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Unformatted text preview: IEOR 4404 Solutions to the Practice Midterm Exam Simulation March 3, 2012 Prof. Mariana OlveraCravioto Page 1 of 11 Solutions to the Practice Midterm Exam Place all answers on the question sheet provided. The exam is open book/notes/handouts/homework. You are allowed to use a calculator, but not a computer. Write all answers clearly and in complete sentences. All answers should be supported by analysis or an argument. This exam has a total of 100 points. First Name: Last Name: 1(a) 1(b) 1(c) 1(d) 1(e) 1(f) 1(g) 1(h) 1(i)(i) 1(i)(ii) 2(a) 2(b) 3 Total Honor Code I resolve i ) not to give or receive aid during this examination, and ii ) to take an active part in seeing that other students uphold this Honor Code. Signature: 2 IEOR 4404, Solutions to the Practice Midterm Exam 1. We are interested in using simulation to study the performance of an internet server under different communication protocols. The server receives processing requests in the form of packets; a packet is a formatted unit of data. There are different ways in which one can model internet traffic, this question discusses what is known as an onoff sources model. An OnOff Sources Model: Traffic is assumed to come in from many independent sources, and each source can be either on or off. When a source is On, it sends packets to the server according to a Poisson process with rate . When it is Off it does not send any packets. There can be several sources on at the same time. On sessions arrive at exponential interarrival times with rate ; more specifically, if at time t a source just turned On, the next source will turn On at time t + X , where X is an Exponential( ) random variable, independent of everything else. The length of an On period is random and has a Pareto distribution with parameters ( , ), i.e., it has CDF F ( x ) = ( 1 ( x/ ) , x , , x < . (a) [6 pts] The table below contains the first 6 arrival times of On sources and their corresponding durations. Session 1 2 3 4 5 6 Start time 2 5 7 12 13 17 Duration 16 3 2 3 9 5 How many sources are On at time 19? Solution: We compute the time at which each On session ends to be: Session 1 2 3 4 5 6 End time 18 8 9 15 22 22 Therefore, at time 19 there are 2 sources on. IEOR 4404, Solutions to the Practice Midterm Exam 3 (b) [6 pts] Give an algorithm to generate random variates from distribution F ( x )....
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