Initial Track Capacity Allocation

5.5 Initial Track Capacity Allocation

Terminal delays are estimated in the simulation framework by measuring the delays of shipments carried by the trains at the terminals once shipments are moved through the network according to the train timetable. These terminal delays are fed to the train slot

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generation model. Thus, an initial timetable is required for the first run of the simulation platform that does not require the terminal delays as input.

For a given route, associated frequency, and residual track capacity, an initial timetable is constructed by assigning as many trains to a train slot as are permissible or by assigning a preset number of trains to train slots. Track capacity constraints must not be violated. In this initial run, only the freight basecase flows are employed in assessing the residual track capacities. In later runs, the residual capacities are computed based on updated estimates of flows in the network given new rail services. Trains are assumed to travel at a constant average speed. Train slots are allocated in proportion to the suggested frequencies along the routes. This procedure of assigning trains to train slots is referred to as the initial track capacity allocation technique.

Before applying the initial track capacity allocation technique, the routes are ranked from longest to shortest according to their average travel times, assuming that delays at intermediate terminals are zero. In each iteration of the initial track capacity allocation technique, the route with the highest rank is selected (if not previously selected) and a train slot is constructed along that route. Each train slot, by definition, must connect the origin and destination nodes ordered in time. In addition, the train slot designates the order in which intermediate terminals are visited. A train slot consists of a departure arc, several process/siding and movement arcs, and an arrival arc along the time-space network. To determine potential departure times (i.e. a departure arc in the time-space network), the minimum required headway between trains employing the same track and heading toward the same terminal must be considered. The process/siding arc must accommodate the minimum

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required terminal process time for the shipments. Given the earliest time that the train can leave from the terminal after the train finishes its required activity (e.g. shipments pick- up/drop-off or the train cars classification/reclassification), an earliest feasible track time capacity on the movement arc is sought between the departure terminal and the arrival terminal. The arc employed for the arrival of the train at the destination terminal is the arrival arc. Once track time capacity on every track segment between all consecutive terminals is assigned, the train slot is constructed. The initial track capacity allocation technique is described next.

Initial Track Capacity Allocation Technique

Step 1. (Initialization)

Let k F denote the frequency of the train slots constructed on route k . F = 0 , ∀ k ∈ K .

Step 2. (Select a route)

2.1 Check k F , ∀ k ∈ K . If F reaches the required frequency, K = K \k { } . If K = ∅ , terminate. Otherwise, let B denote a set of the routes which do not

meet train frequency requirements. B= K .

2.2 If B = ∅ , return to Step 2.1. Otherwise, select a route k ∈ B with the longest travel time. B = B \k { } . Construct a train slot along route k for the available

track capacity p A in G. p

Step 3. (Construct a train slot)

3.1 Choose feasible departure arc q ( α , u ) , where u ∈ E

i and α = f .

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Search the earliest available track time capacity between pseudo super-source node α and the origin terminal

f in the arc set p A in p G . If a feasible train departure arc cannot be identified, K = K \k { } and return to Step 2.2. Otherwise,

continue.

3.2 Choose feasible movement arc ( q , r u v ) , where v ∈ E i , u ∈ E i , u ≠ v . Let q denote the train i’s earliest feasible departure time at terminal u. Starting

from time q, search the earliest available track time capacity from terminal u to terminal v. If a feasible movement arc cannot be identified, return to step 2.2. If the arrival terminal v is a destination terminal g, go to Step 3.4. Continue, otherwise.

3.3 Choose feasible process/siding arc ( r , q v u ) , where v ∈ E i , u ∈ E i , u = v . Let r denote the train i’s arrival time at terminal v and q denote the time when the

train finishes its required activity at the terminal. Return to Step 3.2.

3.4 Choose feasible arrival arc r ( v , β ) , where v ∈ E

i and v = g .

One train slot is obtained. Let k F = F + 1 . Return to Step 2.2.