1
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6
7
8
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10
A B C D E G H I J K
Template for the M/M/s Queueing Model
Data Results
Range Name
Cells
l = 0.5 (mean arrival rate) L = 3 L G4
m = 0.666667 (mean service rate)
Lq = 2.25 Lambda C4
s = 1 (# servers) Lq G5
W = 6 Mu C5
Pr(W > t) = 0.434598
Wq = 4.5 n F13:F38
when t = 5 P0 G13
r = 0.75 Pn G13:G38
Prob(Wq > t) = 0.325949 Rho G10
35
36
37
38
A B C D E G H I J K
22 0.00044595
23 0.00033446
24 0.00025085
25 0.00018814
1
2
3
4
5
6
7
8
9
10
A B C D E G H I J K
Template for the M/M/s Queueing Model
Data Results
Range Name
Cells
l = 10 (mean arrival rate) L = 1 L G4
m = 20 (mean service rate)
Lq = 0.5 Lambda C4
s = 1 (# servers) Lq G5
W = 0.1 Mu C5
Pr(W > t) = 0.006738
Wq = 0.05 n F13:F38
when t = 0.5 P0 G13
r = 0.5 Pn G13:G38
Prob(Wq > t) = 0.003369 Rho G10
35
36
37
38
A B C D E G H I J K
22 1.1921E-07
23 5.9605E-08
24 2.9802E-08
25 1.4901E-08
1
2
3
4
5
6
7
8
9
10
13
A B C D E G H I J K
Template for the M/M/s Queueing Model
Data Results
Range Name
Cells
l = 15 (mean arrival rate) L = 3 L G4
m = 20 (mean service rate)
Lq = 2.25 Lambda C4
s = 1 (# servers) Lq G5
W = 0.2 Mu C5
Pr(W > t) = 0.082085
Wq = 0.15 n F13:F38
when t = 0.5 P0 G13
r = 0.75 Pn G13:G38
00.25 0.25 Time1 C9
35
36
37
38
A B C D E G H I J K
22 0.00044595
23 0.00033446
24 0.00025085
25 0.00018814
1
2
3
4
5
6
7
8
9
10
13
27
28
29
30
31
32
33
A B C D E G H I J K
Template for the M/M/s Queueing Model
Data Results
Range Name
Cells
l = 25 (mean arrival rate) L = 2.05128205 LG4
m = 20 (mean service rate)
Lq = 0.80128205 Lambda C4
s = 2 (# servers) Lq G5
W = 0.08205128 Mu C5
Pr(W > t) = 0.001022
Wq = 0.03205128 n F13:F38
when t = 0.5 P0 G13
r = 0.625 Pn G13:G38
00.23076923 0.23076923 Time1 C9
14 0.00064051
15 0.00040032
16 0.0002502
17 0.00015638
18 9.7735E-05
19 6.1084E-05
20 3.8178E-05
0
0.05
0.1
Probability
Number of Customers in System
35
36
37
38
A B C D E G H I J K
22 1.4913E-05
23 9.3207E-06
24 5.8254E-06
25 3.6409E-06
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 0.2 (mean arrival rate) L = 2.5 LG4
1/m = 4 (expected service time)
Lq = 1.7 Lambda C4
s= 1 (standard deviation) Lq G5
s = 1 (# servers) W = 12.5 OneOverMu C5
Wq = 8.5 Rho G10
sC7
r = 0.8 Sigma C6
WG7
P0 = 0.2 Wq G8
sL
LqWWq
2.5 1.7 12.5 8.5
4 4 3.2 20 16
33.3 2.5 16.5 12.5
22.8 214 10
12.5 1.7 12.5 8.5
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A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 0.2 (mean arrival rate) L = 2.263191222 LG4
1/m = 3.314 (expected service time)
Lq = 1.600391222 Lambda C4
s= 4 (standard deviation) Lq G5
s = 1 (# servers) W = 11.31595611 OneOverMu C5
Wq = 8.001956109 Rho G10
sC7
r = 0.6628 Sigma C6
WG7
P0 = 0.3372 Wq G8
1
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6
7
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11
12
13
14
15
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17
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 0.2 (mean arrival rate) L = 4 L G4
1/m = 4 (expected service time)
Lq = 3.2 Lambda C4
s= 4 (standard deviation) Lq G5
s = 1 (# servers) W = 20 OneOverMu C5
Wq = 16 Rho G10
sC7
r = 0.8 Sigma C6
WG7
P0 = 0.2 Wq G8
m 1/m
Lq
3.2
0.3 43.2
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16
17
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19
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21
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 0.2 (mean arrival rate) L = 4 L G4
1/m = 4 (expected service time)
Lq = 3.2 Lambda C4
