# Show all your work by pasting Screenshots of your Arena for appropriate question

Show all your work by pasting Screenshots of your Arena for appropriate questions. Also, upload your work (Arena models) [10 points] Explain why simulations are important as decision making tools.

[10 points] Discuss the advantages of simulations compared to actual systems.

[10 points] Briefly explain “Discrete Event Simulation”. Provide examples.

[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)Develop a simulation model for above system in Arena.

Simulate the model for 30 days. (replication length)

How much time a customer waits in line before being able to pump gas?

On average, how many customers wait in line? (Queue length)

What is the utilization of the gas pump?

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.

[30 points] Consider the above gas station. Assume that there are 3 type of customers who come to the gas station. 1st type of customers fills the gas and leave the gas station. 2nd type of customers goes inside the convenience store at the gas station while the gas is being filled to use the rest-room. 3rd type of customers goes inside the convenience store, use the rest-room and buy something. 30% of the customers are type 1 and they need on average 2 minutes to be served. 50% of the customers are type 2 and they need on average 3 minutes to be served. 20% of the customers are type 3 and they need 4.5 minutes to be served. Assume that while customers use the facilities, their car is parked at the gas pump and no other customer can use the pump until the customer exits the gas station. (Hint: Refer the modified pharmacy model)Develop a simulation model for above system in Arena.

Simulate the model for 30 days. (replication length)

How much time a customer waits in line before being able to pump gas?

On average, how many customers wait in line? (Queue length)

What is the utilization of the gas pump?