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ISYE6644 (Simulation) Midterm 1.
What are some characteristics of simulation models? - ANSWER1. Discrete (vs. continuous)
- Stochastic (vs. deterministic)
- Dynamic (vs. static) What is simulation? - ANSWERSimulation is the imitation of a real-world process of system over time. Simulation involves the generation of an artificial history to draw inferences concerning the operating characteristics of the real system that is represented. What is simulation good for? - ANSWER1. Describe / analyze real or conceptual system behavior.
- Ask "what if" questions.
- Aid in system design and optimization
- Can simulate almost anything What are the reasons to simulate? - ANSWER1. Will the system accomplish its goals?
- Current system won't accomplish its goals, now what?
- Need incremental improvement.
- Create a specification or action plan
- Solve a problem, like a bottleneck.
- Resolve disputes
- Sell an idea What are the advantages of simulation? - ANSWER1. Can study models too complicated for analytical / numerical treatment
- Study detailed relations that might be lost in the analytical or numerical treatment
- Use as a basis for experimental studies of systems
- Use to check results and give credibility to conclusions obtained by other methods.
- Reduce design blunders
- Really nice demo method
- (sometimes) very easy What are the disadvantages of simulation? - ANSWER1. Sometimes not so easy
- Sometimes very time consuming / costly
- Simulations give "random" output (and lots of misinterpretation of results is possible)
- To do a certain problem, better methods than simulation may exist We are interested in modeling the arrival and service process at the local McBurger Queen burger joint. Customers come in every once in a while, stand in line, eventually get served, and off they go. Generally speaking, what kind of model are we talking about here? (More than one ANSWER below may be right.)
A) He invented the t distribution that is used ubiquitously in statistics. B) He invented the s distribution that is used ubiquitously in statistics. C) He invented tea. D) He invented the word "ubiquitous". E) He is the brother of Louis Gossett Jr., best known for his fine acting in many films, including An Officer and a Gentleman. - ANSWERA) He invented the t distribution that is used ubiquitously in statistics. What was the first use of a computer simulation? - ANSWERStan Ulam and Johnny von Neumann in 1946 after world war 2. They used simulation in the context of the development of the H bomb. The simulated thermonuclear reactions actually, chain reactions. What was the main development in the simulation field in the 1960s? - ANSWERIndustrial applications
- manufacturing
- queueing models Who was Harry Markowitz? - ANSWERHe was one of the first guys to develop a language called SIMSCRIPT. He also won a nobel prize for some of the work he did in optimizing financial portfolios (portfolio theory). In terms of simulations origins in manufacturing, what are some of the ways that simulation was/is used? - ANSWER1. Calculated the movement of parts and interaction of system components.
- Evaluates part flow thru the system
- Examines conflicting demand for resources
- Studies contemplated changes before their introduction
