9.+Formul%c3%a1rio+Teoria+de+Filas

Prévia do material em texto

Formulário Teoria de Filas 
 
































0
1
0
0
0
11
021
0
.
.
.
.
1
.
.
).(
.
.
.
n
nn
n
n
nn
nn
nn
n
q
qq
sn
nq
n
n
n
P
CP
PCP
C
WW
WL
WL
PsnL
PnL
s
s












Fórmulas Gerais Fórmulas M/M/1 
   
   
 
































.
.
1
).(
1
1
.
.1.
.1.
2
0
0
q
t
q
o
to
q
n
n
n
n
W
etP
W
etP
L
L
P
PP
C
Prof Dsc Paulo Ribas – prof.paulo.ribas@gmail.com 
 
 
 
   
 
 
       tsqq
s
n
nq
sts
t
q
q
q
q
s
q
sn
n
n
n
s
s
n
n
sn
n
n
n
n
n
ePtP
PP
s
e
s
P
etP
LL
WW
L
W
s
P
L
snP
ss
snP
nP
s
sn
P
sn
ss
sn
nC
s
snn
sns
.1..
1
0
1.
0
.
2
0
0
0
1
0
0
.01
0
1
1
.
1!.
.
1.
1
1!.
..
.
!.
0.
!
.
1
1
.
!!
1
!.
1
!
.
.
.













































 


































































































































































Fórmulas M/M/s Fórmulas M/M/1/k 
 
 
 k
k
n
n
k
k
q
q
q
n
k
n
kk
n
n
n
n
PP
k
L
LW
L
W
PLL
kn
kn
P
P
kn
kn
C





















































1..
1
.1
1
1
0
.
1
1
1
11
0
1
0
1
1
0
1
1
0
0
















Fórmulas M/G/1 
 






1
1.2
.
1
222
0







q
q
q
q
q
WW
L
W
LL
L
P
Fórmulas M/D/1 
São as mesmas do 
M/G/1, considerando-se 
2 = 0. Única alteração: 
 



1.2
2
qL
Prof Dsc Paulo Ribas – prof.paulo.ribas@gmail.com 
 
Fórmulas M/M/2 
Prof Dsc Paulo Ribas – prof.paulo.ribas@gmail.com 
 
𝜇𝑛 = 2. 𝜇 ∀ 𝑛 > 2 
𝜇𝑛 = 𝑛. 𝜇 ∀ 𝑛 ≤ 2 
𝜌 =
𝜆
2. 𝜇
 
 
𝑃0 =
1
1 +
𝜆
𝜇 +
𝜆
𝜇 
2
2 − 𝜆 𝜇 
 
𝑃1 =
𝜆
𝜇 . 𝑃0 
𝑃𝑛 =
𝜆
𝜇 
𝑛
2 𝑛−1
. 𝑃0 ∀ 𝑛 ≥ 2 
𝐿𝑞 =
𝑃0.
𝜆
𝜇 
2
𝜌
2. 1 − 𝜌 2
 
 
𝑊𝑞 =
𝐿𝑞
𝜆
 
𝑊 = 𝑊𝑞 +
1
𝜇
 
𝐿 = 𝜆. 𝑊𝑞 +
1
𝜇
= 𝐿𝑞 +
𝜆
𝜇
 
𝑃 𝜔𝑞=0 = 𝑃0 + 𝑃1 
 
𝑃 𝜔𝑞>𝑡 = 1 − 𝑃 𝜔𝑞=0 . 𝑒
−2𝜇 1−𝜌 𝑡 
 
𝑃 𝜔>𝑡 = 𝑒
−𝜇𝑡 . 1 +
𝑃0.
𝜆
𝜇 
2
2 1 − 𝜌
.
1 − 𝑒
−𝜇𝑡 1−𝜆 𝜇 
1 − 𝜆 𝜇 
 ∀ 𝜆 𝜇 ≠ 1 
 
𝑃 𝜔>𝑡 = 𝑒
−𝜇𝑡 . 1 +
𝑃0.
𝜆
𝜇 
2
2 1 − 𝜌
. 𝜇𝑡 ∀ 𝜆 𝜇 = 1 
 
 
M/M/s 
M/D/s