An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 12

The Burger Dome waiting line model in Section 11.2 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 I customer per minute.
a. Use a worksheet based on Figure 12.15 to simulate the operation of this waiting line. Assuming that customer arrivals follow a Poisson probability distribution, the inter arrival times can be simulated with the cell formula -(1/ ? )*LN(RAND()), where ? = 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 500 customers. The analytical mode in Chapter 11 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 I minutes 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 impact of this change on the average waiting time?