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Modeling Simulation Class_Exam2006_1


1. ์‹œํ—˜ ์ผ์ž

2006. 10. 20. PM6:00

2. ์ž‘์„ฑ์ž

๊ฐ•์ธ์ˆ˜, ๋ฐ•์˜์ฐฝ

3. ์‹œํ—˜ ๋‚ด์šฉ

1. Single Queue, Single Server ๋ฌธ์ œ (10 points)
(a) (5 points) ์Šค์ผ€์ฅด ํ‘œ ์ฃผ๊ณ ..(์ด๋ฒˆ์—๋Š” Single Queue, Single Server) ์ด ์‹œ๋ฎฌ๋ ˆ์ด์…˜์—์„œ ์‚ฌ์šฉ๋˜๋Š” ์ƒํƒœ์™€ ์ด๋ฒคํŠธ์— ๋Œ€ํ•ด ์“ฐ์‹œ์˜ค.
(b) (5 points) FEL ์ž‘์„ฑํ•˜์‹œ์˜ค.

2. (10 points)
์šด์ „ ๋ฉดํ—ˆ ์‹œํ—˜์„ ๋ณธ๋‹ค. ์šด์ „ ๋ฉดํ—ˆ ์‹œํ—˜์€ ์ด 2๋‹จ๊ณ„๋กœ ๊ตฌ๋ถ„๋˜์–ด ์น˜๋Ÿฌ์ง„๋‹ค.
Step 1) ํ•„๊ธฐ ์‹œํ—˜. AM9, PM1 ์‹œ ๊ฒฝ์— ์ด๋ฃจ์–ด์ง€๋ฉฐ, ์‹œํ—˜์‹œ๊ฐ„์€ 50๋ถ„ ํ‰๊ฐ€ ์‹œ๊ฐ„์„ 10๋ถ„ ๊ฐ–๋Š”๋‹ค. ํ•œ๋ฒˆ์˜ ์‹œํ—˜์— ์ตœ๋Œ€ ์‘์‹œ์ธ์›์€ 50๋ช…์ด๋ฉฐ, ํ•ฉ๊ฒฉ๋ฅ ์€ 80%์ด๋‹ค.
Step 2) ์‹ค๊ธฐ ์‹œํ—˜. ํ•„๊ธฐ ์‹œํ—˜ ํ•ฉ๊ฒฉ์ž์— ํ•œํ•ด์„œ ์น˜๋ฃจ๊ฒŒ ๋œ๋‹ค. ์‹œํ—˜์€ ์ฐจ 2๋Œ€๋ฅผ ๊ฐ€์ง€๊ณ  ์ด๋ฃจ์–ด์ง€๋ฉฐ, ์‹œํ—˜์„ ์ค€๋น„ํ•˜๋Š”๋ฐ 1๋ถ„์˜ ์‹œ๊ฐ„์ด ์†Œ์š”๋˜๋ฉฐ, ๋ณดํ†ต 6๋ถ„ ๊ฐ€๋Ÿ‰์˜ ์‹œ๊ฐ„์ด ์†Œ์š”๋œ๋‹ค. ๋‹จ, ์‹œํ—˜ ๋„์ค‘์— ๊ฒฐ๊ฒฉ ์‚ฌ์œ ๊ฐ€ ๋ฐœ๊ฒฌ๋ ์‹œ 6๋ถ„์ด ์•ˆ๋˜์–ด๋„ ์‹œํ—˜์ด ์ข…๋ฃŒ๋˜๊ฒŒ ๋œ๋‹ค.
ํ•ด๋‹น ์šด์ „๋ฉดํ—ˆ ์‹œํ—˜์€ ์ „์ฒด ๊ณผ์ •์ด PM5์‹œ์— ์ข…๋ฃŒ๋œ๋‹ค.
(a) ํ•ด๋‹น ๋ชจ๋ธ์„ ๊ตฌ์„ฑํ•˜๊ณ  ํ•„์š”ํ•  ๊ฒฝ์šฐ ๊ฐ€์ •์„ ํ•ด๋„ ์ข‹๋‹ค. (7 points)
(b) ๊ตฌ์„ฑ๋œ ๋ชจ๋ธ์ด ์•ˆ์ •์ ์ธ์ง€ ๋ช…ํ™•ํ•œ ์ด์œ ๋ฅผ ๋Œ€๊ณ  ์„ค๋ช…ํ•˜๋ผ. (3 points)

