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ie230_e2_sp2007_sol.pdf-IE 230 Seat # ________ Name

IE 581 — Introduction to Stochastic Simulation Name ___ < KEY > ___ One page of hand-written notes, front and back. Closed book. 50 minutes. Score ___________________________ Schmeiser Page 1 of 4 Test #2, Spring 2002 IE 581 — Introduction to Stochastic Simulation Name ___ < KEY > ___ 1. True or false. (3 points if correct, 2 points if left blank.) (If you wish, write an explanation of your thinking.) (a) T F ← The Box-Muller method of generating independent standard normal random variates is an example of composition. (b) T ← F When generating multivariate normal random vectors with covariance matrix Σ using the Cholesky decomposition matrix C , the computation of C needs to be done only once regardless of the number of vectors to be generated. (c) T ← F The acronym NORTA is another name for what the instructor called the "three-step" method of generating random vectors. (d) T F ← In next-event simulation, the meaning of "event" is the same as in probability, where we speak of the probability of an event. (e) T F ← Summing independent random variates is called composition. (g) T F ← Next-event simulation advances time in fixed increments ∆ ( t ). (h) T F ← For any random variables X and Y and for any real numbers x and y , the following holds: F X , Y ( x , y ) = F X ( x ) F Y | X = x ( y ), where F denotes a cdf. (i) T F ← An event graph shows the relationships between the probabilities of various events. (j) T F ← In next-event simulation, the "next event" is the event scheduled by the current event. (k) T ← F In next-event simulation, time is continuous and events occur at points in time. (l) T ← F In the three-step method, x i = F i - 1 ( u i ) in Step 3 yields a random variate x i that is from the distribution with cdf F i , regardless of whether the i th marginal distribution is discrete or continuous. 2. In dynamic systems, data collection can be observational (O) or time based (T). Circle the data collection method needed to compute each point estimator. (a) average number in list 1 T ← O (b) fraction of the time that the cleaner is idle T ← O (c) fraction of arriving customers who find the cleaner idle T O ← (d) average number in the system T ← O Schmeiser Page 1 of 4 Test #2, Spring 2002 IE 581 — Introduction to Stochastic Simulation Name ___ < KEY > ___ 3. In next-event simulation, an event does fundamental three things: (1) schedule future events, (2) update the system state, and (3) update statistical accumulators. In the cleaning-and-patching example, we studied the "end_patching" event, which was implemented with the following C function. void end_patching( void ) { /* The patched part leaves the system. */ _<2>_list_remove( FIRST, LIST_STATION_P ); _<3>_sampst(sim_time - transfer[2], SAMPST_DELAY_P); _<3>_sampst(sim_time - transfer[1], SAMPST_DELAY_SYSTEM); _<1>_if (list_size[LIST_STATION_P] > 0) { /*The patcher begins works on the next part.*/ event_schedule( sim_time + expon( mean_patching_time, STREAM_SERVICE_P ), EVENT_END_PATCHING ); } } In the four blank lines, enter "1", "2", or "3" to indicate the purpose of the associated line(s) of code. If a line is not related to any of the three purposes, enter "O" for "other". Schmeiser Page 2 of 4 Test #2, Spring 2002

IE | 581 | Simulation Design and Analysis | exam | IE 581 — Introduction to Stoch

IE 336 Seat # ___________ Name (one point) ___ < KEY > ___ 3. Consider the three-state rate matrix 3 2 1 0 1.0 − 0.5 0 − 3.0 0.1 0 2.0 0.4 . Assume that at time t = 6 the system is equally likely to be in any of the three states. (a) (eight points) From time t = 6, determine the expected time until the system is next in State 1. (If in State 1 at time t = 6, wait until the next visit.

IE | 336 | Operations Research stochastic Models | question bank | IE 336 Seat # __ Name

Rubric Later questions depend on responses to earlier questions. A. [10 points ] • Labels and objective values [5 points] – -1 (total) if wrote “ C ” and “ D ” instead of “says C ” and “says D ” – -0.5 for each missing/wrong label (events, alternatives, and probabilities) – -0.5 for each missing/wrong objective value • Form [5 points] – -4 if ﬁrst node not uncertain

IE | 546 | DECISION ANALYSIS | question bank | Rubric Later questions depend 

1 NAME_________________________________ EMAIL________________________ (Last Name First) IE 59000 – Test 1 Spring 2010  Closed book, closed notes  5 questions, 10 points each; maximum score is 50 points  50 minutes; approximately 10 minutes per question  Be brief; use illustrations  DO NOT WRITE on the back of the test sheets Q1. Consider the followi

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