The Burger Dome waiting line model in Section 16.1 studies the waiting time of customers at its fast-food restaurant. Burger Dome€™s single-channel waiting line system has an arrival rate of 0.75 customers per minute and a service rate of 1 customer per minute.
a. Use a worksheet based on Figure 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 - µ*LN(RAND()), where µ = 1. Run the Burger Dome simulation for 500 customers. The analytical model in Chapter 14 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 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 minute. 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 EXCEL WORKSHEET FOR THE HAMMONDSPORT SAVINGS BANK WITH ONEATM

1 Hammondsport Savings Bank with One ATM 3 Interarrival Times (Uniform Distribution) 4 Smallest Value 5 Largest Value 7 Service Times (Normal Distribution) 9 Std Deviation 8 Mean 0.5 10 12 Simulation 13 InterarrivaArmiv Service Waiting Service Completion Time 15 16 17 18 Customer Time Time Start TimeTime TTme Timein System 0.0 1.0 0.0 0.0 2.3 2.3 2.5 2.2 2.5 2.7 5.2 9.8 13.6 154 2498.7 2500.7 2502.5 2505.8 2509.3 1.3 4.9 3.5 3.7 7.6 2.2 11.1 1.8 4 13.6 2496.824981 2497.02498.7 2499.72500.7 2503.4 2503.4 2507.4 2507.4 996 997 998 0.5 0.2 2.7 3.7 4.0 0.6 2.0 011 1012 013 014 015 016 017 1018 019 1020 1021 1022 1023 1024 1025 3.7 2.8 2.4 0.0 0.0 2.4 1000 Summary Statistics Number Waiting Probability of Waiting Average Waiting Time Maximum Waiting Time Utilization of ATM Number Waiting1 Min Probability of Waiting > 1 Min 0.43 549 0.6100 1.59 13.5 0.7860 393