From:Principles of Highway Engineering and Traffic Analysis 5th edition, problem

Question

From:Principles of Highway Engineering and Traffic Analysis 5th edition, problem 5.16

**Please show in depth step by step solution! I dont understand how the book solution shown on chegg got each of those points on the graph!!! I need an explanation and equations on how you solved for all of the points!!***

Vehicles begin to arrive at a parking lot at 6:00 AM at a rate of eight per minute. Due to an accident on the access highway, no vehicles arrive from 6:20 to 6:30 AM. From 6:30 AM on, vehicles arrive at a rate of two per minute. The parking lot attendant processes incoming vehicles (collects parking fees) at a rate of four per minute throughout the day. Assuming D/D/1 queuing, determine the total vehicle delay.

Explanation / Answer

number of vehicles arriving between 6:00 and 6:20 = 20 x 8 = 160

number of vehicles processed by the attendant = 20 x 4 = 80

no vehicles come in the next 10 minutes

number of vehicles processed by the attendant in the 10 minutes = 10 x 4 = 40

total number of vehicles processed = 120

cars left = 160 - 120 = 40

number of vehicles coming = 2 per minute

let the total vehicle delay be "t"

then,

2t = 4t - 40

2t = 40

t = 20

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