3. Triangular Distribution ๊ทธ๋ž˜ํ”„ ์ฃผ๊ณ 
y = a(x-30) ( 30 < x < 90) y = b(x-110) (90< x < 110) ํ˜•ํƒœ์˜ ๊ทธ๋ž˜ํ”„๋กœ 90 ์ง€์ ์—์„œ ๊ต์ฐจํ•˜๋Š” ๊ทธ๋ž˜ํ”„์ž„
(a) (5 points) Peak Value ๊ตฌํ•˜๊ธฐ - ๊ทธ๋ž˜ํ”„์˜ ๊ฐ€์žฅ ๋†’์€ ์ง€์ ์˜ ๋†’์ด๋ฅผ ๊ตฌํ•˜๋ผ๋Š” ๋ฌธ์ œ๋กœ ํŒŒ์•…ํ–ˆ์Œ. pdf ์ „์ฒด์˜ ๋„“์ด๊ฐ€ 1์ด๋ผ๋Š” ์‚ฌ์‹ค์„ ์ด์šฉํ•˜๋Š” ๋ฌธ์ œ
(b) (5 points) Expectation ๊ตฌํ•˜๊ธฐ - (๊ณ„์‚ฐ์ด ๊ต‰์žฅํžˆ ์ง€์ €๋ถ„ํ•จ. ์†Œ์ˆ˜์  ๋‚œ๋ฌด)

4. (Extra)
(a) (5 points) Arena์— ๋‚˜์˜ค๋Š” 4๊ฐ€์ง€ ํƒ€์ž…์˜ ๋ชจ๋ธ ์„ค๋ช…
(b) (5 points) Continuous Probability Function์—์„œ X = x0 ์ผ๋•Œ์˜ ํ™•๋ฅ ์ด ์™œ 0์ธ๊ฐ€? Discrete Probability Function์—์„œ์˜ X = x0์ผ๋•Œ์™€ ๋น„๊ตํ•˜์‹œ์˜ค.

