Model Description


The TPACS model developed by TransPosition is implemented in custom-built analytical software. The model is structured differently from the usual four-step-model. This model is based on an explicit formulation of a random utility model, without the simplifications inherent in the logit equation. It does not use zones or matrices, but instead allows all travel to occur from node to node. It avoids the problems of aggregation inherent in most strategic models, and allows very detailed networks to be used; the usual approach is to include all roads and full timetabled public transport. It also allows for very large models, covering entire metropolitan areas, states and countries. The model has strong capabilities in modelling multi-modal systems, freight, pricing and regional analysis.

At its heart, the model is a network-driven approach that seeks to understand the causes of travel and route/mode choice. It brings together the three components of travel:

  • Demand: Measured by population, employment and other activities
  • Supply: Including road and public transport networks; capacity; pricing; and operations
  • Behaviour: Focused on the user’s perception of benefits and costs of travel

The original Segmented Stochastic Slice Simulation (4S) model was named for the following features:

  • Segmented: Uses a comprehensive breakdown of different travel markets, and allows all behavioural parameters to vary by market segment (value of time, tolls, destination utilities etc.)
  • Stochastic: Uses Monte Carlo methods to draw values from probability distributions. Every parameter can be a random variable
  • Slice: Takes very efficient slices (samples) of the travel market across the whole model area and through the distributions
  • Simulation: Uses a traveller/vehicle state-machine with very flexible transition rules to effectively simulate all aspects of travel choice

Although these features still hold, due to the confusion with the four-step model naming, in 2021 the model was renamed to the TransPosition Agent Cloud Simulation model (TPAC model). The TPACS model differs in many ways from the traditional Four Step Model, and has many compelling advantages over many of the newer models as well.

  • It has an elegant, theoretically sound basis that allows for realistic modelling of a very wide range of issues. This includes active transport, mode choice, toll modelling, behaviour change, induced demand and time-of-day analysis.
  • Models can be prepared with much less effort and arbitrary coding – by eliminating zones, centroids, and centroid connectors the manual effort in putting networks together is vastly reduced. Also these aspects (zones, centroids and centroid connectors) are somewhat arbitrary abstractions that make the model highly dependent on manual inputs and individual assumptions.
  • It is very computationally efficient – by focusing all of the computational effort on tasks that are likely to contribute to the final outcome, and by having a single iterative structure (rather than traditional models’ use of a whole range of separate iterations for convergence) complex models can be run with practical run times. As an example of this, TransPosition has applied models of the whole of Queensland at the lot/local street level, and the whole of Australia at the Collection District (CD) and collector road level. A full integrated, multi-modal toll choice model for South East Queensland can be run in around 5 hours.
  • Its simple core allows it to be easily extended to include time choice models, tour-based models, activity models, links to micro-simulation, latent class models and land-use/transport interaction. The current model includes intersection delays; a detailed fuel use calculations; and multi-commodity, multi-vehicle class freight.

As an example of the efficiency of the approach, TransPosition has developed a model of the whole of the Australian state of Queensland (population 4.8m) at the local street level, and the whole of Australia (population 23m) at the collector road level. A full integrated, multi-modal toll choice model of South East Queensland (SEQ - a conurbation of 3.4m people) can run in under an hour, which includes transit and walk/cycle assignment.

More details on the theoretical Basis to the Model, the background and benefits to this approach can be found in a paper presented by Peter Davidson to the Australian Transport Research Forum in 2011 – “A new approach to transport modelling - the Stochastic Segmented Slice Simulation (4S) model and its recent applications”. Another paper “Modelling toll roads - Where have we gone wrong?” by Peter Davidson in 2011, investigates the weaknesses of existing approaches for toll road modelling.

