This notebook was produced in support of a paper written for the MagLev 2024 Conference titled "The Potential of Dynamic Skip-stop to Address the Coverage Paradox in Urban Transport through Superconducting MagLev Rail Technology"
A key section of the paper is describing the Coverage Paradox, a phenomenon of urban rail transport systems due to the structure of the system concept. This is presented in a paper by Blumenfeld et. al. [1].
The purpose of this script is to illustrate the coverage paradox with an interactive notebook where users can change the parameters of a rail system and see how it has an impact on the door-to-door journey time showing the behaviour of the coverage paradox.
The script is contained in the single marimo notebook file:
coverage_paradox_notebook.py
To use, clone the repository (or just the file) to a local machine, open a terminal and naviagate to the saved directory.
To run the programme in app mode use the command:
marimo run coverage_paradox_notebook.py
To view and alter the underlying programme use the command:
marimo edit coverage_paradox_notebook.py
Both will open the marimo web interface.
With the notebook running, there are 3 sections:
Variables The 7 parameters that the users can adjust.
Optimum Door-to-door Journey Time
The number of stations and interstation distance that result in the minimum average door-to-door journey time (
Plots Altair plots for:
- Number of stations and duration of journey components
- Interstation distance and percentage of door-to-door journey time spent on vehicle
Pandas dataframe will full caculation results
The aim of this is to calculate the door-to-door journey time for a passenger travelling on an urban rail transport system.
The overall formula is:
Where:
-
$T_j$ Average door-to-door journey time, the average total time to travel from origin to destination. -
$T_a$ Access time, the time spend walking to or from the transit vehicle. -
$T_w$ Wait time, the time elapsed between arriving at the transit vehicle and it departing on the journey. -
$T_v$ Vehicle time, the time spent travelling in the transit vehicle.
The variable parameters are:
-
$S_j$ Door-to-door journey distance ($km$ ), the total distance to be travelled -
$tphpd$ Trains per hour per direction -
$V_{v-max}$ Maximum Line Speed ($m/s$ ), maximum speed of vehicle -
$A_{v-acc}$ Mean Acceleration ($m/s^2$ ), the rate of acceleration of the vehicle from stationary to$V_{v-max}$ -
$A_{v-dcc}$ Mean Deceleration ($m/s^2$ ), the rate of deceleration of the vehicle from$V_{v-max}$ to stationary -
$T_{dwell}$ Dwell Time ($mins$ ), the time spent stationary dwelling at each station -
$V_{walk}$ Average walking speed ($km/h$ ), average speed for passenger walking
The Variable Input Parameters are then taken and put into 3 classes which convert the input units to SI. The
Vehicle(line_speed,acceleration,deceleration)- The time and distance taken to accelerate and decelerate to line speed are also calculated and recorded as attributes of the class (
acc_dcc_distance,acc_dcc_time)
- The time and distance taken to accelerate and decelerate to line speed are also calculated and recorded as attributes of the class (
Operations(headway,dwell_time)Journey(journey_distance,walking_speed)
The Simulation class runs all of the calculations, taking instances of the Vehicle, Operations and Journey classes. There is a minimum interstation distance, defined by the acc_dcc_distance from which can then be derived a maximum number of stations. The class then runs over the possible number of stations and stores the resulting journey time components in an instance of the Individual_Simulation class, the set of all of this are stored in a class attribute simulation_results list.
The calculations are then:
Where:
-
$N_{stations}$ Number of stations -
$S_{is}$ interstation distance, distance between each station -
$T_{is}$ intersation time, time taken for vehicle to travel between each station -
$S_{acc-dcc}$ acceleration deceleration distance, distance taken to accelerate and decelerate from$V_{v-max}$ -
$T_{acc-dcc}$ acceleration deceleration time, time taken to accelerate and decelerate from$V_{v-max}$ -
$T_{hw}$ vehicle headway
There is a function of the class Simulation that converts simulation_results from a list of instances of Individual_Simulation to a pandas dataframe.
There are also functions of the class Simulation that produce the altair charts used in the notebook
The National Travel Survey gave commuting figures for London of an average number of trips per year of 126 and the average distance travelled per year at 1,074 miles [2]. This gives an average commuting distance of 13.7km per commuting trip.
The average walking pace of 4.7km/h is taken from a meta-anaysis paper [3].
The other parameters are taken from a specification released by Siemens for a fleet of trains produced for the Munich metro [4].
For this demonstration it is fundementally assumed that the journey exists in 1-dimensional space.
It is assumed that the population distribution is homogeneous and therefore the interstation distance is constant along the line. From this it is also derrived that the average distance for any user's origin and destination from a station is a quarter of the interstation distance.
There is no account taken of time taken to walk from the station enterance to the platform or impact of crowds at peak times. This would normally add some time and would include time to scan tickets and other station activities.
It is assumed that passengers arrive randomly and do not plan to arrive for a train at a specific time. Therefore on average they will have to wait half of the headway between two trains to board their next service.
It is assumed that the rate of acceleration and deceleration of trains is constant. A more standard method is the Davis equation but this was not chosen to be used in this case to keep the user interface simple.
It is assumed that vehicles travel with a constant headway between all services. Any fluctuations or delay is not included in this calculations.
It is also possible to set the dwell time greater than would be possible with the headway. This is a limitation and could be addressed in future revisions of the programme.
The script is tested working with python 3.11.9 and the following packages:
marimo 0.7.0altair 5.3.0pandas 2.2.2
[1] Marcelo Blumenfeld, Clive Roberts, and Felix Schmid. “A systems approach to developing a new metro for megalopoleis”. en. In: Proceedings of the Institution of Civil Engineers - Transport 169.5 (Oct. 2016), pp. 249–261. ISSN: 0965-092X, 1751-7710. DOI: 10.1680/jtran.16.00018.
[2] Department of Transport. NTS9918: Average number of trips and distance travelled by trip purpose, ethnic group, region and rural-urban classification of residence: England, 2002 onwards. Aug. 2023. URL: https://assets.publishing.service.gov.uk/media/64e8b53d7af6dd001368efdf/nts9918.ods (visited on 07/17/2024).
[3] Elaine M. Murtagh et al. “Outdoor Walking Speeds of Apparently Healthy Adults: A Systematic Review and Meta-analysis”. en. In: Sports Medicine 51.1 (Jan. 2021), pp. 125–141. ISSN: 0112-1642, 1179-2035. DOI: 10.1007/s40279-020-01351-3.
[4] Siemens. Siemens to supply new metro for Munich: Background Paper. en. Sept. 2012. URL: https://assets.new.siemens.com/siemens/assets/api/uuid:52c1eaca-f058-43ae-9943-7fc99f595de7/rl-metro-munich-e.pdf (visited on 07/18/2024)
This research has been funded by a PhD scholarship from the University of Birmingham.
Many thanks go to my supervisor Dr Marcelo Blumenfeld for their guidance, support and input on this project.
MagLev-2024-Coverage-Paradox-Notebook Copyright (C) 2024 Chris Davis
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