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Random walk on a graph -- Simulating a drunk outbreak

You've got a brilliant idea coming back from the pub: you will create a startup that maintain a network of public toilets, and you will charge the city council based on how many people use them. You have everything sorted: you will have connected toilets coated with a smart compound to keep them clean. One problem remains: you need to optimise the placement of the toilets so you get a maximum of use to charge with the minimum amount of hardware. With this project, you will simulate drunk people wandering in town in order to make decisions about your business, and you will display your simulation using pyGlet.

I provide a map of the city taken from OpenStreeMap. The map is a compressed XML file that describes the city as a graph where each intersection or bend in a road is a vertex (also called node), and each road is an edge. I also provide a parser that reads the XML file and returns a graph to be used with the NetworkX library.

The simplest model is to represent drunk persons as "tokens" on the graph which starts on a random node, and which randomly move from one node to a connected one. Once this simple rule is implemented, more complex ones can be added:

  • Are the drunk people more likely to start near pubs?
  • Do the drunk people aim for a random "home" on the map?
  • Do they aim for your toilets if there are some in the area?
  • Do they gather where they are other drunk people?
  • Do they try to avoid police patrols?
  • Are they actually zombies?

Beyond the project, similar models are used to simulate metabolic pathways.

Here is how to use the provided code:

# Assuming your code, the provided code, and the map file are in the same directory
import osm2graph

import gzip  # the map file is compressed with the gzip algorithm

with gzip.open('planet_-1.275,51.745_-1.234,51.762.osm.gz') as infile:
    graph = osm2graph.read_osm(infile)

# Get a list of all the node names
node_names = list(graph.nodes)
# Get the name of the first node
first_node = node_names[0]
# Get the longitude and latitude of the first node
longitude = graph.nodes[first_node]['lon']
latitude = graph.nodes[first_node]['lat']

# Get a list of the edges. Each edge is a tuple of the node names at its
# extremities.
edge_list = list(graph.edges)

Look at the documentation of NetworkX to see how to manipulate the graph object.