Problem 12-23 The Burger Dome waiting line model studies the waiting time of customers at its fast-food restaurant. Burg

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Problem 12 23 The Burger Dome Waiting Line Model Studies The Waiting Time Of Customers At Its Fast Food Restaurant Burg 1 (314.59 KiB) Viewed 10 times

Problem 12-23 The Burger Dome waiting line model studies the waiting time of customers at its fast-food restaurant. Burger Dome's single-server waiting line system has an arrival rate of 0.75 customers per minute and a service rate of 1 customer per minute. Adapt the Black Sheep Scarves spreadsheet shown below to simulate the operation of this waiting line. Make sure to use the random values for both interarrival and service times generated in the worksheet_12-23. Assuming that customer arrivals follow a Poisson probability distribution, the interarrival times can be simulated with the cell formula -(1/A)*LN(RAND()), where λ = 0.75. Assuming that the service time follows an exponential probability distribution, the service times can be simulated with the cell formula -*LN(RAND()), where = 1. Run the Burger Dome simulation for 1000 customers. Discard the first 100 customers and collect data over the next 900 customers. The analytical model indicates an average waiting time of 3 minutes per customer. What average waiting time does your simulation model show? Round your answer to 3 decimal places. 1 2 3 4 9 10 11 12 13 14 15 16 17 18 19 20 1011 1012 1013 1014 1015 5 6 7 8 Mean 1016 1017 1018 1019 1020 1021 A B C D E Black Sheep Scarves with One Quality Inspector 1022 1023 1024 Interarrival Times (Uniform Distribution) Smallest Value 0 Largest Value Service Times (Normal Distribution) Standard Dev Simulation Customer 1 2 3 4 5 996 997 998 999 1000 minutes 2 0.5 1.4 1.3 4.9 Interarrival Arrival Service Waiting Service Completion Time Time Time Time Time in System. Time Start Time 1.4 1.4 2.3 2.7 3.7 2.5 7.6 7.6 2.2 11.1 11.1 0.0 2.5 11.8 13.6 1.8 3.6 2496.8 2498.1 1.3 1.9 2497.0 2498.7 1.7 3.7 1.0 2.8 0.0 2.4 0.0 1.9 Summary Statistics Number Waiting Probability of Waiting Average Waiting Time Maximum Waiting Time Utilization of Quality Inspector Number Waiting > 1 Min Probability of Waiting > 1 Min minutes 3.5 0.7 0.5 0.2 2.7 2499.7 2500.7 3.7 2503.4 2503.4 4.0 25074 2507.4 0.0 1.0 0.0 F 549 0.6100 1.59 13.5 0.7860 393 0.4367 2.3 1.5 2.2 2.5 1.8 0.6 2.0 1.8 G 2.4 1.9 3.7 5.2 9.8 13.6 15.4 2498.7 2500.7 2502.5 H 2505.8 2509.3 a. One advantage of using simulation is that a simulation model can be altered easily to reflect other assumptions about the probabilistic inputs. Assume that the service time is more accurately described by a normal probability distribution with a mean of 1 minute and a standard deviation of 0.2 minutes. This distribution has less service time variability than the exponential probability distribution used in part (a). What is the impact of this change on the average waiting time? Round your answer to 3 decimal places.