PracticeMidterm2soltns

PracticeMidterm2soltns - ISyE 3044: Simulation Analysis and...

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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, Chi-square tests, q-q 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 Chi-square 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 u.-——;.—_—-"" Observed O“ Eapecietb ‘31 t “ Interval 24 2 E5 “2 a; Interval 2” " __3_—'; 1 5 1H7. 9‘ _ Interval 3 I 27 " 1 6 £4 {13 Interval 4 I 20 Z S l __ Bug} Perform a 1- alpha = 95% Chi-square test with the observed data. (Use the Chi-square l . book to determine quantiles. For the test, I will provide you with possible quantiles.) Is the data a good fit? 1 _, 5.05% #:e‘SJ-sd 7- 740-0337- I“ . tut» sci . W a ‘> ~ . \ ' Jaime K . Q “If "“wws Pas-HNW’A :2”) we. w ‘ J r-‘H‘C‘ ( a. 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 p-value of < 0.01 for the Chi-square test signifies a good fit. F All 3 t: sesam— SHORT ANSWER 1. A Chi-square 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 S: \ {Jammie‘sejs "— 0-03? lie‘r‘l : Y“ o 0:, (Z ~ 2. What does the significance level of a test stand for (definitiori of Type-I error)? The Prabobxlv‘rj oi- a 4035*: reset-lion 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 .e’ -' I‘l PM A N 3 CM 4. What is the difficulty with using the normal distribution for service times? fL SQfiflLE tinne,_ Ctu\ isobag ra-dxxse. daAoQS. — glflee Normal i5, Judged-fl cit Dix 0,9303%? I? I 2 _ '51“; 311"“. J W“ M 0. K ISyE 3044: Simulation Analysis and Design Practice Midterm 2 Arena Questions 7% “a There are eight workers at a car hand-wash 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 . Thefi-m 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 ' ' [\J r re Q l r 65 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: Seize-Delay- @936 {A 5 e 3. A co-worker 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“»; inf-ii SlfiS‘l‘W5/ r: {E‘LYINd-diefi filoj‘x’f lo 1M "Fqu MQM in fieb 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 e-mailers. 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, first-come-first- 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 product-operator 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 long-run 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? ' -- \A x' . an “M ifl‘ifadwcfl ox new a’t’mflotfi‘e is Que m \ Us Tape-1 [aX‘c-ribuic ‘ Mam: Priod‘wj [Iij Act/Me \jou awe it“ N. 69qu bfreod-smir Vane: L SH” :xf‘tofiei‘talogoeue “Home Maw who " M \s Q(\D{‘\H' 3 01¢ Emdfimue. is {X‘P‘r-(iioustfl AW ISyE 3044: Simulation Analysis and Design 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? momma-1:1». flaws) 2. Why is L (total number of entities in a queue) not used for rough-cut 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 chi-squared) (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 {is i {‘x o d\)\ (iii) The number of parts tested until one fails Gaowflwk L S. TRUE or FALSE (a) T If there are too little data, the p-values 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 {kiwi one ethos M3 04x3 \JCJLlJ? \S 6. od\\\’) \Xlt—Q-l‘fi ' 10 ...
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PracticeMidterm2soltns - ISyE 3044: Simulation Analysis and...

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