Vehicles arrive at a toll booth with a mean arrival rate of 2 veh/min (the time between arrivals is exponentially distributed). The toll booth operator processes vehicles (collect tolls) at a uniform deterministic rate of one every 20 seconds. What is the average length of queue (in vehicles), time spent in the system and waiting time spent in the queue?

Subject is Transportation Engineering The answer to the question is provided what need a is a detailed explanation of each part of the question of how the came about the answers shown in simplest terms

Drivers arrive at a toll booth at a rate of 5 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that it will take a) more one minute between consecutive drivers? b) between 30 seconds and 90 seconds between consecutive drivers?

13. An incident that occurs on a particular highway results in traffic incurring an average delay of one hour per vehicle. An estimated 2,000 vehicles are impacted by the incident. If the distribution of traffic is comprised of 5% five-axle trucks, 2% three-axle trucks, 4% six-tire trucks, 2% four-tire trucks, 4% medium auto for business purposes, 3% small auto for business purposes, and the remainder are automobiles for personal purposes, what is the value of the total delay incurred by the traffic.