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A B C D E F G H I J
Problem 9-26
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l)30 Average server utilization (r)0.2833
Probabilities
Number of Units Probability
Cumulative
Probability
0 0.4248 0.4248
1 0.3611 0.7859
7 0.0003 0.9999
8 0.0001 1.0000
9 0.0000 1.0000
10 0.0000 1.0000
11 0.0000 1.0000
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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 0.85 1 5.666666667 0.15 0.85 4.816667 5.666667 0.160556 0.188889
2 0.36125 1.85 0.62826087 0.4035 0.425 0.187376 1.037376 0.006246 0.034579
13 1.94E-11 2.3396469 2.07746E-11 0.4274 0.065385 6.21E-13 0.85 2.07E-14 0.028333
14 1.18E-12 2.3396469 1.25504E-12 0.4274 0.060714 3.47E-14 0.85 1.16E-15 0.028333
15 6.68E-14 2.3396469 7.0814E-14 0.4274 0.056667 1.82E-15 0.85 6.06E-17 0.028333
16 3.55E-15 2.3396469 3.74792E-15 0.4274 0.053125 8.99E-17 0.85 3E-18 0.028333
17 1.77E-16 2.3396469 1.8678E-16 0.4274 0.05 4.2E-18 0.85 1.4E-19 0.028333
Maint hourly cost $20
Server hourly cost $12
Servers L Server cost/day Wait cost/day Total cost/day
15.6667 $96.00 $906.67 $1,002.67
Hire 2 servers.