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)0.1000
6 0.0531 0.5217
7 0.0478 0.5695
8 0.0430 0.6126
9 0.0387 0.6513
10 0.0349 0.6862
Case: Winter Park Hotel (Current System)
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 0.0122 0.8906
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 0.9 1 9 0.1 0.9 8.1 9 0.45 0.5
12 5.9E-10 2.4596031 6.37428E-10 0.40657 0.075 2.1E-11 0.9 1.17E-12 0.05
13 4.08E-11 2.4596031 4.38561E-11 0.40657 0.069231 1.33E-12 0.9 7.37E-14 0.05
14 2.62E-12 2.4596031 2.80442E-12 0.40657 0.064286 7.83E-14 0.9 4.35E-15 0.05
15 1.57E-13 2.4596031 1.67498E-13 0.40657 0.06 4.35E-15 0.9 2.41E-16 0.05
16 8.86E-15 2.4596031 9.38434E-15 0.40657 0.05625 2.27E-16 0.9 1.26E-17 0.05
27 5.34E-30 2.4596031 5.52444E-30 0.40657 0.033333 7.75E-32 0.9 4.3E-33 0.05
28 1.72E-31 2.4596031 1.77353E-31 0.40657 0.032143 2.39E-33 0.9 1.33E-34 0.05
29 5.33E-33 2.4596031 5.49776E-33 0.40657 0.031034 7.16E-35 0.9 3.98E-36 0.05
30 1.6E-34 2.4596031 1.64757E-34 0.40657 0.03 2.07E-36 0.9 1.15E-37 0.05
1
2
3
4
5
6
7
8
12
13
22
23
24
25
26
37
38
39
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)0.3000
Average time in the system (W) 0.3333
2 0.0810 0.2710
3 0.0729 0.3439
4 0.0656 0.4095
5 0.0590 0.4686
6 0.0531 0.5217
17 0.0167 0.8499
18 0.0150 0.8649
19 0.0135 0.8784
Case: Winter Park Hotel (Quick Server)
40
51
52
53
54
55
66
67
68
69
70
A B C D E F G H I J
20 0.0122 0.8906
8 1.07E-05 2.4595913 1.20296E-05 0.40657 0.1125 6.2E-07 0.900001 2.3E-08 0.033333
9 1.07E-06 2.4596019 1.18625E-06 0.40657 0.1 5.36E-08 0.9 1.98E-09 0.033333
10 9.61E-08 2.459603 1.05589E-07 0.40657 0.09 4.25E-09 0.9 1.57E-10 0.033333
11 7.86E-09 2.4596031 8.56216E-09 0.40657 0.081818 3.1E-10 0.9 1.15E-11 0.033333
12 5.9E-10 2.4596031 6.37428E-10 0.40657 0.075 2.1E-11 0.9 7.78E-13 0.033333
23 3.43E-24 2.4596031 3.56795E-24 0.40657 0.03913 5.91E-26 0.9 2.19E-27 0.033333
24 1.29E-25 2.4596031 1.33572E-25 0.40657 0.0375 2.12E-27 0.9 7.84E-29 0.033333
25 4.63E-27 2.4596031 4.80109E-27 0.40657 0.036 7.29E-29 0.9 2.7E-30 0.033333
26 1.6E-28 2.4596031 1.65953E-28 0.40657 0.034615 2.42E-30 0.9 8.96E-32 0.033333
27 5.34E-30 2.4596031 5.52444E-30 0.40657 0.033333 7.75E-32 0.9 2.87E-33 0.033333
1
2
3
4
5
6
7
8
9
10
19
20
21
22
33
34
35
36
37
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)15.75 Average server utilization (r)0.8925
Service rate (m)17.647 Average number of customers in the queue (Lq)7.4098
Number of Units Probability
Cumulative
Probability
0 0.1075 0.1075
1 0.0959 0.2034
2 0.0856 0.2891
13 0.0245 0.7965
14 0.0219 0.8184
15 0.0195 0.8379
