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Fórmulas teoría colas fagv
1.
Politécnico Colombiano JIC Facultad
de Ingenierías – Programas Informáticos Investigación de Operaciones - Algunas Fórmulas Teoría de Colas Prof.: Francisco A. González Vidal serviciodecanalesdeNúmeroKS colalaenpromedioTiempoW desocupadosistemadeladProbabilidP sistemaalllegadasdepromedioTasa q 0 == = = =λ serviciodetiemposlosdeestandarDesviación sistemaelenpromedioTiempoW colalaenunidadesdepromedioNúmeroLq canalporserviciodepromedioTasa = = = = σ µ sistemaelenclientesdeNùmeron sietmadellimitadoTamañoN sistemaelenunidadesndeadProbabilid)(P sistemaelenunidadesdepromedioNúmeroLs ocupadoestésistemaelquedeadProbabilid n = = == = = Pnt Pw MODELO (M/M/1): (DG/∞/∞): Abierto WW Pp −=1 µ λ =Wp -1 L γ γ = λµ λ - L = γ γ γ − − = 1 qL γ γ − = 1 2 qL ( )λµµ λ − = 2 qL γ−= LLq ( )γ λ −= LWq 1 λ q q L W = ( )λµµ λ − =qW ( )1 1 += LW µ λµ− = 1 W ( )γλ γ − = 1 W λ L W = µ 1 += qWW 0PP n n = µ λ MODELO (M/M/S): (DG/∞/∞): Abierto − + = ∑ − = λµ µ µ λ µ λ k k kn P k k n n ! 1 ! 1 1 1 0 0 ( ) ∑ − = =< 1 0 0 ! 1k n n n PknP µ λ ( ) ∑ ∞ = =≥ kn nk kk k PknP γ ! 0 ( ) − =≥ λµ µ µ λ k k k PknP k ! 1 0 ( ) ( ) −− = 2!1 L 0 λµ λµµ λ kk k Pq Numero promedio de estaciones desocupadas −= µ λkE ( ) ( )!1 20 µ λ λµ λµµ λ + −− = kk PL k µ λ += qLL 1 Semestre 2014-1
2.
Politécnico Colombiano JIC Facultad
de Ingenierías – Programas Informáticos Investigación de Operaciones - Algunas Fórmulas Teoría de Colas Prof.: Francisco A. González Vidal λ q q L W = ( ) ( ) −− = 20 !1 λµ µµ λ kk PW k q 1 µ += qWW λ L =W ( ) ( ) λµ λ λµ λµµ λ 1 !1 20 + −− = kk PW k ≥ < = − knSi 1 k! 1 KnSi ! 1 0 0 P k P n P n kn n n µ λ µ λ MODELO (M/G/1): (DG/∞/∞): Abierto µ λ=wP wPP −=10 ( ) − + = µ λ µ λλσ 12 2 2 qL µ λ+= qLL λ L W = λ q q L W = 1 µ −=WWq ( ) ( )λµµ σµλ − + = 2 122 qW MODELO (M/D/1): (DG/∞/∞): Abierto µ λ=wP wPP −=10 − = µ λ µ λ 12 2 qL µ λ+= qLL λ L W = 1 µ −=WWq ( )λµµ λ − = 2 qW λ q q L W = TABLA DE P0 PARA SISTEMAS ABIERTOS ƿ S= 1 S=2 S=3 S=4 S=5 0,1 0,9 0,9048 0,904 8 0,9048 0,9048 0,2 0,8 0,8182 0,8187 0,8187 0,8187 0,3 0,7 0,7391 0,740 0,7408 0,7408 2 Semestre 2014-1
3.
Politécnico Colombiano JIC Facultad
de Ingenierías – Programas Informáticos Investigación de Operaciones - Algunas Fórmulas Teoría de Colas Prof.: Francisco A. González Vidal 7 0,4 0,6 0,6667 0,6701 0,6703 0,6703 0,5 0,5 0,6000 0,6061 0,6065 0,6065 0,6 0,4 0,5385 0,547 9 0,5487 0,5488 0,7 0,3 0,4815 0,495 2 0,4965 0,4966 0,8 0,2 0,4286 0,447 2 0,4491 0,4493 0,9 0,1 0,3793 0,403 5 0,4062 0,4065 1 0,3333 0,363 6 0,3673 0,3678 3 Semestre 2014-1
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