Note that the variability of model outputs is dependent on the number of repeated values drawn in the Monte Carlo sampling (these are called slices in the model). If too few slices are taken, then the outputs can vary from run to run. But taking more slices increase the running time of the model. Previous trials have shown that the variance in output decreases significantly as more slices are added, but the rate diminishes after a few hundred slices. For most studies 1000 slices are used, with the whole run and repeated 6 times, then averaged out across all runs. This approach minimises the risk that the output of a single run has an undue impact on the overall result. To further reduce this risk, the pseudo-random factors within the model are seeded with a value shared across all scenarios. This means that each scenario is tested with a synchronised set of random factors, thereby minimising the impact of randomness on comparisons between scenarios.

Personal Travel

The private travel model covers all of the travel made by individuals, whether it is for private purposes or related to work. It is assumed that all personal travel has some discretion with respect to mode choice, although the preferences may vary by person type and travel purpose. The model allows for any combination of car driver, car passenger, walking, cycling and public transport.

The model uses a fairly detailed trip purpose breakdown, including highly segmented non-home-based travel. Travel is trip based, with separate trips for the forward and return journeys, and for any substantial stops in multi-stop tours. Trip production is based on trip rates for each market segment – the rates give people’s average desired number of trips in a day. If the circumstances are not amenable for the trip (either the costs are too high or the Monte-Carlo selected utility is too low) then travel will not occur. Thus the model has some degree of accessibility-responsive trip rate; strictly it is based on relaxation of supressed demand rather than induced demand but the overall effect is very similar. The coefficients in the model that describe personal travel are calibrated using data from the Household Travel Survey. This survey involved asking households to record all of their travel over one or more days. The trip rates, trip lengths, mode choice and time of day choice are used directly or compared with model outputs in calibration. The model is also calibrated against traffic counts and observed toll road usage.


The development of any freight model is hampered by lack of data. It is very difficult to get accurate or comprehensive data on where and why trucks travel, what they are carrying and how they make their choices. Apart from classified traffic counts, no local data on freight markets or trip rates are usually available. In lieu of local data, surveys from other studies have been used. Finally, assumptions about mode choice (road/rail and road vehicle type) are made for each industry linkage. These various assumptions are combined to give commercial vehicle market segments for modelling, as detailed in Market Segment Assumptions. Note that imports and exports are usually dealt with through specific market analysis of the Port of interest based primarily on any reports available by the Port corporation.

Tolling Choice

The decision whether or not to pay a toll depends on the trade-off between the time and money saved by using the tolled facility (compared with the best free alternative) and the cost incurred by the toll. The problem is that not everybody makes this trade-off in the same way – some people will have a high value of time, for example, and will be relatively less concerned with the toll. Others will have a high operating cost on the free route, so the benefit of the tolled facility is higher. One answer to this is segmentation – the range of decision factors can be simplified to a smaller number of separate markets. The other approach is to allow for variability in preferences. In some models this is done analytically, using simple assumptions about how variations in cost perception will modify travellers’ propensity to use the toll. One particular assumption leads to the logit toll choice model, used in many toll assessments in Australia. The problem with this approach is that it requires unrealistic assumptions about variability. In particular, rather than assuming that value coefficients (such as value of time) vary across the population, it assumes that variability comes from an independent error term, completely unaffected by the characteristics of the alternatives in question. It does not allow for variations in taste, value of time, or vehicle operating costs and also brings into consideration completely unrealistic options.

The approach used in the TPACS model is to incorporate toll choice into the standard model choice structure. Because the model has an integrated destination/mode/route choice structure, no decision needs to be made regarding where to put toll choice – it simply becomes part of a holistic travel choice. This is in contrast to the traditional approach, where toll choice is a completely separate sub-model which must be inserted somewhere into the four step model. Another advantage of the TPACS model is that the toll choice is integrated with the congestion model, so again there is no need to make difficult decisions about how to achieve convergence between toll choice and mode or destination choice in the face of congestion.

The TPACS model allows for taste variation through Monte Carlo simulation. All behavioural parameters, such as value of time, vehicle operating cost, and congestion sensitivity, are specified with random distributions, and the model considers how people will make choices under a range of specific values.