes Spring 2010 Homework 6: Poisson Processes Due 2:30pm, March 10, 2010 (drop box) Be sure to write your name and section number or day&time on your homework. In all questions, be sure to give the justification for your answers. There are 5 equally weighted problems for 100 total points. Problem 1 Customers can be served by any of three servers, where the service times of server i are exponentially distributed with rate i ,i = 1 , 2 , 3. Whenever a server becomes free, the customer who has been waiting the longest begins service with that server. (a) If you arrive to find all three servers busy and no one waiting, find the expected time until you depart the system. (b) If you arrive to find all three servers busy and one person waiting, find the expected time until you depart the system. Problem 2 Customers arrive at a two-server service station according to a Poisson process with rate . Whenever a new customer arrives, any customer that is in the system immediately departs. A new arrival enters service firstcustomer arrives, any customer that is in the system immediately departs....
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