Fórmulas de teoría de colas

[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

λefec = λ(M-L)

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