This repository is meant for publishing some of the code related to the real time bus holding problem under capacity limitations applied in public transit (in particular, bus services).

Currently, this repository contains a couple of modules:

1. The singapore_scenario.aimms.py script in the folder Singapore_scenario contains the devised bus holding model introduced in the paper An analytic solution for real-time bus holding subject to vehicle capacity limits, which is currently published at Transportation Research Part C: Emerging Technologies. This script contains all necessary functions to calculate the solution of the mathematical program for different parameter values and idealized/real scenarios. In the same script, the proposed analytic solution of the paper An analytic solution for real-time bus holding subject to vehicle capacity limits is also computed demonstrating its equivalency to the solution of the mathematical program.

2. The comparison_with_benchmark.py script that computes the analytic solution for different parameter values. For this, we have created 4 scenarios: scenario I.py, scenario II.py, scenario III.py, scenario IV.py.

In case you use this code for scientific purposes, it is appreciated if you provide a citation to the paper:

Gkiotsalitis, K., and E. C. Van Berkum. An analytic solution for real-time bus holding subject to vehicle capacity limits. Transportation Research Part C: Emerging Technologies 121 (2020): 102815.

MIT License

Note that the script comparison_with_benchmark.py is written in Python. Running or modifying this script requires an installed version of Python 3.6.

Note that the mathematical program of the bus holding problem under capacity limitations singapore_scenario.aimms is written in AIMMS that uses CPLEX. Running or modifying this script requires an installed version of AIMMS. A free academic license in available at: https://aimms.com/english/developers/licensing/free-licenses/aimmsacademiclicense/