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Unformatted text preview: ISyE 3044: Simulation Analysis and Design
Practice Midterm 2 Practice Midterm 2 Subjects Covered in Midterm 2:
1. Input Analysis  MLEs, Chisquare tests, qq plots, and modeling based on limited data
2. Arena Basics — module names and pictures, constructing ﬂowcharts, details of Basic Process
modules, schedules, attributes, results, length of runs, modeling of basic manufacturing
systems.
3. Rough Cut analysis — Poisson Processes, calculation of arrivalx’serviee rates, M/M/l and WWC
queues, networks of queues. Input Analysis
Chisquare test: You are given a set of data with a sample mean of 1.33. Through careful inspection of the system, you decide to use an Exponential distribution with rate 3/4 (l/(sample mean))as a ﬁtted
distribution. (:1) Construct 4 equally probable sub intervals of the range of the Expo(3;’4) by determining the
boundaries. You may leave your answer as a formula. ﬂ) 1 11+ ISyE 3044: Simulation Analysis and Design
Practice Midterm 2 (b) After constructing the equally intervals, we observed that out of 100 samples (01 — E3 )1
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Interval 4 I 20 Z S l __ Bug} Perform a 1 alpha = 95% Chisquare test with the observed data. (Use the Chisquare l . book to determine quantiles. For the test, I will provide you with possible quantiles.) Is the data a
good ﬁt? 1 _, 5.05%
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TRUE ORFALSE Poisson models the number of trials required to achieve k successes. I: P‘l’ S E Binomial models the time between independent events like arrivals F R L S E Normal accurately models the combined time of a sum of a nu ber of component process. TKU E
A bounded distribution could be modeled by a Beta. TKO £1 _
An unbounded (positive and negative) process could be modeled by a singleﬂlﬁxponential. F imag I:
A pvalue of < 0.01 for the Chisquare test signiﬁes a good ﬁt. F All 3 t: sesam— SHORT ANSWER
1. A Chisquare tests the ﬁt of a distribution with one estimated parameter and involves 10 sub
intervals with a signiﬁcance l]evel of 0.05. What is the Chi—square quantile for the test? am new”  a a .. 1 IS“ 3
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2. What does the signiﬁcance level of a test stand for (definitiori of TypeI error)? The Prabobxlv‘rj oi a 4035*: resetlion at in. Auuwluilﬁﬁﬁ 3. The distribution of a service time has a minimum of 3, maximum of 6, and most likely value of
5. What distribution and parameters can model this service time? Tsxswguwtlsﬁ, 65
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4. What is the difficulty with using the normal distribution for service times? fL
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Practice Midterm 2 Arena Questions 7% “a
There are eight workers at a car handwash center that opens at 103m and closes at 6pm£lwé ;;;ke;t )
W. The number of car arrivals follows a Poisson process with rate 6fhou . Theﬁm to clean a car follows a normal distribution with mean 15 minutes and variance 9 minutes. 1. Draw the Arena ﬂowchart of the system. If you do not remember the names of the modules,
please provide details about what the module is capable of doing. Creche PFOCQSE’ 2. Fill in the 3 blanks to appropriately model the Process module ISyE 3044: Simulation Analysis and Design
Practice Midterm 2 Process Name: Car Wash Resources baa“ Logic Type: F I
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Adm Resource v m Cl sake Daley H : Resource Name: Resources; 2°10 m (ijchS lo be [0(3L£33€d ’ Resource, Flea.
