[40 points] Consider the following system: At a remote gas station, there is only one pump. Assume that the customers arrive at the gas station according to a Poisson distribution with a mean of 12 per hour. The time that it takes a customer to fill the tank is random, and an analysis of the service time has indicated that the time can be modeled with an exponential distribution with a mean of 3 minutes. Customers who arrive at the gas station are served in the order of arrival and though space is available at the gas station to accommodate waiting customers. The gas station is open 24 hours a day. (Hint: Refer the Pharmacy model we discussed in-class) a. Develop a simulation model for above system in Arena. b. Simulate the model for 30 days. (replication length) C. How much time a customer waits in line before being able to pump gas? d. On average, how many customers wait in line? (Queue length) e. What is the utilization of the gas pump? f. If the mean of number of customers arrive at the gas station increases to 15 per hour, re- run the simulation and calculate c), d) and e). Compare the results with previous case (12 per hour rate). If the mean number of customers arrive at the gas station increases to 20 per hour, discuss the long-term system stability of the gas-station. 8