Systematic comparison of trip distribution laws and models

R package

We recently developed an R package to facilitate the use of this package (and more) with R.

Description

This package has been designed to estimate mobility flows as described in [1]. In this paper, we propose a comparison between the gravity and the intervening opportunities approaches widely used to simulate mobility flows. To fairly compare the two approaches, we need to differentiate the trip distribution laws, gravity or intervening opportunities, and the modeling approach used to generate the flows from the laws. Indeed, both the gravity and the intervening opportunities laws can be express as the probability of having a trip from one place to another and based on these probabilities, the total number of commuters or migrants can then be calculated using different level of constrained models.

First, we compute the probability pij to observe a trip from region i to another region j based on the "travel demand" mi of the region i (the population is typically used as a surrogate), the "attractivity" mj of the region j (usually related to the population in j too) and the distance dij between the two regions. In this package we consider eight probabilistic laws:

• Gravity law with an exponential distance decay function (GravExp).
• Normalized gravity law with an exponential distance decay function (NGravExp).
• Gravity law with a power distance decay function (GravPow).
• Normalized gravity law with a power distance decay function (NGravPow).
• Schneider's intervening opportunities law (Schneider) [2].
• Radiation law (Rad) [3].
• Extended radiation law (RadExt) [4].
• Uniform law (Rand).

The importance of the distance and/or the scale is adjusted with a parameter beta (except for the original radiation law and the uniform law).

Second, several constrained models are proposed to generate a spatial network from these distribution of probability respecting different level of constraints (preserving the marginals Oi and/or Dj of the observed OD matrix) according to the model:

• Unconstrained model (UM).
• Production constrained model (PCM).
• Attraction constrained model (ACM).
• Doubly constrained model (DCM).

Contents of the package

All the inputs and outputs files are in csv format with column names in the first row and no row names (the value separator is a semicolon ";"). Note that the row number and the column number for the matrices is an implicit ID. See the example for more detailed.

Inputs:

• Parameters.csv: File containing the four parameters:
  • Law: GravExp, NGravExp, GravPow, NGravPow, Schneider, Rad, RadExt or Rand.
  • Model: UM, PCM, ACM or DCM.
  • Beta: Parameter used to adjust the importance of the distance and/or the scale. Not necessary for the original radiation law or the uniform law.
  • Replication: Number of replications r.
  • Write_pij: true to write the matrix of probabilities pij in a csv file.
• Inputs.csv: File with n lines (n represents the number of regions) and 4 columns (mi and mj, Oi and Dj).
• Distance.csv: n x n distance matrix.
• OD.csv: n x n observed OD matrix.
• Sij.csv: n x n "opportunity" matrix. Only for the intervening opportunities laws, can be generated with the function Sij.java.

Functions:

• TDLM.java: This class takes as inputs all the inputs described above (except Sij.csv depending of the case). It returns r simulated OD matrices S_1.csv, ..., S_r.csv.
• Sij.java: This class takes as inputs the files Inputs.csv and Distance.csv and it returns the "opportunity" matrix sij.csv.
• GOF.java: This class takes as inputs the files Inputs.csv, OD.csv, Distance.csv and r simulated OD matrices S_1.csv, ..., S_r.csv. It returns a file GOF.csv containing the three goodness-of-fit measures described in the paper (CPC [5] [6] [7], CPL and CPCd) between the observed OD matrix and each of the simulated OD matrices.

Compiling

The package contains the source code (Java) and an example of inputs (see below). Java Code can be easily run and compiled with IDEs such as Apache Netbeans or Eclipse. If you are not familiar with these softwares you can also compile and run Java Code from a Command Line.

Before the Java virtual machine can run a Java program, the source code must be compiled into byte-code using the javac compiler using the command:

javac TDLM.java

Once you have successfully compiled your Java Code, you can run the code using the command:

java TDLM

The Java files and the inputs must be in the same directory.

Example

A zip file containing all the inputs of the USA case study is available here.

• Parameters.csv:
  • Law: GravExp
  • Model: UM
  • Beta: 0.0374466723531956
  • Replication: 5
  • Write_pij: true
• Inputs.csv: File with 3108 lines and 4 columns:
  • mi = population in county i.
  • mj = population in county j.
  • Oi = number of out-commuters in county i.
  • Dj = number of in-commuters in county j.
• Distance.csv: 3108 x 3108 distance matrix. Great circle distance between the centroids of the counties.
• OD.csv: 3108 x 3108 observed OD commuting matrix.

The inputs come from the United State Census Bureau. The commuting trips between United States counties in 2000 are available online. This dataset is the USA dataset in the paper and it has also been used in [3] and [6].

References

[1] Lenormand et al. (2016) Systematic comparison of trip distribution laws and models. Journal of Transport Geography 51, 158-169.

[2] Schneider (1959) Gravity models and trip distribution theory. Papers of the regional science association 5, 51-58.

[3] Simini et al. (2012) A universal model for mobility and migration patterns. Nature 484, 96-100.

[4] Yang et al. (2014) Limits of Predictability in Commuting Flows in the Absence of Data for Calibration. Scientific Reports 4, 5662.

[5] Gargiulo et al. (2012) Commuting network model: getting to the essentials. Journal of Artificial Societies and Social Simulation 15, 6.

[6] Lenormand et al. (2012) A Universal Model of Commuting Networks. PLoS ONE 7, e45985.

[7] Lenormand et al. (2014) Generating French Virtual Commuting Network at Municipality Level. Journal of Transport and Land Use 7, 43-55.

Citation

If you use this code, please cite:

Lenormand M, Bassolas A & Ramasco JJ (2016) Systematic comparison of trip distribution laws and models. Journal of Transport Geography 51, 158-169.

If you need help, find a bug, want to give me advice or feedback, please contact me! You can reach me at maxime.lenormand[at]inrae.fr