Selección del disco medidor

In this subsection we use the characteristics of trucks studied in part I in order to evaluate the time that it takes to complete turns at intersections. These data are used by the routing algorithm that is developed subsequently.

f

_e

g

d

h

c

The following figures describe the truck position and velocity profiles at turns that take place at intersections:

(b)

(a)

Fig 26: Truck position and velocity profile at turns

A c V t V B C Time D Velocity Tab Tbc Tcd Brake Turn Accelerate D C Tbc B A Brake Turn Accelerate Tab Tcd

Fig. 26-a shows a typical profile of truck turning at a sharp turn. Let’s assume that the truck approaches the point A as indicated by an arrow in Fig. 26-a. At this point, the truck speed is reduced while the vehicle performs the breaking maneuver as shown in Fig. 26- b. Tab is the time that breaking maneuver takes place. In other words in this duration of time, the initial constant velocity, Vc, will be reduced to the speed in turn, Vt, as the truck reaches the point B (Fig. 26-b)

The truck performs the turning maneuver at the constant speed of Vt in the time Tbc (From point B to C in Fig. 26-a and 26-b). After the turning maneuver is completed (point C in Fig 26-a and Fig 26-b), the vehicle starts increasing its speed from Vt to Vc with a constant acceleration (point C to D) in Tcd seconds. When the truck reaches the speed of Vc, it continues its trip with the same constant velocity as indicated by an arrow in point D in the Fig 26-a.

Using the notation of Fig 26, the total time To of the turning maneuver can be calculated as follows:

To = Tab+Tbc+Tcd+Tidle

where Tab and Tcd can be obtained through solving the following equation:

Tab= 2Xab/(Vc+Vt) : Tcd= 2Xcd/(Vc+Vt)

where Xab (Xcd) is the distance from point A to point B (point C to point D) and Vc, Vt are the speeds at points A and D and B and C respectively as shown in Figure 26.

Tbc can be also computed using the following formula:

Tbc=Xbc/Vt

where Xbc is the distance from B to C and Vt is the speed of vehicle in the turn BC (see Figure 26)

Tidle is the time the truck spends waiting at the traffic light.

The values of turn velocity Vt , acceleration and deceleration during the turning maneuver, turning radii (which will determine Xbc) etc., that will be used in the simulation runs, are obtained from the truck characteristics studied in Part I of this report. 3.4 Modified Dynamic Routing Algorithm

The dynamic algorithm presented in section 3.1 is modified to include the cost in time at intersections due to traffic light delays and time taken for a truck to complete a particular turn. The nodes now include the possible choices at intersections for different turning directions as well as delays due to traffic lights. In the following dynamic shortest path algorithm we have:

l(i): temporary label of node i l*(i): permanent label of node i

Tij(t): travel time from node i to node j at time t

Toij (t) is the time it takes for the truck to turn and/or wait at the traffic light at node i with destination j

Vij(t): mean speed from node i to node j in time t

Lij: the distance between node i and node j (length of link (i, j)) t(i): time the truck arrives at node i

s: starting point

Algorithm:

Step 1: Set t(s) = departure time

Tij(t(s))= Lij/Vij(t(s))+ Toij(t(s)) i, j∈V

l(i)= t(s)+Tsi(t(s)) for i≠s and i∈V, and Tsi(t(s))=∞ for i≠s and (s, i)∉E

Step 2: After (k-I) permanent labels have been established, among all the remaining temporary labels l(i), pick

Change l(k) to l*(k). If there is no temporary label left go to step 4.

Step 3: Update all nodes i’s temporary labels which (k, i)∈E by l(i) = min [l(i), l*(k) + Tki(t(s))]

Return to Step 2.

