Question

A gas station with only one gas pump employs the following policy: If a customer has to wait, the price is $3.50 per gallon; if she does not have to wait, the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 20 per hour. Service times at the pump have an exponential distribution with a mean of 2 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the expected price of gasoline per gallon.

Answer 1

To determine the expected price of gasoline per gallon, we need to calculate the average price considering both scenarios: when the customer has to wait and when they do not have to wait. Using the Poisson process and exponential distribution, we can calculate the probabilities of these scenarios and multiply them with the corresponding prices to get the expected price.

Step-by-step explanation:

To determine the expected price of gasoline per gallon, we need to calculate the average price considering both scenarios: when the customer has to wait and when they do not have to wait.

In the scenario where the customer has to wait, the price is $3.50 per gallon. In the scenario where the customer does not have to wait, the price is $4.00 per gallon. We need to determine the probabilities of these two scenarios.

Using the Poisson process with a mean rate of 20 per hour, we can calculate the probability of a customer arriving within a certain time period. Then, using the exponential distribution with a mean of 2 minutes, we can calculate the probability of a customer being served within a certain time period.

By multiplying these probabilities with the corresponding prices, we can calculate the expected price of gasoline per gallon.