CE361 Introduction to Transportation Engineering

Out:  Friday 28 September 2001

Homework 3

Due:  Friday 5 October 2001

 

QUEUEING SYSTEMS

 

Dear Consultant:

 

A stop-sign-controlled intersection near a growing employment center (industrial and commercial) has become the site of long traffic backups during peak periods.  For example, on a typical weekday from 4:40 PM to 6:00 PM, the average traffic volume on each approach is 300 vehicles per hour.  Because all four approaches have queues of vehicles waiting to be “served”, the service rate drops to a congested rate of 4 vehicles per minute per approach.  Before any improvements are proposed, let us see if the existing situations can be analyzed.

 

 

1.       Review of Course Notes Chapter 3, Lessons 4 and 5.

A.      (2 points) Is the general level of the presentation in Chapter 3, Lessons 4 and 5 too simple, too difficult, or about right for you?

B.      (3 points) Which sections were the most helpful in understanding the material?  Which sections were confusing or otherwise inadequate?  Which concepts need to be presented better?  Specific comments, please.

 

2.       Queueing Diagram.  For the questions below, present your work clearly.

  1. (20 points)  Draw the queueing diagram that illustrates the situation described in the introduction to this HW.  Label the diagram clearly. 
  2. (10 points)  What is the maximum queue length that will occur?
  3. (10 points)  What is the longest time any vehicle will have to wait?
  4. (10 points)  At what time will the peak period queue dissipate, if at 6:00 PM the arrival rate drops to 75 vehicles per hour and the service rate improves to 8.5 vehicles per minute per approach?
  5. (15 points)  What is the total vehicle delay incurred from 4:40 PM until the queue dissipates?

 

3.       Queueing Equations.  In CNotes Example 3.5.1, the onramp was assumed to be an M/M/1 queueing system with l = 400 vph and m = 500 vph.  Let us consider a second onramp, with l = 800 vph and m = 1000 vph.

  1. (10 points)  What is the average queue length on the second onramp?
  2. (10 points)  What is the average waiting time on the second onramp?
  3. (10 points)  How long will the average driver spend waiting on the second onramp?