The Burger Dome waiting line model in Section 11.1 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.
a. Use an Excel worksheet based on Figure 12.15 to simulate the operation of this waiting line. Assuming that customer arrivals follow a Poisson probability distribution, the interarrival times can be simulated with the cell formula - (1/λ)*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 - m*LN(RAND()), where μ = 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 in Chapter 15 indicates an average waiting time of 3 minutes per customer. What average waiting time does your simulation model show?
b. One advantage of using simulation is that a simulation model can be altered easily to reflect other assumptions about the uncertain 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?
Figure 12.15

1 Black Sheep Scarves with One Quality Inspector 3 Interarrival Times (Uniform Distribution) 4 Smallest Value 5 Largest Value 7 Service Times (Normal Distribution) 8 Mean 9 Standard Dev 10 0.5 12 Simulation 13 14 15 16 17 18 19 20 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 Interarrival Armiva Service Waiting Service Completion Time Customer Time Time Start Time Time Time 2.3 1.5 2.2 Time in System 2.3 0.0 1.3 4.9 3.5 0.7 0.5 0.2 2.7 3.7 4.0 5.2 9.8 13.6 15.4 2498.7 2500.7 2502.5 2505.8 2509.3 0.0 0.0 11.1 13.6 2496.82498.1 2497.02498.7 2499.7 2500.7 2503.42503.4 2507.42507.4 11.1 11.8 2.5 3.6 996 997 1.8 0.6 2.0 1.3 3.7 2.8 2.4 0.0 0.0 2.4 1000 Summary Statistics Number Waitin Probability of Waitin Av Maximum Waiting Time Utilization of Quality Ins Number Waiting1 Min Probability of Waiting> Min 0.4367 549 0.6100 1.59 Waiting Time 0.7860 393