Question

1. The arrival times of vehicles entering a toll facility is 50 vehicles per hour an assumed to be Poisson distributed. The public agency is looking at different toll processing options where the processing time will range from 30 veh/sec to 70 veh/sec., all of which are assumed to follow an exponential distribution.  Create graphs showing the range of estimated impacts of these toll processing options in 5 second increments along the x-axis and the following expected values of impacts along the y-axis.

1. What is the expected (i.e. average) length of queue at the toll facility (not including the vehicle being served)?
2. What will be the average waiting time of a vehicle in the system?
3. If the cost of the system generally increases with lower processing times, what would you recommend for the suggested processing time and why?

Answer 1

Exponetial distribution is the probability distribution of the time between the events which follow poisson distribution.It is mainly used to model the time elapsed between the events, Here the the arrival time of vehicle in 50 per hour and the processing time is 50 vehicle per seconds which is very fast so the the further reduction of processing time is not recommended as there is not much waiting for any vehicle in the queue or in the system the calculations and plotted graph atached