Assignment:
Plans are being made to open a small gas station in a central location in Springfield. The owner must decide how much space should be provided for waiting cars. This is an important decision since land prices are high. It is assumed that customers (cars) arrive according to a Poisson process with a mean rate of 20 per hour. However, if the waiting area is full, customers will go elsewhere. The time it takes to service one customer is exponentially distributed with a mean of 4 min. The gas station will have two gas pumps. Before making a decision about how much land to acquire, the owner wants to analyze the situation further using queuing modeling.
a. Identify an appropriate queuing model to describe this queuing process. Use the corresponding formulas to calculate the fraction of time that sales will be lost for the following options regarding spaces for waiting cars (excluding the ones being served, i.e., filling gas or paying):
i. 0 spaces for waiting cars
ii. 2 spaces for waiting cars
iii. 4 spaces for waiting cars
b. Assuming the gas station is open 24 h a day, what is the expected number of lost customers per day for alternatives (i), (ii), and (iii) in (a)? If, on average, a customer generates a profit of $3 for the owner of the gas station, what is the expected lost profit per day under alternatives (i), (ii), and (iii)?
Provide complete and step by step solution for the question and show calculations and use formulas.