4. ๋‹ต

2.
1) ๋‚˜์˜ ๊ฒฝ์šฐ ํ•ด๋‹น ๋ฌธ์ œ๋ฅผ ๊ฐ„๋‹จํ•œ ํ™•๋ฅ  ๋ชจ๋ธ + Single Queue, Multi Server ์˜ ๋ฌธ์ œ๋กœ ํŒŒ์•…ํ–ˆ๋‹ค. ํ™•๋ฅ ๋ชจ๋ธ์€ 1์ฐจ ํ•ฉ๊ฒฉ์ž๋ฅผ ๊ฐ€๋ฆฌ๋Š”๋ฐ ์“ฐ์ด๊ณ , SQMS๋ชจ๋ธ์€ ์‹ค๊ธฐ ์‹œํ—˜์„ ๊ฐ€๋ฆฌ๋Š”๋ฐ ์‚ฌ์šฉํ•˜๊ณ , ๊ฐ€์ •์œผ๋กœ ์‹ค๊ธฐ ์‹œํ—˜์€ 7๋ถ„์„ ์ตœ๊ณ  ์ ์œผ๋กœ๊ฐ–๋Š” Triangle Distribution ์ด๋ผ๊ณ  ๊ฐ€์ •ํ•˜๊ณ  ํ’€์ดํ–ˆ์Œ.
2) ๋ถ€์กฑํ•œ ์‹œ๊ฐ„, ๋žœ๋คํ•จ์ˆ˜๋ฅผ ์‚ฌ์šฉํ•  ์ˆ˜ ์—†๋Š” ์ƒํ™ฉ์ด๋ผ๋Š” ์ ์„ ๋งํ•˜๊ณ , TD ์˜ ๊ธฐ๋Œ€์น˜๋ฅผ ๊ตฌํ–ˆ๋‹ค. ๋Œ€์ถฉ ๊ตฌํ•ด๋ณด๋‹ˆ 7.55 ๋ถ„๊ฐ€๋Ÿ‰์ด ์†Œ์š”๋œ๋‹ค๋Š” ์‚ฌ์‹ค์„ ์•Œ์•˜๋‹ค. (์ขŒ์šฐ ๋Œ€์นญํ˜•์œผ๋กœ ๊ฐ€์ •ํ–ˆ๊ธฐ ๋•Œ๋ฌธ์—... -_-) ๋”ฐ๋ผ์„œ ํ•œ ํŒจ๊ฑฐ๋ฆฌ์˜ ์‹ค๊ธฐ ์‹œํ—˜ํ•ฉ๊ฒฉ์ž์˜ ์ตœ๋Œ€ ์ธ์›์€ 40๋ช… ์†Œ์š”๋˜๋Š” ์‹œ๊ฐ„์€ ์ด 5์‹œ๊ฐ„์ด์ง€๋งŒ SQMS ๋ชจ๋ธ์ด ํ์ž‰์—์„œ ์ตœ๋Œ€์˜ ํšจ์œจ์„ ๋ฐœํœ˜ ํ•  ์ˆ˜ ์žˆ์œผ๋ฏ€๋กœ, ์–‘์ชฝ์˜ ์„œ๋ฒ„์— ๋ฐ˜์”ฉ์„ ๋‚˜๋ˆ„์–ด์„œ ์‹œํ—˜์„ ๋ณด๋ฉด 2์‹œ๊ฐ„ ๋ฐ˜๊ฐ€๋Ÿ‰์ด ํ•„์š”ํ•˜๋‹ค๊ณ  ํŒ๋‹จ. ํ•„๊ธฐ๊ฐ€ ์ข…๋ฃŒ๋˜๋Š” ์‹œ๊ฐ„์€ 10:00 + 2:30. 14:00 + 2:30 ๋”ฐ๋ผ์„œ ๋‹น์ผ์˜ ์‹œํ—˜์ด ์™„์ „ํžˆ ์ข…๋ฃŒ๋˜๋Š” 17:00 ๋ถ„ ์•ˆ์— ์‹œํ—˜์„ ๋๋‚ผ ์ˆ˜ ์žˆ๊ธฐ ๋•Œ๋ฌธ์— ํ•ด๋‹น ๋ชจ๋ธ์€ ์•ˆ์ •ํ•˜๋‹ค๊ณ  ์ ๊ธด์ ์—ˆ๋‹ค. -_-;;
๋‹จ ๋ฌธ์ œ๋Š” ์„œ๋ฒ„ ์ฒ˜๋ฆฌ ์‹œ๊ฐ„์ด ํŽธ์ฐจ๊ฐ€ ๋ถ„๋ช…ํžˆ ํดํ…๋ฐ ์ด๋ฅผ ๊ณ ๋ ค๋ชปํ•ด์„œ ์ข€ ์•ˆ์Šต์ธ๋‹ต. ์†”์งํžˆ ๋‚˜๋„ 3๋ฒˆ ๊ณ„์‚ฐํ•˜๋‹ค๊ฐ€ ์‹œ๊ฐ„์„ ๋‹ค ๋ณด๋‚ด์„œ -_-;; - ๋ฐ•์˜์ฐฝ

5. ๋ง๋ง

3๋ฒˆ ํ‘ธ๋А๋ผ ํ•œ์‹œ๊ฐ„์€ ๋ณด๋‚ธ๊ฑฐ ๊ฐ™๋‹ค. ๋‹ˆ๋ฏธ๋Ÿด-_-; --์ธ์ˆ˜
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