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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)0.2000
6 0.0524 0.7903
7 0.0419 0.8322
8 0.0336 0.8658
9 0.0268 0.8926
10 0.0215 0.9141
Problem 9-20 1-Crew
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20 0.0023 0.9908
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 0.8 1 4 0.2 0.8 3.2 4 0.8 1
12 1.43E-10 2.2255409 1.53711E-10 0.4493 0.066667 4.93E-12 0.8 1.23E-12 0.2
13 8.83E-12 2.2255409 9.40747E-12 0.4493 0.061538 2.77E-13 0.8 6.93E-14 0.2
14 5.04E-13 2.2255409 5.35064E-13 0.4493 0.057143 1.46E-14 0.8 3.64E-15 0.2
15 2.69E-14 2.2255409 2.84219E-14 0.4493 0.053333 7.19E-16 0.8 1.8E-16 0.2
16 1.35E-15 2.2255409 1.41611E-15 0.4493 0.05 3.35E-17 0.8 8.37E-18 0.2
27 2.22E-31 2.2255409 2.28828E-31 0.4493 0.02963 3.14E-33 0.8 7.85E-34 0.2
28 6.34E-33 2.2255409 6.53082E-33 0.4493 0.028571 8.63E-35 0.8 2.16E-35 0.2
29 1.75E-34 2.2255409 1.79978E-34 0.4493 0.027586 2.29E-36 0.8 5.74E-37 0.2
30 4.67E-36 2.2255409 4.79488E-36 0.4493 0.026667 5.9E-38 0.8 1.48E-38 0.2
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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
Average waiting time in the queue (Wq)0.2250
Average time in the system (W) 0.3750
2 0.1440 0.7840
3 0.0864 0.8704
4 0.0518 0.9222
5 0.0311 0.9533
6 0.0187 0.9720
17 0.0001 0.9999
18 0.0000 0.9999
19 0.0000 1.0000
Problem 9-20 2-Crews
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20 0.0000 1.0000
8 4.17E-07 1.8221178 4.50346E-07 0.5488 0.075 2E-08 0.6 5.01E-09 0.15
9 2.78E-08 1.8221182 2.9755E-08 0.5488 0.066667 1.17E-09 0.6 2.92E-10 0.15
10 1.67E-09 1.8221183 1.77264E-09 0.5488 0.06 6.21E-11 0.6 1.55E-11 0.15
11 9.09E-11 1.8221183 9.61313E-11 0.5488 0.054545 3.04E-12 0.6 7.61E-13 0.15
12 4.54E-12 1.8221183 4.78357E-12 0.5488 0.05 1.38E-13 0.6 3.45E-14 0.15
23 3.05E-28 1.8221183 3.1366E-28 0.5488 0.026087 4.61E-30 0.6 1.15E-30 0.15
24 7.64E-30 1.8221183 7.83275E-30 0.5488 0.025 1.1E-31 0.6 2.76E-32 0.15
25 1.83E-31 1.8221183 1.87793E-31 0.5488 0.024 2.53E-33 0.6 6.34E-34 0.15
26 4.23E-33 1.8221183 4.3296E-33 0.5488 0.023077 5.61E-35 0.6 1.4E-35 0.15
27 9.4E-35 1.8221183 9.61291E-35 0.5488 0.022222 1.2E-36 0.6 3E-37 0.15
Number of crews L Truck cost/day Crew cost/day Total cost/day
1 4.0 trucks 4.0 x 8 hrs x $80 = $2,560 3 x $22 x 8 hrs = $528 $3,088
Problem 9-20 Costs