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Queuing Midterm 2011

Queuing Midterm 2011. Problem 1 (25%). (a) , similar to lec5 p.15 +17%. +6%. +7%. Problem 1 (25%). (a) , similar to lec5 p.15. +4%. Problem 1 (20%). (b) +7%. Problem 2 (20%). (a) transition diagram 8% 寫成固定 λ -3% 寫成固定 3 μ -3%

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Queuing Midterm 2011

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  1. Queuing Midterm 2011

  2. Problem 1 (25%) • (a) , similar to lec5 p.15 +17% +6% +7%

  3. Problem 1 (25%) • (a) , similar to lec5 p.15 +4%

  4. Problem 1 (20%) • (b) +7%

  5. Problem 2 (20%) • (a) transition diagram 8% • 寫成固定λ-3% • 寫成固定3μ-3% • 畫超過n個state -2% • 畫成bulk service -6% n λ (n-1) λ (n-2) λ λ 0 1 2 3 …… n-1 n μ 2μ 3μ 3μ

  6. Problem 2 (20%) • (b) average number of failed disk 12% • 寫出P0~Pk的balance equation +7% • 把P1~Pk用P0代換 +3% • 剩下小細節: ΣPk=1 =>求出P0 =>ans=ΣkPk+2%

  7. Problem 2 (20%) • (b) average number of failed disk 12% • 寫成固定λ去算其他都正確 -6% • 寫成固定3μ去算其他都正確 -6% • 寫成固定λ且固定3μ去算 其他都正確 -9%

  8. Problem 3 M/M/k/k (20%) • Transition diagram +8% • Balance Equation +9% λ λ λ λ 0 1 2 3 …… k-1 k μ 2μ 3μ kμ +5% +4%

  9. Problem 3 (20%) • Blocked probability +3% • 寫成M/M/1/K去算其他都正確 -8% • 寫成M/M/K/∞去算其他都正確 -6% • 直接寫Pi=XXP0, 沒推導過程, 但結果正確 -5~7%

  10. Problem 4 (15%) • 投影片lec2 p.11

  11. Problem 5 (20%) • Transition diagram +6% • Balance Equation +4% 1 1 1 1a 0 1 2 3 …… 1b 4 4 4

  12. Problem 5 (20%) • 求Pk+4% • 求E[N] +3%

  13. Problem 5 (20%) • 求T or W+3% • 如果寫 且 =1/μ-1pt • 如果畫成如下, 以上每部分 +4,2,2,2,2% 1 1 0 1 2 3 …… 1 4 4 4

  14. Problem 5 (20%) • 如果畫成如下, 以上每部分 +4,2,2,2,2% • 如果畫成如下, 以上每部分 +3,2,2,1,1% 1 1 1 1 0 2 3 …… 8 4 1 1 0 2 3 …… 1 4 4 4

  15. Problem 5 (20%) • 如果畫成如下, 以上每部分 +5,2,2,2,2% • 如果畫成如下, 以上每部分 +2,2,1,1,1% 1 1 1 1 0 2 3 …… 1 4 4 4 1 0.5 0.5 1 0 2 3 …… 4 4 4 1 2 1 2 0 3 4 …… 8 4 4

  16. Problem 5 (20%) • 如果畫成如下, 以上每部分 +5,2,2,2,2% 1 1 1 1a 0 1 1 2 3 …… 1b 4 4 4

  17. Problem 6 (20%) • 投影片lec2 p.15

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