=========================preview======================
(civl262)[2009](s)Quiz8-solution~PPSpider^_10075.pdf
Back to CIVL262 Login to download
======================================================
CIVL 262 C Introduction to Transportation System
Tutorial Quiz 8 17 April 2009
Name : Student ID :
QUESTION 1. The v-k relationship for a particular roadway was found to be:
Speed is in miles per hour and density k is in vehicles per mile, determine the free-flow speed, capacity (maximal flow rate), and jam density of the roadway. Traffic moving on the roadway at a density of 30 veh/mile is stopped for 30 seconds at a red traffic signal. After this red time, a green time of G seconds is provided to clear traffic. After which, the traffic signal returns to 30 seconds of red, and so on in a cyclic manner. Determine the minimum green time G needed so that the queue will not grow from cycle to cycle (the stopped flows density is jam density and the release traffic moves at the capacity of the roadway).
QUESTION 2. A bus system consisting of 50 buses (50-seaters) charges $1.00 per ride (currently, the buses are fully utilized). It has been decided to put 10% more buses into service. What should be the new fare per ride in order to achieve full utilization of capacity if the price elasticity of demand for ridership is -0.4? What will be the additional consumers' surplus generated by this action.
QUESTION 3. A rapid transit system has estimated the following costs of operation for one of its routes, making a variety of combinations of cars per train. Plot the information for each combination, indicating the total cost, the average cost, and the marginal cost of operating the system. What is the optimum number of cars per train that should be operated?
Solutions
Question 1. From model, , we get the
relationship
and
relationship
. The free flow speed, capacity and jam density are shown in the figures, geographically.
At initial situation (A), density is =30 veh/hr, from the
relationship, we know the corresponding flow veh/hr. After the traffic is stopped by red light (B), the speed
, flow , and density is jam density veh/mile. The speed of the shock wave can be calculated as
mile/hr. The direction is backward. During the red traffic light, the queue is formed .
After the green light begins (C), the vehicles are released and a new shock wave is formed at the front platoon. In this situation, the vehicles are released at capacity
veh/hr, and the corresponding density
veh/mile. The speed of the new shock wave can be calculated as
U mile/hr. The direction is backward. During the green traffic light, G,
, the queue will surely be cleared. The required green-light time should be
seconds.
(The assumption that the vehicles are released at capacity implies the vehicles leave at speed and . There is no problem for Question 1.)
Question 2. To keep the full utilization (50 (1+10%) buses times 50 seats each = 2750 trips), the percentage change of the fare should satisfy , or
$ per ride. The generated cons