Question

At an impaired driver checkpoint, the time required to conduct the impairment test varies (according to an exponential distribution) depending on compliance of the driver, but takes 60 seconds on average. If an average of 30 vehicles per hour arrive (according to a Poisson distribution) and there is a single lane at the checkpoint, determine the average time spent in the system. a. 0.033 min/veh b. 1.0 min/veh c. 1.5 min/veh d. 2.0 min/veh

Answer 1

Answer:

Option (d) 2 min/veh

Explanation:

Data provided in the question:

Average time required = 60 seconds

Therefore,

The maximum capacity that can be accommodated on the system, μ = 60 veh/hr

Average Arrival rate, λ = 30 vehicles per hour

Now,

The average time spent by the vehicle is given as

⇒ $\frac{1}{\mu(1-\frac{\lambda}{\mu})}$

thus,

on substituting the respective values, we get

Average time spent by the vehicle = $\frac{1}{60(1-\frac{30}{60})}$

or

Average time spent by the vehicle = $\frac{1}{60(1-0.5)}$

or

Average time spent by the vehicle = $\frac{1}{60(0.5)}$

or

Average time spent by the vehicle = $\frac{1}{30}$ hr/veh

or

Average time spent by the vehicle = $\frac{1}{30}\times60$ min/veh

[ 1 hour = 60 minutes]

thus,

Average time spent by the vehicle = 2 min/veh

Hence,

Option (d) 2 min/veh