Section 5 Problems

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

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

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?...
View Full Document

## 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).

Ask a homework question - tutors are online