Example 10.1 - Customers in Line Arrival rate 1 Service rate 2 Interarrival Time 1.0000 Service time 0.5000 System Utilization 0.5000 Probability system is empty 0.5000 Average number in line 0.5000 Average number in system 1.0000 Average time in line 0.5000 Average time in system 1.0000 n = 10 P(10 units in system) = 0.0005 P(n < 10 units in system) = 0.9990 n P(n) P(n < n) 0 0.5000 1 0.2500 0.5000 2 0.1250 0.7500 3 0.0625 0.8750 4 0.0313 0.9375 5 0.0156 0.9688 6 0.0078 0.9844 7 0.0039 0.9922 8 0.0020 0.9961 9 0.0010 0.9980 10 0.0005 0.9990 11 0.0002 0.9995 12 0.0001 0.9998 13 0.0001 0.9999 14 0.0000 0.9999 15 0.0000 1.0000 16 0.0000 1.0000 17 0.0000 1.0000 18 0.0000 1.0000 19 0.0000 1.0000 = = 1/= 1/= = P 0 = L q = L s = W q = W s =
Excel con formulario para resolver problemas de colas
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Population Size N = 4 4Number of servers S = 1 2Average service time T = 7.5 7.5Average time between service calls U = 60 60P(wait) - from table D = 0.3210 0.0370 Efficiency factor - from table F = 0.9570 0.9980 Service factor 0.111 0.111 Average number waiting L = #NAME? #NAME?Average waiting time W = #NAME? #NAME?Average number running J = #NAME? #NAME?Average number being serviced H = #NAME? #NAME?
Per TimeUnit
Service cost = $7.00Downtime cost = $40.00
Comparison of Downtime Cost
Number of Servers 1 2
Number of Machines Down (H+L) #NAME? #NAME?
Cost per Hour of Machines Down #NAME? #NAME?[ (H+L) x $40 per unit time ]
Cost of Service $7.00 $14.00($7 per unit time )
Total Cost per Unit Time #NAME? #NAME?
=
Note: You must enter D and F (based on N, , and M) from the table in the text
Comparison of Downtime Cost
1 2
$0$2$4$6$8
$10$12$14$16
Comparison of Dow ntime Cost for Different Num ber of Servers Cost of Server