Network model of commuter’s choices In the case shown in Figure P6.3, a commuter wishes to travel from his residence near station A to his place of employment at D. The commuter’s transportation choices are:
Headways between subways on all lines are exactly 10 minutes. Moreover, the subway schedules are coordinated so that a line 2 train to D passes through B exactly 4 minutes after a line 1 train has stopped at B. and similarly, a line 3 train to D passes through C exactly 4 minutes after a line 1 train has stopped at C. Assume that transfer times and stop time are negligible.
Headways between buses at A are also constant and equal to 10 minutes.
a.Assuming that the commuter is aware of the bus schedule and of the subway schedule and that he times his arrival at A so that it coincides with the passage of whatever vehicle he chooses to ride, prepare a network model for the situation shown in Figure P6.3. The network model should be such that a shortest-path algorithm, such as Algorithm 6.1, can be used to find the shortest path from A to D.b.Assume now that all headways in this problem (for buses and subways) have negative exponential pdf’s all with means of 10 minutes. The commuter now arrives at a random time relative to the passage of buses or subways from A. In addition, all subway lines are operating independently of each other or of the bus. Prepare a network model for this new situation such that one can determine, through a shortest-path algorithm, the transportation mode and route that offers the shortest expected travel time between A and D.c.What is the preferred route (and mode) in each of parts (a) and (b) ? What is the shortest expected travel time in each case?
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