#230 Vehicles begin to arrive at a park entrance

Vehicles begin to arrive at a park entrance - Civil Engineering

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Free Chegg Question

Vehicles begin to arrive at a park entrance at 7:45 A.M. at a constant rate of six per minute and at a constant rate of four vehicles per minute from 8 A.M. on. The park opens at 8:00 A.M. and the manager wants to set the departure rate so that the average delay per vehicle is no greater than 9 minutes ( measured from the time of the first arrival until the total queue clears). Assuming D/D/1 queuing, what is the minimum departure rate needed to achieve this?

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Free Chegg Answer

Vehicles arrive at the rate of 6 per minute from 7.45 A.M. constant rate of vehicle arrival is equal to 4 per minute from 8 aM

Park will open at 8.00 AM There should not be delay more than 9 minutes for any vehicles.

Summarize the vehicle arrival at the park entrance as below.

The queue will occur at the time after 15 minutes.

Assume that the queue will be completely cleared t minutes after the first 15 minutes.
Arrival ate is 90 + (t) x 4.

Take the departure rate is denoted as p.

The number of vehicles departed will be p x t will the queue has cleared.