Análise de sistemas GIB/M/s/c via ordenação estocástica 1 Introdução

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GI B /M/s/c j j ∈ Ak Ak λ k−1 j=0 ¯πj ¯ Bk−j−1. Ak k ∈ {1, 2, ..., c ⋆ } r S qk(r) = λ c ⋆ j=0 rj · ηjk k ∈ S p = q(¯π) q S j ∈ S c ⋆ l=j ηil i i ∈ S j ∈ S c ⋆ +∞ ∞ s ηil = bn · l=j n=1 0 0 (Y (t) ≥ j |Y (0) = δ c ⋆(i + n))tA(s) i ∈ S Y n ∈ IN δ c ⋆(i+n) i s 0 (Y (t) ≥ j |Y (0) = δ c ⋆(i + n))t δ c ⋆(i + n) Y j [0, s] i c ⋆ l=j ηil i .1 .∞ L1 L∞ a b S a ≤st b ⇒ q(a) ≤st q(b) q c⋆ < ∞ .⋆ = .1, .∞ j ∈ S βij = q(a) − q(b)⋆ ≤ (c ⋆ + 1) a − b⋆ c ⋆ l=j η0l ⋆ c l=j ηil − c ⋆ l=j ηi−1 l i = 0 1 ≤ i ≤ c ⋆ .
βij i, j ∈ S c ⋆ l=j ηil i, i ∈ S c ⋆ l=j ηil = i βkj, i, j ∈ S. k=0 g S k ∈ S ql(g) = λ gn · ηnl = λ c ⋆ l=k c ⋆ c ⋆ l=k n=0 = λ c ⋆ gn n=0 i=0 c ⋆ n=0 n c βik = λ ⋆ gn c ⋆ l=k c ⋆ βik i=0 n=i ηnl gn = λ c ⋆ i=0 βik ¯ Gi−1. a b S a ≤st b Āi−1 ≤ ¯ Bi−1 i ∈ S c = q(a) d = q(b) βik i, k ∈ S ¯Ck−1 = ql(a) = λ βikĀi−1 ≤ λ βik ¯ Bi−1 = ql(b) = ¯ Dk−1 c ⋆ l=k c ⋆ i=0 k ∈ S c⋆ < ∞ j ∈ S |qj(b) − qj(a)| = λ c ⋆ (bn − an) · ηnj n=0 c ⋆ i=0 c ⋆ l=k ≤ λ |bn − an| · ηnj ≤ |bn − an| ηnj ηnj ≤ c ⋆ k=0 ηnk = λ −1 n ∈ S q(b)−q(a)1 = c ⋆ c ⋆ n=0 c ⋆ n=0 j=0 |qj(b)−qj(a)| ≤ (c ⋆ +1) b−a1. · ∞ |qj(b) − qj(a)| ≤ c ⋆ n=0 |bn − an| j ∈ S c < ∞ ρ < 1 N ¯ Y (N) p (N) = q(π (N) ) ¯p (N) = q(¯π (N) ) p (N) ≤st p ≤st ¯p (N) .
Page 1 and 2: GI B /M/s/c
Page 3 and 4: s µ ρ
Page 5 and 6: M (N) = ¯M (N) = ∞ n=1 ∞ n=1 b
Page 7 and 8: ¯ Xk+1 − i| ¯ Xk = i ≤ ¯ b
Page 9: j, k ∈ S ηjk = = = = +∞ S2

Análise de sistemas GIB/M/s/c via ordenação estocástica 1 Introdução

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