- Prevent design blunders YES or NO? Has anyone closely related to the field of computer simulation ever won a Nobel Prize? - ANSWERYes - Harry Markowitz won the 1990 Nobel Prize in Economics for his work in the field of portfolio optimization. He is highly regarded in the simulation community for his conception and development of the general-purpose simulation language SIMSCRIPT. Who is Dr. Harold Shipman? - ANSWERHe killed his patients using heroin overdoses Caught after carelessly revising a patient's will, leaving all her assets to himself Doctored his records to show his patients had needed morphine but the software recorded the dates of these modifications hung himself in prison Which of the following are areas where simulation has found substantial applica- tion? (More than one ANSWER below may be correct.) A) Inventory and Supply Chain Analysis B) Financial Analysis C) Manufacturing
Inscribe a circle in a unit square and toss 1000 random darts at the square. Suppose that 800 of those darts land in the circle. Using the technology developed in this lesson, what is the resulting estimate for ๐ A) - 3. B) 2. C) 3. D) 3. E) 4.0 - ANSWERD) 3. Since the estimate ๐ฬ = 4 x (proportion in circle). Note that (a) is the University of Georgia ANSWER, and is completely incorrect. What is a characteristic of a bad random number generator? - ANSWERIt must generate a random number distribution for every seed imaginable. What is a random walk simulation? - ANSWERTake a normal step up or down every time unit and plot where you are as time progresses. This "random walk" converges to Brownian motion Einstein and Black+Scholes won nobel Prizes for this research. TRUE or FALSE? All random number generators perform pretty much the same. - ANSWERFalse
Suppose customers to a barber shop show up at times 4 and 11. Moreover, suppose that it takes the barber 12 minutes to serve customer 1 and then 14 minutes to serve customer 2. When does customer 2 leave the barber? A) 18 B) 25 C) 30 D) 40 - ANSWERC) 30 - Since customer 2's service starts only when customer 1 leaves, which happens at time 4 + 12 = 16. At a high level, how are random numbers generated in a computer? - ANSWER1. Generate pseudo-random numbers (PRNs) using a deterministic algorithim (not really random but appears to be)
- Generate other random variables by starting with the PRN and applying transformations to get any other type of random variable. Suppose we are using the (terrible) pseudo-random number generator ๐๐=(5๐๐โ1+3)mod(8), with starting value ("seed") ๐0=1. Find the second PRN, ๐2=๐2/๐=๐2/8. A) 0 B) 1/ C) 3/ D) 3 - ANSWERC) 3/ ๐1=(5๐0+3) mod(8) = 8 mod(8) = 0, and then ๐2=(5๐1+3) mod(8) = 3 mod(8) = 3. So ๐2=๐2/8=3/
- Make independent runs (replications) of the simulation, each under identical conditions
- Sample means from each replication are assumed to be approximately i.i.d. normal
- Use classical statistics techniques on the i.i.d. sample means (not on the original observations) How are steady-state simulations analyzed? - ANSWERFirst deal with initialization (start-up) bias
- usually "warm up" simulation before collecting data
- failure to do so can ruin statistical analysis Many methods for dealing with steady-state
- ex: batch means What is the method of batch means in analyzing steady-state simulations? - ANSWER-Make one long run (vs. many shorter reps)
- warm up simulation before collecting data
- chop remaining observations into contiguous batches
- sample means from each batch are approximately i.i.d. normal
- use classical statistics on the i.i.d. batch means TRUE or FALSE? Simulation outputs such as consecutive customer waiting times are almost always independent and identically distributed normal random variables. - ANSWERFalse - Output is pretty much never i.i.d. normal
Let's simulate a bank that closes at 4:30 p.m. What kind of simulation approach would you take? A) Steady-state simulation B) Terminating simulation C) Arnold SChwarzenegger simulation D) I'm from the university of georgia. What is simulation? and what is a bank?
