Part 1: A single-lane freeway exit toll booth has a traffic flow volume of 300 vehicles per hour. The toll booth operator averages about 10 seconds to process a toll.

Assume that the arrival times can be represented by a Poisson distribution and the service times by an exponential distribution (M/M/1 model). Determine:

- Probability of no cars in the system Mean Time Waiting in the line

- Mean Time in the system

- Utilization

- Average number of cars in the line

- Average number of cars in the system

- Probabilities of 1,2,3. . . cars in the system

Simulate the behaviour of this WL in EXCEL for 1100 customers, discard the first 100 cus- tomers and collect data over the next 1000 customers. Find approximations to

- Probability of no cars in the system Mean Time Waiting in the line

- Mean Time in the system

- Utilization

- Maximum Time Waiting in the line

- Probability of waiting more than 5, 10, 15, 20. . . seconds

Part 2: The company decided to introduce Credit Card payments which reduce the serving time considerably: it has been estimated that a good model for the time would be a Normal distribution with a mean 6 and a standard deviation of 0.8 seconds. The problem is that the company expects only 30% of the customers to use this service.

Simulate the waiting line with this new serving discipline. Compare the new results with those obtained in Part 1.