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3
4
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7
8
9
15
16
17
18
40
19
21
23
27
29
30
31
32
A B C D E F G H I J
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l)7Average server utilization (r)0.7000
Probabilities
Number of Units Probability
Cumulative
Probability
10.2471 0.4235
30.1211 0.7175
70.0291 0.9322
90.0142 0.9668
10 0.0100 0.9767
11 0.0070 0.9837
12 0.0049 0.9886
Case: New England Foundry (Existing)
11
41
42
43
44
46
48
52
53
54
55
56
67
68
69
70
71
A B C D E F G H I J
Computations
n or s
(lam/mu)^n/n!
Cumsum(n-1)
term2 P0(s) Rho(s) Lq(s) L(s) Wq(s) W(S)
0 1
11.4 1-3.5 -0.4 1.4 -4.9 -3.5 -0.7 -0.5
30.4573333 3.38 0.8575 0.23599 0.466667 0.177065 1.577065 0.025295 0.225295
50.0448187 3.9974 0.062248148 0.24633 0.28 0.005963 1.405963 0.000852 0.200852
95.694E-05 4.0551339 6.74246E-05 0.2466 0.155556 3.06E-06 1.400003 4.38E-07 0.2
10 7.971E-06 4.0551908 9.2687E-06 0.2466 0.14 3.72E-07 1.4 5.32E-08 0.2
11 1.015E-06 4.0551988 1.16245E-06 0.2466 0.127273 4.18E-08 1.4 5.97E-09 0.2
12 1.184E-07 4.0551998 1.33991E-07 0.2466 0.116667 4.36E-09 1.4 6.23E-10 0.2
13 1.275E-08 4.0552 1.42846E-08 0.2466 0.107692 4.25E-10 1.4 6.07E-11 0.2
24 5.18E-21 4.0552 5.50136E-21 0.2466 0.058333 8.4E-23 1.4 1.2E-23 0.2
25 2.901E-22 4.0552 3.07315E-22 0.2466 0.056 4.5E-24 1.4 6.42E-25 0.2
26 1.562E-23 4.0552 1.651E-23 0.2466 0.053846 2.32E-25 1.4 3.31E-26 0.2
27 8.1E-25 4.0552 8.54276E-25 0.2466 0.051852 1.15E-26 1.4 1.65E-27 0.2
28 4.05E-26 4.0552 4.26305E-26 0.2466 0.05 5.53E-28 1.4 7.9E-29 0.2
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10
19
20
21
22
23
34
35
36
37
38
A B C D E F G H I J
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l)4Average server utilization (r)0.6667
Service rate (m)6Average number of customers in the queue (Lq)1.3333
Number of servers (s) 1 Average number of customers in the system (L) 2.0000
Number of Units Probability
Probability
0 0.3333 0.3333
1 0.2222 0.5556
2 0.1481 0.7037
3 0.0988 0.8025
14 0.0011 0.9977
15 0.0008 0.9985
16 0.0005 0.9990
17 0.0003 0.9993
18 0.0002 0.9995
Case: New England Foundry (New – Maintenance)
18
48
49
50
51
52
63
64
65
66
67
5 0.0010974 1.9465021 0.001266223 0.51341 0.133333 0.0001 0.666767 2.5E-05 0.166692
6 0.0001219 1.9475995 0.000137174 0.51342 0.111111 8.8E-06 0.666675 2.2E-06 0.166669
7 1.161E-05 1.9477214 1.2835E-05 0.51342 0.095238 6.94E-07 0.666667 1.73E-07 0.166667
8 9.677E-07 1.947733 1.05569E-06 0.51342 0.083333 4.93E-08 0.666667 1.23E-08 0.166667
9 7.168E-08 1.947734 7.74175E-08 0.51342 0.074074 3.18E-09 0.666667 7.95E-10 0.166667
20 1.236E-22 1.947734 1.27871E-22 0.51342 0.033333 2.26E-24 0.666667 5.66E-25 0.166667
21 3.924E-24 1.947734 4.05276E-24 0.51342 0.031746 6.82E-26 0.666667 1.71E-26 0.166667
22 1.189E-25 1.947734 1.22628E-25 0.51342 0.030303 1.97E-27 0.666667 4.92E-28 0.166667
23 3.447E-27 1.947734 3.54961E-27 0.51342 0.028986 5.44E-29 0.666667 1.36E-29 0.166667
24 9.574E-29 1.947734 9.84779E-29 0.51342 0.027778 1.44E-30 0.666667 3.61E-31 0.166667
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A B C D E F G H I J
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Probabilities
Number of Units Probability
Cumulative
Probability
0 0.5714 0.5714
11 0.0001 1.0000
12 0.0000 1.0000
13 0.0000 1.0000
14 0.0000 1.0000
15 0.0000 1.0000
Case: New England Foundry (New – Molding)
11
45
46
47
48
49
60
61
62
63
64
2 0.0918367 1.4285714 0.116883117 0.64706 0.214286 0.020626 0.449198 0.006875 0.149733
3 0.0131195 1.5204082 0.015306122 0.65116 0.142857 0.001661 0.430233 0.000554 0.143411
4 0.0014057 1.5335277 0.001574344 0.65142 0.107143 0.000123 0.428694 4.1E-05 0.142898
5 0.0001205 1.5349334 0.000131781 0.65144 0.085714 8.05E-06 0.428579 2.68E-06 0.14286
6 8.606E-06 1.5350538 9.26812E-06 0.65144 0.071429 4.64E-07 0.428572 1.55E-07 0.142857
17 1.561E-21 1.535063 1.60109E-21 0.65144 0.02521 2.7E-23 0.428571 8.99E-24 0.142857
18 3.716E-23 1.535063 3.80664E-23 0.65144 0.02381 6.05E-25 0.428571 2.02E-25 0.142857
19 8.382E-25 1.535063 8.57541E-25 0.65144 0.022556 1.29E-26 0.428571 4.3E-27 0.142857
20 1.796E-26 1.535063 1.83547E-26 0.65144 0.021429 2.62E-28 0.428571 8.73E-29 0.142857
21 3.666E-28 1.535063 3.74195E-28 0.65144 0.020408 5.08E-30 0.428571 1.69E-30 0.142857