16 0.0174 0.8553
17 0.0156 0.8709
Case: Winter Park Hotel (Slow Servers)
47
48
49
50
51
62
63
64
65
66
4 0.026438 2.4092659 0.034030671 0.40928 0.223125 0.004 0.8965 0.000254 0.056921
5 0.004719 2.4357034 0.005744501 0.40959 0.1785 0.000511 0.893011 3.25E-05 0.056699
6 0.000702 2.4404226 0.000824631 0.40963 0.14875 5.9E-05 0.892559 3.75E-06 0.05667
7 8.95E-05 2.4411245 0.00010258 0.40963 0.1275 6.14E-06 0.892506 3.9E-07 0.056667
8 9.98E-06 2.441214 1.12388E-05 0.40963 0.111563 5.78E-07 0.892501 3.67E-08 0.056667
19 9.47E-19 2.4412251 9.93932E-19 0.40963 0.046974 2.01E-20 0.8925 1.27E-21 0.056667
20 4.23E-20 2.4412251 4.42452E-20 0.40963 0.044625 8.47E-22 0.8925 5.38E-23 0.056667
21 1.8E-21 2.4412251 1.87625E-21 0.40963 0.0425 3.41E-23 0.8925 2.17E-24 0.056667
22 7.29E-23 2.4412251 7.59627E-23 0.40963 0.040568 1.32E-24 0.8925 8.35E-26 0.056667
23 2.83E-24 2.4412251 2.94227E-24 0.40963 0.038804 4.87E-26 0.8925 3.09E-27 0.056667
1
2
3
4
5
6
16
17
18
29
30
31
32
33
A B C D E F G H I J
Cumulative
Case: Winter Park Hotel (Single Line)
11
42
43
44
45
46
47
58
59
60
61
62
73
(lam/mu)^n/n!
Cumsum(n-1)
1
2
3
4
5
6
7
8
15
16
17
18
19
20
26
27
28
29
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 0.1000 0.1000
6 0.0531 0.5217
7 0.0478 0.5695
8 0.0430 0.6126
9 0.0387 0.6513
Case: Winter Park Hotel (ATM)
11
40
41
42
43
54
55
56
57
58
69
70
71
72
73
A B C D E F G H I J
20 0.0122 0.8906
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 7.862E-09 2.4596031 8.56216E-09 0.40657 0.081818 3.1E-10 0.9 1.72E-11 0.05
12 5.896E-10 2.4596031 6.37428E-10 0.40657 0.075 2.1E-11 0.9 1.17E-12 0.05
13 4.082E-11 2.4596031 4.38561E-11 0.40657 0.069231 1.33E-12 0.9 7.37E-14 0.05
14 2.624E-12 2.4596031 2.80442E-12 0.40657 0.064286 7.83E-14 0.9 4.35E-15 0.05
15 1.574E-13 2.4596031 1.67498E-13 0.40657 0.06 4.35E-15 0.9 2.41E-16 0.05
26 1.602E-28 2.4596031 1.65953E-28 0.40657 0.034615 2.42E-30 0.9 1.34E-31 0.05
27 5.34E-30 2.4596031 5.52444E-30 0.40657 0.033333 7.75E-32 0.9 4.3E-33 0.05
28 1.717E-31 2.4596031 1.77353E-31 0.40657 0.032143 2.39E-33 0.9 1.33E-34 0.05
29 5.327E-33 2.4596031 5.49776E-33 0.40657 0.031034 7.16E-35 0.9 3.98E-36 0.05
30 1.598E-34 2.4596031 1.64757E-34 0.40657 0.03 2.07E-36 0.9 1.15E-37 0.05
1
2
3
4
5
6
7
8
12
15
16
17
18
19
20
21
22
23
24
25
36
37
38
39
A B C D E F G H I J
Cumulative
Probability
Case: Winter Park Hotel (Remaining with 4 Servers)
11
50
51
52
53
54
65
66
67
68
69
1
2
3
4
5
6
7
8
9
18
19
20
21
32
33
34
35
36
A B C D E F G H I J
Cumulative
Probability
Case: Winter Park Hotel (Remaining with 5 Servers)
11
46
47
48
49
50
61
62
63
64
65