Step 4: If Vki(t(n)) ≠ Vki(t(s)) (n∈V) then s = n, Go to step 1

Otherwise stop if destination node has been reached and if not, repeat step 4.

l k l i

i

4 CASE STUDY

Several researchers have studied the truck travel patterns in the Los Angeles (LA) region, especially the dependence of these travel patterns on the locations of the major trip generators – manufacturers, warehouses, the ports, and rail yards – as well as on locations of existing trucking terminals [Hall and Lin, 1991, Banerjee et al. 1999]. Of special interest are areas with high concentration of manufacturers and warehouses, such as the area in Los Angeles City Central. This area is in the proximity of the Ports of Los Angeles and Long Beach; Union Pacific’s Long Beach intermodal terminal 20 miles south of downtown (ICTF); and the Santa Fe, and Union Pacific intermodal terminals in the vicinity of the downtown.

The recent study by the City of L.A. [Banerjee et al. 1999]) analyzed truck movement and access problems in urban industrial districts. The focus of the study was the geographical area in Central L.A. City East, at the northern end of the Alameda corridor, with a high concentration of trucks and a history of congestion and delay problems. The area includes the major rail intermodal terminals near Downtown LA, LA Intermodal Center, East LA and Hobart rail yards.

After discussions with the city of L.A., this area was chosen as a case study for the current METRANS project. The static and dynamic algorithms described in Sections 2 and 3, were modified and applied to this area as a case study. The first step was to establish a transportation network within the selected area. The transportation network consists of the truck routes within the area under study. It is represented by a set of 54 nodes, and 83 links. A link connects two nodes and a node is the intersection of two or more links. Links may be either directed, in which case they specify the direction of movement, or undirected. In this network representation, an intersection is represented by a single node, and each approach by one undirected link. The established transportation network with the node numbers and the corresponding links is shown in Figure 27.

Fig. 27. Truck route network used for the case study: Central L.A. City East

This network has been modified to account for additional links due to different turning possibilities at intersections and delays at traffic lights. The result was the introduction of additional nodes as shown in Figure 28.

Fig. 28: The traffic network with modifications to account for intersection movements

5 SIMULATIONS

The algorithms presented in sections 2 and 3, for route planning and dynamic route guidance are applied to the network of Figure 28, and tested in simulation under different traffic conditions.

In each simulation, an origin (O) and a destination point (D) are defined, for an individual truck's trip. Origin and destination addresses are located on a digitized map and their positions stored as latitude and longitude coordinates. This is done using the address geocoding abilities of ArcView GIS. Since traffic conditions vary with the time of the day, each simulation run is using two different sets of average speeds: off-peak speeds and peak hour speeds. For a given origin / destination (O/D) pair, five simulation runs are performed:

(a) Shortest geometric distance route. This is the baseline route for each O/D pair, and it is obtained by applying the algorithm using the link lengths as the associated cost. The shortest distance route is denoted by (I) in the simulation figures.

(b) Static route planning for off-peak conditions. Dijkstra's algorithm is applied to the established network, including penalties for intersection turns. The (static) minimum time route is denoted by (II) in the simulation figures.

(c) Dynamic route guidance for off-peak conditions. The initial route in this case is the same as the one obtained in part (b). As the trip progresses, however, updated information about traffic conditions becomes available. The algorithm is continuously recalculating the optimal path, and informs the drivers of any changes in the original route. The (dynamic) minimum time route is denoted by (III) in the simulation figures.

(d) Static route guidance for peak conditions. This is the same as part (b), with different network traffic conditions. The obtained route is denoted again by (II). (e) Dynamic route guidance for peak conditions. This is the same as part (c), with

different network traffic conditions. The obtained route is denoted again by (III) in the simulation figures.

The software calculates the optimal route in each case, and it provides driving directions in plain English, so that the dispatcher or driver can follow the route easily.

All the O/D pairs are chosen based on the study of the "Goods Movement Improvement Program, Phase I" (prepared by City of Los Angeles Department of Transportation, LADOT). Average speeds are based on the SCAG study: "SCAG Region Transportation Performance Indicators Technical Report " (97 RTP), and on the 98 RTP Technical Appendix – Freight Component.

Freeways Surface streets

Off-peak speeds 45 mph 25 mph