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 reduces the serving time considerably: it has been estimated that a good model for the time would be a Normal distribution with mean 6 and standard deviation 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.