Queuing System

1. A theme park has a single entrance gate where visitors must stop and pay for parking. The average arrival rate during the peak hour is 150 veh/h and is Poisson distributed. It takes, on average, 20 seconds per vehicle (exponentially distributed) to pay for parking. What is the average waiting time for this queuing system?

a) 4.167 min/veh b) 2.0 min/veh c) 1.667 min/veh d) 0.833 min/veh

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2. At an impaired driver checkpoint, the time required to conduct the impairment test varies (according to an exponential distribution) depending on the compliance of the driver, but takes 60 seconds on average. If an average of 30 vehicles per hour arrive (according to a Poisson distribution) at the checkpoint, determine the average time spent in the system.

a) 0.033 min/veh b) 1.5 min/veh c) 1.0 min/veh d) 2.0 min/veh

3. A toll road with three toll booths has an average arrival rate of 850 veh/h and drivers take an average of 12 seconds to pay their tolls. If the arrival and departure times are determined to be exponentially distributed, how would the probability of waiting in a queue change if a fourth toll both were opened?

a) 0.088 b) 0.534 c) 0.313 d) 0.847

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