[MGOC10] ExamAidSheet.doc

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Department
Management (MGO)
Course
MGOC10H3
Professor
Vinh Quan
Semester
Fall

Description
MGTOC10 Analysis for Decision Making Final Exam Aid Sheet λ e −λ − μt P[x] = , P[service time ≤ t] = 1 − e x! L = λW, L = λW , W = W + 1/μ L = L + λ/μ q q q , q (M/M/1) : (FCFS/∞/∞) model 1 1 λ n n P 0 ∞ = 1 = 1 −μ λ  ∞ ∞ λ   λ  λ2 ∑ (λ / μ ) , Pn = μ  P0 , Lq = ∑ (n − 1)Pn = ∑ (n − 1)μ   1 − μ = μ (μ − λ ) n = 0 1 − λ / μ   n =1 n =1 W q L /q, W = W + 1qμ, L = L + λ/q, P = 1- w = λ/µ 0 (M/M/k) : (FCFS/∞/∞) Model n (λ/μ )  P0 0≤n≤k P = 1  n! k 0 k−1(λ /μ) n (λ /μ)k  kμ , P= , L = (λ / μ) (λμ ) P ∑  +   n  n q (k − 1)!(kμ − λ) 2 0 n=0 n!  k! kμ −λ  (λ/μ ) P n>k  n−k 0 k!k k L = L + λ / μ W = L Lq P = (λ / μ)  kμ P q , λ , W q λ , w k! kμ − λ  0 (M/G/1) : (FCFS/∞/∞) λ σ +(λ /μ) 2 P 0 1− λ / μ , L q 2(1−λ /μ) Pw= 1- P 0 λ/µ, L = L + λqμ, W = L /q, W q W + 1/μ q (λ / μ) If:(M/D/1) : (FCFS/∞/∞) then L q 2(1− λ / μ) (M/G/k) : (FCFS/k/∞) 1 (λ / μ) / n! P n λ k n n = 0, 1, … k, L = (1 − k ) w = 1/µ ∑ (λ / μ) / n! μ n=0 (M/M/1) : (FCFS/N/∞)  1−ρ n  ifρ≠1 λ ρP0n
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