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

Answer 2

Based on the vehicles coming per hour and the compliance of the driver, the average time spent in the system is b. 1.0 min/veh.

There are 30 vehicles coming per hour which means that the rate per minute is:

= 60 / 30

= 1 car every 2 minutes

There is a single lane at the checkpoint which means that only one car can go through at a time.

Each car will spend 60 seconds or a minute to be inspected which gives enough time for another vehicle to arrive and be inspected immediately it arrives for 60 seconds.

The total time spent in the system is therefore 60 seconds per car.

In conclusion, option B is correct.

Find out more on Poisson distributions at https://brainly.com/question/10196617.