Refer to the first 100 minutes of the computer simulation of the current operation of Herr Cutter's barber shop presented in Figure 12.7 and summarized in Figure 12.8. Now consider the alternative of adding an associate. Perform a simulation of this alternative by hand by using exactly the same interarrival times (in the same order) and exactly the same service times (in the same order) as in Figure 12.7.
FIGURE 12.7
A computer simulation of Herr Cutter's barber shop (as currently operated) over a period of 100 customer arrivals.

a. Determine the new waiting time before beginning a haircut for each of the 5 customers who arrive in the first 100 minutes. Use these results to estimate Wq, the expected waiting time before the haircut.
b. Plot the new version of Figure 12.8 to show the evolution of the number of customers in the barber shop over these 100 minutes.
FIGURE 12.8: This graph shows the evolution of the number of customers in Herr Cutter's barber shop over the first 100 minutes of the computer simulation in Figure 12.7.

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н Herr Cutter's Barber Shop (exponential) Mean Interarival Time 4 30 minutes (uniform) Min Service Time 15 minutes Max Service Time 25 minutes Average Time in Line (Wa Average Time in System (W 10 12.8 minutes 11 33.0 minutes 12 13 Time Time Time Time Time 14 Customer Interarrival of Service Service Service in in Arrival Arrival Time Begins Time Ends Line System 15 16 0.5 0.5 0.5 21.9 22.3 0.0 21.9 21.9 17 45.6 46.0 46.0 21.9 67.9 0.0 Range Name Cells 18 2.6 48.6 67.9 20.8 88.8 19.4 40.2 Average TimelnLine Average TimelnSystem DI1 D10 107.7 19 4 1.5 50.1 88.8 18.9 38.7 57.6 77.7 47.2 27.6 107.7 17.2 124.9 30.0 20 C16:CI15 InterarrivalTime 29.2 106.9 124.9 16.3 141.2 18.0 34.3 21 MaxService Time Meanlnterarrival Time D8 125.5 15.7 22 18.6 141.2 24.6 165.8 40.3 D4 147.4 23 21.8 165.8 22.7 188.6 18.5 41.2 MinServiceTime D7 154.8 166.9 24 7.4 188.6 24.3 212.9 33.8 58.1 ServiceTime F16:FI 15 TimelnLine 25 10 12.1 212.9 18.4 231.3 46.0 64.4 H16:H115 22.2 22.2 TimelnSystem TimeOfArrival I16:1115 96 48.8 3,132.8 3,132.8 3,155.0 0.0 111 D16:DI15 97 112 12.3 3,145.1 3,155.0 25.0 3,180.0 9.9 34.9 TimeServiceBegins TimeServiceEnds E16:E115 98 113 82.7 3,227.7 3,227.7 19.0 3,246.7 0.0 19.0 G16:GI15 114 99 4.0 3,231.8 3,246.7 20.1 3,266.8 14.9 35.0 3,317.0 115 100 85.2 3,317.0 19.5 3,336.5 0.0 19.5 Average Time in Line (Wa)-AVERAGE(TimelnLine) Average Time in System (W)-AVERAGE(TimelnSystem) 10 11 Average Time in Line (Wa) -AVERAGE(TimelnLine) Average Time in System (W) =AVERAGE(TimelnSystem) 10 11 13 Time Time 14 Interarrival of Service Service 15 Time Arrival Begins Time =-MeanInterarrivalTime*LN(RANDO) =InterarrivalTime =-MeanInterarrivalTime*LN(RANDO) =D16+InterarrivalTime =MAX(G16,D17) =-MeanInterarrivalTime*LN(RANDO) =D17+InterarrivalTime =MAX(G17,D18) 16 =TimeOfArrival =MinServiceTime+(MaxServiceTime-MinServiceTime)*RANDO 17 =MinServiceTime+(MaxServiceTime-MinServiceTime)*RANDO 18 =MinServiceTime+(MaxServiceTime-MinServiceTime)*RANDO 19 20 Н 13 Time Time Time 14 Service in in 15 Ends Line System =TimeServiceBegins+ServiceTime =TimeServiceBegins-TimeOfArrival =TimeServiceEnds-TimeOfArival =TimeServiceBegins+Service Time |=TimeServiceBegins-TimeOfArrival =TimeServiceBegins+Service Time |=TimeServiceBegins-TimeOfArrival 16 17 =TimeServiceEnds-TimeOfArrival 18 =TimeServiceEnds-TimeOfArrival 19 20