Section 5 Problems - . It has been decided that A gets the...

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ORIE3510 Introduction to Engineering Stochastic Processes Spring 2010 Section 5 problems 5.20 Consider a two-server system in which a customer is served first by server 1, then by server 2, then departs. The service times at server i are exponential random variables with μ i ,i = 1 , 2. When you arrive, you find server 1 free and two customers at server 2 - customer A in service and customer B in line. (a) Find P A , the probability that customer A is still in service when you move over to server 2. (b) Find P B , the probability that B is still in the system when you move over. (c) Find E ( T ), where T is the time you spend in the system. 5.34 Two individuals, A and B , both require kidney transplants. If A does not receive a new kidney, she will die after an exponential time with rate μ A , and B after an exponential time with rate μ B . New kidneys arrive in accordance with a Poisson process with rate
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Unformatted text preview: . It has been decided that A gets the rst kidney (or B if A is already dead) and the next one to B (if still living). (a) What is the probability that A obtains a new kidney? (b) What is the probability that B obtains a new kidney? 5.35 Show that denition 5.1 of a Poisson process implies denition 5.3. 5.42 Let { N ( T ) ,t } be a Poisson process with rate . Let S n denote the time of the n th event. Find (a) E ( S 4 ) (b) E ( S 4 | N (1) = 2) (c) E ( N (4)-N (2) | N (1) = 3] 5.60 Customers arrive at a bank at a Poisson rate . Suppose two customers arrived during the rst hour. What is the probability that (a) both arrived during the rst 20 minutes? (b) at least one arrived during the rst 20 minutes?...
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This note was uploaded on 10/29/2011 for the course ORIE 3510 taught by Professor Resnik during the Spring '09 term at Cornell University (Engineering School).

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