There are two alternative Plans for operating a high-speed inter-city rail service. In Plan I, the service connects city A with city B through city C where the rail makes a stop to load or unload passengers. The rail transportation system is assumed to be perfectly symmetrical with respect to direction of travel. PLAN I The link travel times are 2 hours between each pair of cities in both directions. The time it takes to service the train at each node is 0.5 hours. In the alternative Plan II, the train company considers to stop servicing the smaller city C, in order to provide a better level of service for the users in the city A and city B. PLAN II According to Plan II, the travel time between the major cities A and B in both directions will be reduced to 3.5 hours. The time it takes to service the train in both city A and city B is still 0.5 hours. Q2 (A) Calculate the train-cycle for Plan I and Plan II. Q2 (B) How many trains do you need to operate 12 trains/day uniformly distributed throughout the day for Plan II? Q2 (C) With that number of trains, for both Plan I and Plan II, what rail service frequency can be provided for each Plan, assuming that the trains are uniformly distributed through the day?
There are two alternative Plans for operating a high-speed inter-city rail service. In Plan I, the service connects city A with city B through city C where the rail makes a stop to load or unload passengers. The rail transportation system is assumed to be perfectly symmetrical with respect to direction of travel.
PLAN I
The link travel times are 2 hours between each pair of cities in both directions. The time it takes to service the train at each node is 0.5 hours. In the alternative Plan II, the train company considers to stop servicing the smaller city C, in order to provide a better level of service for the users in the city A and city B.
PLAN II
According to Plan II, the travel time between the major cities A and B in both directions will be reduced to 3.5 hours. The time it takes to service the train in both city A and city B is still 0.5 hours.
Q2 (A)
Calculate the train-cycle for Plan I and Plan II.
Q2 (B)
How many trains do you need to operate 12 trains/day uniformly distributed throughout the day for Plan II?
Q2 (C)
With that number of trains, for both Plan I and Plan II, what rail service frequency can be provided for each Plan, assuming that the trains are uniformly distributed through the day?
Q2 (D)
Calculate the travel demand between all pairs of cities for both Plan I and Plan II as well as the corresponding company revenues for all city pair services and in total. The travel demand Q between any pair of cities is given by the following formula:
Q= K F / T P *1000
where
K is coefficient taken from the K Matrix between any city pair;
T is the travel time (hours) between city pairs;
F is the train service frequency (trains per day);
P is the fare price (€) taken from the P Matrix between city pairs.
The following information in the form of origin-destination matrices are also given about the travel demand and the fare price between any pair of cities.
K Matrix of coefficients used to estimate demand between any pair of cities
|
|
City B |
City C |
City A |
|
City B |
50 |
200 |
|
|
City C |
50 |
|
100 |
|
City A |
200 |
100 |
|
Fare P Matrix of travel cost (in euro) between any pair of cities
|
|
City B |
City C |
City A |
|
City B |
30 |
60 |
|
|
City C |
30 |
|
30 |
|
City A |
60 |
30 |
|
Q2 (E)
From the train company viewpoint and according to the revenue maximizing or ridership maximizing objectives, explain whether or not the train should make a stop at city C?
Q2 (F)
Assuming now that only Plan II exists, and considering the travel and service times and the K matrix as fixed, how (i) a reduction in fare prices and (ii) an increase of train frequency (adding a new train), would be justified on the basis of a revenue maximizing and a ridership maximizing strategy.
Q2 (G)
What are possible limitations and shortcomings in the model used in the above analysis?
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