(End of list) —.__ Dela}.I Type; Llnlls: Allocation: T [A S T S iExpression *1 I N \QUA e g v] Value Added v Expression Norma“ l5: 3 F7 Report Statistics fesodrcﬁ SP(QO‘J\§ gellx JV.) iota ?. SHORT ANS WER I. Name the following modules [33/13 3044: Simulation Analysis and Design
Practice Midterm 2 A.Cﬂkﬁ€ B.DQQA€ Q PRXﬁSS 2. Finish the phrase: SeizeDelay @936 {A 5 e 3. A coworker creates model of the same system and runs it for 10 simulated hours (as do you),
but ﬁnds the Arena gives her different results. What can you do to be sure that two models are different? "! ' J RU“ \Onﬁﬁf 'S‘FNLU\.U\\\3AS 0“»; infii SlﬁS‘l‘W5/ r:
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venues. OP/ FUF MOf€ .f'lL?i{7lico..‘i'r2r\_g TRUE or FALSE r
a. Arena attributes are details maintained for every single entity. T K U E b. Arena variables are details maintained for every single entity. S E
6. Travel between modules joined by a connector occurs instantaneously. T R U E: d. Arena does not record average time in system automatically. F R L S E ISyE 3044: Simulation Analysis and Design
Practice Midterm 2 4. There is a parking deck for a small shopping mall. People park their cars at the parking deck and go shopping. When they are done with shopping, they comebaek all out their cars, a
parking fees at cashiers, and leave. The parking deck has @5233 up to 50 carslandihrflpgab
booths are available. The following is the Arena model fort e parking deck. Fill out t e table on the answer sheet. If you choose Delay as Action, then you do not need to provide Resource
Name, Quantity, and Capacity. S“ Scene. Pei)? a 5 a
D '. DQ\O&:’> \ u Rough Cut Analysis MySoﬁ develops software products in two basic areas: ﬁnancial and emailers. They currently have a
customer support call center that handles technical questions for owners of their software from the
hours of 8AM to 4 PM Eastern Time. Each product line has its own operators. Most questions are
answered completely by the operators, but a few (4%) also have to be referred to another technical
group that prepares a response (two employees who can each work on one problem, ﬁrstcomeﬁrst
served). The customer does not stay on the line while this group works, but rather receives a return
phone call whenthe problem is solved. The return call is from someone in the same productoperator
group (but not necessarily the same operator) As the busiest time in a day is from 10 AM to 3PM, the
run length is set to 5 hours. ISyE 3044: Simulation Analysis and Design
Practice Midterm 2 Arrival every
ExpoILS) minutes
Type = Finano'al Call Two Finandal Operators
DelayT'rme Tr‘ra(2, 4t 9} minutes Type == Financial Call Two Tech Support Operators
Delayr Time Expo(3l]) minutes Type == Email Call Emotlﬁm minutes Three Emailer Operators
Type = Ernaler Call Delay Time Tria{2,4,9) minutes Arrival every l :5 (a) Approximate the longrun utilization of Financial Operator, Emailer Operator and Tech Support
Operator. (Hint: the probability of ﬁnancial return calls from “Tech Support” to “Financial” is
40% because 40% of calls in Tech Support are ﬁnancial calls.) ISyE 3044: Simulation Analysis and Design
Practice Midterm 2 (11) Based on this approximation, does it appear that we could reduce an operator? Justify your
answer. If it does, from which station could we do so? CM Ruled. 9% We
'“ \15 Kn) 2103:: new 95: %: oqellél Z/ CM rah/c2 0N? i/‘Q/Q (0) Returnng calls from Tech Support have priority over answering new class waiting in the hold
EXTR i“ queue. Show what changes you would make to the model in order to assign high priority to
die returning calls so that those calls are processed ﬁrst over new calls. You only need to show QUE ST WM“ those parts of the model that you would change, not the entire model A?
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Practice Midterm 2 SHORT ANSWER 1. If Type A interarrivals are distributed Expo(2.5) and Type B interarrivals are distributed
Expo(5), what is the distribution of interarrivals of the combination of both types? momma1:1». ﬂaws) 2. Why is L (total number of entities in a queue) not used for roughcut analysis? 0 puters and 5 seats for waiting. The appropriate queue notation
\» (B) MMIOIIS; (C) MMIS; (D) MleS. ISyE 3044: Simulation Analysis and Design
Practice Midterm 2 4. What would be the most reasonable guess for each of the following situations? (Choose among
Bernoulli, exponential, geometric, binomial, hypergeometric, poisson, uniform, erlang, gamma, beta, normal, and chisquared) (1) Whether or not the next part passes inspection Eye r' no .3 \\i
(ii) The number of parts that pass inspection out of the next 25
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(iii) The number of parts tested until one fails Gaowﬂwk L S. TRUE or FALSE (a) T If there are too little data, the pvalues of GOF tests are likely to be large.
(b) E Uniform distribution is good for the input with small uncertainty since it always has a fixed range. \ :0 U arm we VGKUQ I
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 Fall '08
 ALEXOPOULOS

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