question 1 demand elasticity commuters in a


Question 1  (Demand Elasticity )

Commuters in a medium-sized city can travel either by automobile or by bus. The demand for automobile travel has been estimated to be

981_Q_1.png All exponents are constant elasticities (direct or cross).

where:

Q     =   automobile trips per hour (peak-hour)

a     =   constant

A     =   travel time by automobile (in minutes)

B     =   travel time by bus (in minutes)

C     =   average cost by automobile (in cents)

D     =   average cost by bus (fare, in cents)

 

(a)      The exponent of D in the above equation is +0.75.  What does this say about the effect of bus fare on the demand for auto travel?

(b)      Is the demand for auto with respect to auto travel-time elastic or inelastic?  Please explain.

(c)       Because of the congestion that is likely to occur on this corridor, the travel time by automobile would increase by 20%, and travel time by bus would increase by 10%.  At the same time, auto travel costs are expected to increase by 5% and bus costs (fare) would be decreased by 15%.  Based on the equation above, what will the percent change in auto travel be?

Question 2 (Congestion Pricing )

Please explain (if possible with diagrams) how is the introduction of a high-occupancy lane (HOV) on a highway equivalent to congestion pricing (e.g., charging monetary toll) in order to bring efficiency (system optimality) in peak traffic flows.

 

Question 3  (UTP - Trip Distribution)

A four-zone study area has the trip productions (origins) and zonal attractiveness shown in the Table 1.   The inter-zonal and intra-zonal friction factors are as given in Table 2.

1823_table_1.jpg

1752_table_2.jpg

Determine all zonal interchange volumes (Tij), using the gravity model.

 

Question 4. (Mode Choice)

A city commuter population has the following modal utility function, Uk = Ak - 0.003C - 0.04T

 

Where        Ak   constant for mode k

                 C    out-of-pocket travel cost in cents.

                 T    riding time in minutes

(a)    Apply the logit model to calculate the market shares of the two travel modes used in the city.

 

                           Mode                        Ak                     C                      T

                           Automobile               -0.20                240                  25

                           Regular city bus        -0.60                  80                  55

 

(b)   Suppose, in addition to the regular city bus, a private company starts its bus service along the same routes as the city bus with the following characteristics:

                           Mode                        Ak                     C                      T

                           Private bus                -0.60                  80                  55

 

            Determine the new market shares of auto, city bus and private bus.

 

Question 5 (10 points) (All-or-nothing / incremental assignment)

For the network shown below, 4 units of flow go from node 1 to node 3.  The average travel time functions on these links are:

ta = 3 + Xa2

tb = 1 + 3Xb

tc = 2 + Xc

(a)    Assign the 4 units of flow from node 1 to node 3 using incremental ( i.e., one unit at a time) capacitated ALL-OR-NOTHING assignment technique.  Show your work step by step as well as the final link flows  (Xa , Xb , Xc ).

(b)   Are the resulting flows in system optimum or user equilibrium?  Please explain.

Question 6 (User-Equilibrium vs. System Optimum Traffic Assignment)

 

For the network shown below, the following origin-destination volumes are the only volumes to be assigned to the network:VAC = 800               VBC = 100      VBD = 900

The link travel time (average travel time) functions are as follows (all times are in minutes): 


t1  =  10 + 0.01 x1

t2  =    3 + 0.02 x2

t3  =    2 + 0.02 x3

t4  =    3 + 0.02 x4

t5  =    4 + 0.02 x5

t6  =  12 + 0.01 x6

 

t7  =    4 + 0.02 x7

(For both parts (a) and (b ), round up your time calculations to the nearest tenth of a minute.)

 

(a)   A CEE 3610 student calculated the user-equilibrium link flows as follows:


x1  =                            780

x2  =   20

x3  = 202

x4  = 120

x5  =                                     182

x6  =                                     818

x7  =                                      82 

Is he correct?  Why?

(b)   Another CEE 3610 student calculated the system-optimum link flows as follows:


x1  =    749

x2  =    51

x3  =    222

x4  =    151

x5  =    171

x6  =    829

x7  =    71


Is she correct?  Why? 

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