- ANSWERB) Terminating Simulation What is the derivative of X^k - ANSWERkx^k- 1 What is the derivative of e^x - ANSWERe^x What is the derivative of sin(x) - ANSWERcos(x) What is the derivative of cos(x) - ANSWER-sin(x) What is the derivative of ln(x) - ANSWER1 / x If the f(x) is position, the first derivative is the velocity, what is the second derivative? - ANSWERacceleration Which of the following methods cannot be used to find the zeroes of a complicated function? A) trial-and-error
B) 1/
C) 13/
D) 1/8 - ANSWERD) 1/
P(sum=3)=P((1,2)or(2,1))=P(1,2)+P(2,1)=2(1/16)=1/8. TRUE or FALSE? f(x)=3eโxforx>0 is a legitimate probability density function. - ANSWERFALSE Correct: In order to be a legit p.d.f., f(x) must integrate to 1; but lo and behold.. .โซRf(x)dx=โซโ03eโxdx=3.โน Suppose X is a continuous random variable with cumulative distribution function F(x). What is the distribution of the nasty random variable F(X)? A) Normal B) Unif (0,1) C) Exponential D) Weibull - ANSWERUnif (0, 1) - this is the Inverse Transform Theorem Suppose U is a Unif (0,1) random variable. Name the distribution of X=โโn(1โU). A) Normal B) Unif (0, 1) C) Exponential
D) Weibull - ANSWERC) Exponential The abbreviation "m.g.f." stands for... - ANSWERMoment Generating Function What is the concept of double expectation? - ANSWERIdea: the average expected value of all of the conditional expected values is the overall population average. TRUE or FALSE? If ๐ and ๐ are uncorrelated, then they're independent. - ANSWERFalse What is the most-important theorem in the universe? - ANSWERCentral limit theorem What is the central limits theorem? - ANSWERIn probability theory, the central limit theorem establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. Let's take a bunch of independent observations from a "well-behaved" distribution. The Central Limit Theorem says that the standardized sample mean of those observations converges to what distribution? - ANSWERNormal What are three things that help define what a statistic is? - ANSWER1) a statistic is a function of the observations X1 through Xn and not dependent on any unknowns. So basically something like the mean, cause you know all the parameters
B). Model validation C) experimental design D) output analysis E) attendance at the university of georgia - ANSWERE) attendance at the university of georgia What is an entity in a simulation? - ANSWEREntities can be permanent (like a machine), or temporary like customers, and can have various properties or attributes (priority of a customer or averaged speed of a server). What is a system? - ANSWERA system is a collection of entities that interact together to accomplish a goal. What is a model? - ANSWERA model is an abstract representation of a system. What is the system state? - ANSWERA set of variables that contains enough information to describe the system. Think of the state as a snapshot of the system? ex knowing how many people are in the queue and if the server is busy for a single server queue model What is a list (or queue)? - ANSWERan ordered list of associated entities (for instance, a linked list, or a line of people). What is an event? - ANSWERAn event is a point in time at which the system state changes (and which can't be predicted with certainty beforehand).
Ex: an arrival event, a departure event, a machine breakdown event. What is an activity? - ANSWERAn activity is a duration of time of specified length (aka an unconditional wait) ex: constant service times, customer interarrival times. What is a conditional wait? - ANSWERA conditional wait is a duration of time of unspecified length. ex: customer waiting time. TRUE or FALSE? The ๐ ๐ฆ๐ ๐ก๐๐๐ ๐ก๐๐ก๐ is a set of variables that contains enough information to describe the system. - ANSWERTrue Characteristics such as the priority or speed of a customer are known as ...? A) variables B) function values C) entities D) attributes E) Activities - ANSWERD) attributes What is the simulation clock? - ANSWERThe simulation clock is a variable whose value represents simulated time (which doesn't equal real time).
What are we allowed to do on the future event list? A) Insert new events B) delete events C) move events around D) all of the above - ANSWERD) all of the above What is a linked list? - ANSWERSingly and doubly linked lists intelligently store the events in an array that allows the chronological order of the events to be accessed. Such lists easily accommodate insertion, deletion, switching of events, etc. What is the event-scheduling approach? - ANSWERConcentrate on the events and how they affect the system state. Help the simulation evolve over time by keeping track of every freaking event in increasing order of time of occurrence. This is a book keeping hassle. What is the process-interaction approach? - ANSWER1. Create customers every once in a while.
- Process (serve) them, maybe after waiting in line.
- Dispose of the customers after they're done being processed.
What is the name of the primary modeling approach that we will be using in this class, especially when we do Arena? Event-scheduling Process-interaction continuous modeling mixed modeling event-interaction - ANSWERprocess-interaction How many simulation languages are there? - ANSWERMore than 100 commercial languages in the ether. When selecting a simulation language, what characteristics do you have to take into consideration? Cost Ease of use Modeling "world view" (e.g., event-scheduling or process-interaction) Random variate generation capabilities output analysis capabilities all of the above - ANSWERall of the above
