Instantaneous Dynamic Equilibria for dynamic Flows

This repository contains a calculation tool for Instantaneous Dynamic Equilibrium Flows (IDE-flows) for both the discrete and the continuous case.

For the definition and more theoretical information about IDE-flows, see this.

Running the program

Discrete Case

In Math/data.py the input data has to be specified. This includes:

• R: a list containing for each player the exact point in time where the player enters the network
• ST: a list containing tuples of length 2 according to the following example: the tuple (i,j) with index k in ST indicates that player k+1 wants to travel from source si to sink tj
• alpha: value in [0,1]. Describes the significance of the traveltime and the waiting time for the cost of an edge. For values towards 0 this is weighted towards the traveltime, for values closer to 1 the waiting time takes more impact. Default value: 0.5, where both quantities take the same impact
• kanten_queue: a list containing all edges, where virtual players shall be added
• start_queue: for each edge in kanten_queue this list contains a point in time, where the virtual inflow into the edge starts
• ende_queue: for each edge in kanten_queue this list contains a point in time, where the virtual inflow into the edge stops
• y0_queue: for each edge in kanten_queue this list contains the amount of virtual inflow that will be added
• graph: directed graph as dictonary, if this is not specified, the program will read the graph from the file GraphenGEXF/myGraph.gexf

Once Math/data.py contains all information, run Math/Main.py, which will create a Math/Application.py.

Continuous Case

In Math/cont_data.py the input data has to be specified. This includes:

• u: a list of inflow rates. For each node this contains a list of tuples of length 2, where each tuple contains two values <starting time> and <flow value>, indicating an inflow of <flow value> flow volume, starting at <starting time> until the <starting time> of the next tuple in the list
• graph: directed graph as dictonary, if this is not specified, the program will read the graph from the file GraphenGEXF/myGraph.gexf
• table_output: Boolean value. If True, an OutputTable will be created, otherwise the program will return the raw data (see Math/cont_data.py)

Once Math/cont_data.py contains all information, run Math/ContMain.py, which will create a Math/ContApp.py.

Graph Editor

The GraphEditor can be used to create .gexf-files for graphs which can then be read into the programs described above. It is based on Sigma, a JavaScript library dedicated to graph drawing, mainly developed by @jacomyal and @Yomguithereal. See also sigma.js-1.2.1/README.md.

To create graphs, open sigma.js-1.2.1/GraphEditor/meinGraph.html. Once the graph is created, its .gexf-file can be downloaded via the Download-Button. Saving it in GraphenGEXF/myGraph.gexf will result in the graph being read into the program.