Cube Voyager Public Transport Crowding

In some urban areas it is necessary to model the effect of crowding on public transport services in order to replicate real-world situations. Cube Voyager’s Public Transport program has the ability to assess crowding for any service large or small.

Users are able to set individual vehicle capacities by number of seats and total crush capacity and assign these to each service in the model to accurately reflect day-to-day public transport capacities. During Cube’s crowd-modeling process, the Public Transport program can then balance demand against capacity.

At each iteration, the program completes the route-evaluation and loading processes, which are repeated for all user classes, and then adjusts the costs in the model to reflect the assigned loads. The iterative process may use either, or both, of the crowd modeling procedures:

  • Link travel time adjustment
  • Wait time adjustment

In addition to the standard features of crowding in Cube, new functionalities have recently been developed to allow for additional control and flexibility to the user over the iterative process.

Iteration-by-Iteration Outputs

Available from Cube version 6.4.2

  • An option to output stop-to-stop tabular results at each iteration has been added.
  • Possibility to list evaluated I-J routes by iteration is also included now, to allow users to investigate route choices evolution iteration-by-iteration.
  • Additionally, it is now possible to output skim matrices for every iteration.

All these outputs can be post-processed by the user, by means of the Cube Voyager Matrix powerful tool, to obtain several statistics.

Iteration-by-Iteration Statistics

Available from Cube version 6.4.2

The automatic “network based” statistics already available from the program were:

  • Change in root mean square error (RMS_change) in Link Perceived Travel Time for crowded links
  • Number of crowded links
  • Change in root mean square error (RMS_change) in Link Perceived Travel Time for all links
  • Total number of links

Additional “matrix based” statistics have been included for better understanding the evolution of the overall PT system iteration-by-iteration:

  • RDIFF: Outputs the Relative Differences between consecutive iterations
  • RMSE: Calculates the Root Mean Square Error between consecutive crowding iterations

Stopping Criteria

Available from Cube version 6.4.3

Two stopping criteria are now available based on the new “matrix based” statistics:

  • RMSESTOP and RMSECUTOFF: Stop the crowding run if the RMSE values from the last three sequential iterations are less than the user specified threshold
  • RDIFFSTOP and RDIFFCUTOFF: Stop the crowding run if the RDIFF values from the last three sequential iterations are less than the user specified threshold

Crowding Curves with Utilization > 100%

Available in next release.

Utilization is a measure of on-board crowding, that can be considered as the ratio between standing passengers and the maximum capacity for standing passengers in the vehicle.

The PT program originally used crowding curves with utilization capped at 100%, and applying a constant value above this limit. A new keyword has been introduced to allow users to define crowding curves adopting utilization values above the 100% cap.

“Smoothing” of the Iterative Process

Available in next release.

It is now possible to use three additional keywords to “smooth” the crowding iterative process by damping loaded volumes (VOLDF) and/or crowding factors (LINKDF) and/or wait-time factors (WAITDF), with damping factors defined by the user.


“Incremental Loading”

Available in next release.

A way to include an incremental loading of demand over the PT network will be introduced in future versions. This can be applied preliminary to the crowding iterative process including the above mentioned new functionalities, or can be selected as the stand alone assignment approach.



Case Study: Simple 2-Lines Test Case

A simple test case is provided below, to show the possibilities available with the new keywords.


Two lines are available to passengers going from their Origin to their Destination:

A demand of 200 passengers is assigned over a 60 minutes period, with therefore high overcrowding.

This type of problem would likely lead to unstable conditions in the system, with demand oscillating between the two alternatives routes.

Thanks to the new functionalities, testing different values of the damping factors, a stable average solution can be obtained, as shown in the below figure, where the two alternative routes have around the same perceived travel time.


By looking at the results from this simple test case we can see that the keywords that have been introduced help in reaching a stable condition even in this very congested system.

This is important to allow average stable conditions to be reached when analysing congested PT systems with the objective of obtaining average answers from the model during scenarios analysis.

It is suggested that users adopt an “incremental refinement” of their models involving PT crowding, to introduce these additional functionalities. For example, users should follow the steps below:

  • Network simplification/rationalization (including lines aggregation)
  • Refinement of routing factors/parameters
  • Accurate definition of the Crowding Curves (also for U>100%)
  • Optimization to find the best combination of parameters (base case, reference case and scenario testing)
  • Re-calibration of the model if necessary


Interested in learning more about Cube Voyager's Public Transport Program?

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Filippo is an experienced and passionate transport modeler based in München, Germany. As Senior Transport Modeller at Citilabs, he assists users in optimizing their use of Cube based on their individual needs and goals. In addition, he oversees Cube user support, training courses and “one-to-one” coaching. Prior to Citilabs, he worked as a consultant and transport modeller over a number of different projects, developing transportation models for highway and multimodal studies. He gained a Master Degree in Civil Engineering from Padova University (Italy) and an MSc in Transport Planning and Engineering from the ITS at Leeds University (UK).