Conversion of Models

The conversion of fixed-time traffic signal control from the simulation to the

optimiza-Overall Process

tion model is straightforward and is successfully used for the studies in Köhler and Strehler (2010, 2011); Strehler (2012). In contrast, converting the network and the de-mand of the base case from Sec. 5.2 to the optimization model is more complex. The semantics of input is different and the problem size has to be reduced. The following steps are described in the subsequent paragraphs:

• Reduce the network size so that it is computationally feasible for the optimization model.

• Convert the demand from x,y coordinates (MATSim convention) to aggregated commodities starting at nodes of the reduced network (optimization model con-vention).

• Adjust the parameters of the network and demand conversion so that the opti-mization model generates useful results within acceptable running times.

• Combine the single steps to a meaningful conversion process.

(a) Subnetwork (black) for the signalized area (b) Subnetwork as graph, not required vertices are removed

Figure 5.14.: Reduction of network size Reduction of Network Size

The bounding box around the signalized area is used to reduce the size of the network. Network Size

All links of the full network are retrieved that start or end in this bounding box. This part or the network is still too big to be used as input for the optimization model. Its size is further reduced heuristically. Only links are selected that cover the bounding box and that have one of the following properties:

• A signal is located at one of the nodes that define the start or end point of the link.

• The speed limit of the link is greater than 10m/s.

• The link is part of the shortest path between signalized nodes. For the shortest path calculations the length of each link defines the cost function.

The resulting subnetwork is shown by the black lines in Fig. 5.14a, the black dashed lines depict the bounding box.

This subnetwork still contains nodes that are not essential for a graph representation in Network to Graph

terms of Sec. 3.1. Nodes with only one incoming and outgoing link in each direction that possess exactly same properties (vertices of degree 2 in an undirected graph) are

(a) O-D pairs with minimum flow of 50 vehi-cles

(b) O-D pairs with minimum flow of 10 vehi-cles

Figure 5.15.: Synthetic population of the Cottbus scenario converted to commodities removed. The resulting graph is shown in blue in Fig. 5.14b. The gray network in the background is identical to the network shown in black in Fig. 5.14a. In a last step, crossings are unfold in the sense of Köhler and Strehler (2010, 2011); Strehler (2012).

The resulting graph serves as input for the optimization model.

Conversion of Demand

With the results of the base case presented in Sec. 5.2 a dynamic traffic assignment for

Persons to

Commodities the virtual population is available. This assignment is converted to static commodities under the assumption that 1 vehicle is equivalent to 1 unit of f low. The morning and the evening peak are converted separately, but using the same procedure. If a route of a virtual person traverses links of the subnetwork shown in black in Fig. 5.14a an O-D pair is created. The first link on the route that is contained by the subnetwork is the origin. The destination is the last link on the route within the subnetwork. If the O-D pair for the link was already created for a different route, the flow for the existing O-D pair is increased by one. If the subnetwork is traversed several times by a route, more than one O-D pair is affected. The resulting O-D pairs are then mapped to the

reduced graph representation shown in Fig. 5.14b and serve as commodities for the optimization.

Parameter Adjustments

Flow is one for many commodities. Others have a flow of up to approx. 300 vehicles. Commodity Reduction

After a first experiment, it turned out, that the optimization is not capable to calculate a good solution for all commodities. To limit the number of commodities, a threshold is introduced. If the flow of a commodity is less than the threshold, the commodity is refused. Fig. 5.15 shows the effect of this threshold: In Fig. 5.15a only commodities are depicted that have a minimum flow of 50. Fig. 5.15b shows O-D pairs with minimum flow of 10. The threshold of 50 removes around 55 % of overall flow in the subnetwork, the threshold of 10 approx. 28 %.

The graph used for optimization needs transit times and capacities as attributes for each ^Network edge. As transit time the travel time at freespeed is taken from the simulation network.

The commodities are gathered for a certain time interval ∆T_OD from the simulation, e.g., the duration of the morning peak. The simulation network specifies the maximum flowc_{f low}per∆t. These intervals can be used to resolve time dependency of capacity. To derive capacities of the static graph, also the effect of the refused commodities should be considered. If the threshold refuses γ of the overall flow in the subnetwork, the capacity of each edge in the optimization model is set to

(1−γ)·c_{f low}·^∆TOD

∆t .

Note, that the subsequent results are computed with γ = 0.0 instead of approx. γ = 0.55 (minimum flow 50) orγ=0.28 (minimum flow 10).

The traffic assignment that results from the optimization model for all commodities with flow greater 10.0 is shown in Fig. 5.16.

Conversion Process

The traffic assignment of the base case is converted for the morning (05:30 to 09:30) and the evening (13:30 to 18:30) peak. The outputs of the conversion are solved by the op-timization separately. Then, only the coordination of traffic signals is converted back to the simulation model. In contrast to the base case, coordination for the morning and evening peak differs. The fixed-time control of the simulation exchanges the coordina-tions at noon.

0 0.01 - 260 260 - 520 520 - 780 780 - 1040 1040 - 1300

Figure 5.16.: Traffic assignment of the optimization model. Edges are colored by to-tal flow assigned. (Source: Own figure, based on results provided by M. Strehler)

Basecase

Base case

Optimization

Traffic Actuated iteration(s)

iteration(s)

iteration(s)

compare

Figure 5.17.: Run sequence for simulation of different traffic signal control strategies