Fórmulas de teoría de colas
Enviado por Lorena Legnin • 27 de Septiembre de 2021 • Síntesis • 701 Palabras (3 Páginas) • 246 Visitas
[pic 1][pic 2]
FÓRMULAS DE COLAS
Relaciones fundamentales: L=λW Lq=λWq W=Wq+1/μ (M/M/1):(GD/∞/∞) ρ<1
ρ = λ/μ P0=1-ρ Pn = P0ρn L = λ/(μ −λ)
Lq = λ2/(μ(μ −λ)) W = 1/(μ −λ) Wq = λ/(μ(μ −λ))
(M/M/s):(GD/∞/∞) ρ<1
Pn = (λ/μ)nP0 / n! para 0≤n≤s Pn = (λ/μ)nP0 / [s!sn-s] para n≥s[pic 3][pic 4]
s-1
P0 = 1/{Σ (λ/μ)n / n! + [(λ/μ)s / s! ][1-λ/(sμ)]−1} ρ = λ/(sμ)
n=0
Lq = [P0(λ/μ)sρ]/[s!(1-ρ)2] Wq = Lq / λ W = Wq + 1/μ L = Lq + λ/μ
(M/M/1):(GD/M/∞) ρ = λ/μ L = [ρ/(1−ρ)]−[(M+1)ρM+1]/[1-ρM+1] P0 = [1 - ρ]/[1 - ρΜ+1] Pn = P0 ρn Si λ=μ, PM = 1/(M+1)[pic 5]
Lq = L – (1- P0) W = L /λefec Wq = Lq /λefec λefec= λ(1-PM)
(M/M/s):(GD/M/∞)
Pn = (λ/μ)nP0 / n! para 0≤n≤s Pn = (λ/μ)nP0 / [s!sn-s] para n≥s hasta M
s M
P0 = 1/{1+Σ (λ/μ)n / n! + [(λ/μ)s / s! ][Σ {λ/(sμ)}n-s]} ρ = λ/(sμ)
n=1 n=s+1
Lq = [P0(λ/μ)sρ]/[s!(1-ρ)2][1-ρM-s-(M-s)ρM-s(1-ρ)]
s-1 s-1
L = Σ nPn + Lq + s(1- Σ Pn) W = L /λefec Wq = Lq /λefec λefec= λ(1-PM)
n=0 n=0
(M/M/1):(GD/∞/M)
M
P0 = 1/[ Σ {M!/(M-n)! (λ/μ)n}] Pn = {M!/(M-n)! (λ/μ)n}P0 λefec = λ(M-L)
n=0
Lq = M – (λ+μ)/λ (1−P0) L = M-μ/λ ( 1-P0) W = L /λefec Wq = Lq /λefec (M/M/s):(GD/∞/M)
s-1 M
P0 = 1/[ Σ {M!/[(M-n)!n!] (λ/μ)n }+ Σ {M!/[(M-n)!s!sn-s] (λ/μ)n }] λefec = λ(M-L)
n=0 n=s
Pn = {M!/[(M-n)!n!] (λ/μ)n}P0 | 0≤n≤s | Pn = {M!/[(M-n)!s!sn-s] (λ/μ)n}P0 s≤n≤M | |
M Lq = Σ (n-s) Pn n=s | s-1 L=Σ nPn + Lq + s n=0 | s-1 (1-Σ Pn) W = L /λefec n=0 | Wq = Lq /λefec |
λefec = λ(M-L)
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