1
2
3
4
14
15
16
26
27
28
29
30
A B C D E F G H I J
Queuing Model M/M/s (Exponential Service Times)
Probability (% of time) system is empty (P0)0.0016
6 0.1024 0.3866
7 0.0877 0.4743
8 0.0752 0.5495
9 0.0644 0.6139
10 0.0552 0.6692
Internet Case: Pantry Shopper (All)
40
41
42
43
44
55
56
57
58
59
70
71
72
73
A B C D E F G H I J
20 0.0118 0.9293
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
1 5.9988 1 -1.200048002 -4.9988 5.9988 -7.19885 -1.20005 -0.07199 -0.012
12 4.533523 394.85999 9.065233621 0.0025 0.4999 0.022434 6.021234 0.000224 0.060212
13 2.091977 399.39352 3.884434198 0.0025 0.461446 0.008253 6.007053 8.25E-05 0.060071
14 0.896382 401.48549 1.568433727 0.0025 0.428486 0.002918 6.001718 2.92E-05 0.060017
15 0.358481 402.38188 0.59738904 0.0025 0.39992 0.000988 5.999788 9.88E-06 0.059998
16 0.134404 402.74036 0.215019917 0.0025 0.374925 0.00032 5.99912 3.2E-06 0.059991
27 9.35E-08 402.94507 1.20192E-07 0.0025 0.222178 8.52E-11 5.9988 8.52E-13 0.059988
28 2E-08 402.94507 2.54902E-08 0.0025 0.214243 1.72E-11 5.9988 1.72E-13 0.059988
29 4.14E-09 402.94507 5.22368E-09 0.0025 0.206855 3.38E-12 5.9988 3.38E-14 0.059988
30 8.28E-10 402.94507 1.03552E-09 0.0025 0.19996 6.42E-13 5.9988 6.42E-15 0.059988
1
2
3
4
5
6
7
8
12
13
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
Average waiting time in the queue (Wq)0.0667
Average time in the system (W) 0.1000
10.2222 0.5556
30.0988 0.8025
70.0195 0.9610
90.0087 0.9827
10 0.0058 0.9884
11 0.0039 0.9923
12 0.0026 0.9949
Internet Case: Pantry Shopper (Express)
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
10.66666667 1 2 0.33333 0.666667 1.333333 20.066667 0.1
30.04938272 1.8888889 0.063492063 0.5122 0.222222 0.009292 0.675958 0.000465 0.033798
50.00109739 1.9465021 0.001266223 0.51341 0.133333 0.0001 0.666767 5E-06 0.033338
97.1683E-08 1.947734 7.74175E-08 0.51342 0.074074 3.18E-09 0.666667 1.59E-10 0.033333
10 4.7789E-09 1.947734 5.12021E-09 0.51342 0.066667 1.88E-10 0.666667 9.39E-12 0.033333
11 2.8963E-10 1.947734 3.08314E-10 0.51342 0.060606 1.02E-11 0.666667 5.11E-13 0.033333
12 1.609E-11 1.947734 1.70369E-11 0.51342 0.055556 5.15E-13 0.666667 2.57E-14 0.033333
13 8.2515E-13 1.947734 8.69754E-13 0.51342 0.051282 2.41E-14 0.666667 1.21E-15 0.033333
24 9.5742E-29 1.947734 9.84779E-29 0.51342 0.027778 1.44E-30 0.666667 7.22E-32 0.033333
25 2.5531E-30 1.947734 2.62308E-30 0.51342 0.026667 3.69E-32 0.666667 1.84E-33 0.033333
26 6.5465E-32 1.947734 6.71876E-32 0.51342 0.025641 9.08E-34 0.666667 4.54E-35 0.033333
27 1.6164E-33 1.947734 1.65734E-33 0.51342 0.024691 2.15E-35 0.666667 1.08E-36 0.033333
28 3.8486E-35 1.947734 3.94248E-35 0.51342 0.02381 4.94E-37 0.666667 2.47E-38 0.033333
1
2
3
4
5
6
7
8
9
15
16
17
18
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)80 Average server utilization (r)0.8889
Probabilities
Number of Units Probability
Cumulative
Probability
0 0.0025 0.0025
1 0.0132 0.0157
2 0.0353 0.0510
3 0.0627 0.1137
14 0.0309 0.7528
15 0.0275 0.7803
16 0.0244 0.8047
17 0.0217 0.8264
18 0.0193 0.8457
Internet Case: Pantry Shopper (Regular)
11
48
49
50
51
52
63
64
65
66
67
5 35.959396 79.55144 -539.3909465 -0.0022 1.066667 –18.768 -13.4346 –0.2346 -0.16793
6 31.963908 115.51084 287.6751715 0.0025 0.888889 5.708039 11.04137 0.07135 0.138017
7 24.353454 147.47474 102.2845054 0.004 0.761905 1.310504 6.643837 0.016381 0.083048
8 16.235636 171.8282 48.70690734 0.0045 0.666667 0.441716 5.775049 0.005521 0.072188
9 9.6211175 188.06383 23.61547022 0.0047 0.592593 0.162273 5.495606 0.002028 0.068695
20 0.0001425 207.12706 0.000194334 0.0048 0.266667 3.41E-07 5.333334 4.26E-09 0.066667
21 3.619E-05 207.1272 4.85146E-05 0.0048 0.253968 7.97E-08 5.333333 9.97E-10 0.066667
22 8.774E-06 207.12724 1.15819E-05 0.0048 0.242424 1.79E-08 5.333333 2.24E-10 0.066667
23 2.035E-06 207.12725 2.6488E-06 0.0048 0.231884 3.86E-09 5.333333 4.83E-11 0.066667
24 4.521E-07 207.12725 5.81311E-07 0.0048 0.222222 8.02E-10 5.333333 1E-11 0.066667