s= 4 (standard deviation) Lq G5
s = 1 (# servers) W = 20 OneOverMu C5
Wq = 16 Rho G10
sC7
r = 0.8 Sigma C6
WG7
P0 = 0.2 Wq G8
m 1/m s
3.2 4 3 2 1 0
0.2 4.5455 8.0655 6.5255 5.4255 4.7655 4.5455
0.2 4.1667 4.0033 3.1633 2.5633 2.2033 2.0833
0.3 3.8462 2.6687 2.0621 1.6287 1.3687 1.2821
0.3 3.5714 2.0129 1.5229 1.1729 0.9629 0.8929
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12
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 30 (mean arrival rate) L = 1.666666667 LG4
1/m = 0.020833 (expected service time)
Lq = 1.041666667 Lambda C4
s= 0.020833 (standard deviation) Lq G5
s = 1 (# servers) W = 0.055555556 OneOverMu C5
Wq = 0.034722222 Rho G10
sC7
r = 0.625 Sigma C6
WG7
P0 = 0.375 Wq G8
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12
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 30 (mean arrival rate) L = 1.145833333 LG4
1/m = 0.020833 (expected service time)
Lq = 0.520833333 Lambda C4
s= 0 (standard deviation) Lq G5
s = 1 (# servers) W = 0.038194444 OneOverMu C5
Wq = 0.017361111 Rho G10
sC7
r = 0.625 Sigma C6
WG7
P0 = 0.375 Wq G8
1
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12
13
14
15
16
17
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23
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 30 (mean arrival rate) L = 1.666666667 LG4
1/m = 0.020833 (expected service time)
Lq = 1.041666667 Lambda C4
s= 0.020833 (standard deviation) Lq G5
s = 1 (# servers) W = 0.055555556 OneOverMu C5
Wq = 0.034722222 Rho G10
sC7
r = 0.625 Sigma C6
WG7
P0 = 0.375 Wq G8
Service Service
Time Time
(seconds) (hours)
Lq
1.04166667
75 0.02083 1.04166667
62 0.01722 0.55229885
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12
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 0.05 (mean arrival rate) L = 3 L G4
1/m = 15 (expected service time)
Lq = 2.25 Lambda C4
s= 15 (standard deviation) Lq G5
s = 1 (# servers) W = 60 OneOverMu C5
Wq = 45 Rho G10
sC7
r = 0.75 Sigma C6
WG7
P0 = 0.25 Wq G8
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11
12
A B C D E F G H I J
Template for the M/G/1 Queueing Model
Data Results
Cell
l = 0.05 (mean arrival rate) L = 3.2439025 LG4
1/m = 16 (expected service time)
Lq = 2.4439025 Lambda C4
s= 11.62 (standard deviation) Lq G5
s = 1 (# servers) W = 64.87805 OneOverMu C5
Wq = 48.87805 Rho G10
sC7
r = 0.8 Sigma C6
WG7
P0 = 0.2 Wq G8
1
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3
4
5
6
7
8
9
10
13
A B C D E G H I J K
Template for the M/M/s Queueing Model
Data Results
Range Name
Cells
l = 2 (mean arrival rate) L = 2.17391304 LG4
m = 1 (mean service rate)
Lq = 0.17391304 Lambda C4
s = 4 (# servers) Lq G5
W = 1.08695652 Mu C5
Pr(W > t) = 0.007902
Wq = 0.08695652 n F13:F38
when t = 5 P0 G13
r = 0.5 Pn G13:G38
00.13043478 0.130434783 Time1 C9
35
36
37
38
A B C D E G H I J K
22 3.3171E-07
23 1.6586E-07
24 8.2928E-08
25 4.1464E-08
Number of Customers in System
1
2
3
4
5
6
7
8
9
10
13
25
26
27
28
29
30
31
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33
34
A B C D E G H I J K
Template for the M/M/s Queueing Model
Data Results
Range Name
Cells
l = 3 (mean arrival rate) L = 4.52830189 LG4
m = 1 (mean service rate)
Lq = 1.52830189 Lambda C4
s = 4 (# servers) Lq G5
W = 1.50943396 Mu C5
Pr(W > t) = 0.023901
Wq = 0.50943396 n F13:F38
when t = 5 P0 G13
r = 0.75 Pn G13:G38
00.03773585 0.03773585 Time1 C9
12 0.01275023
13 0.00956267
14 0.007172
15 0.005379
16 0.00403425
17 0.00302569
18 0.00226927
19 0.00170195
20 0.00127646
21 0.00095735
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Probability