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Mode and route choice
The next sub-model is very important for the future of the transport system in a city. This sub-model reflects the choice of mode, at least at the level between private transport (car, motorcycles) and Public Transport (PT: buses, metro, trains, etc.). This sub-model is usually based on the ?generalised costs? of travelling between two zones by each mode. This generalised cost cijm includes travel times, waiting and walking times, travel costs (fares, fuel, parking, any tolls) and a measure of the comfort and convenience of each mode m.
The most common analytical version of this sub-model is a Logit formulation where the proportion of travellers choosing, for example Public Transport, is given by:
Here, PT indicates Public Transport and m the other mode, generally car.
There is a ?scaling? parameter ? in this Logit formulation that influences how sensitive people are to change mode if their generalised costs change. A large value for ? implies a sensitive change of mode. Incidentally, this Logit analytical form has several other uses whenever a choice is required, even considering multiple alternatives. For example, some use it to model the choice between a toll road and an untolled route. Given the importance of ? in determining the proportion of trip makers choosing an alternative, errors in this parameter will introduce large errors in the estimation of flows.
The final stage in the classic model is route choice and Assignment. This sub-model estimates the number of trips using a particular route in the network and therefore, the total flow on each link. Equilibrium assignment is the most frequently used method when congestion plays a key role in route choice. Under equilibrium for each pair Origin Destination, each driver chooses the best route and all alternative routes have a greater generalised cost; under congestion there may be more than one minimum cost route. The output from this sub-model will be flows on links and PT services, and travel times between each Origin Destination pair. These travel times should, in principle, then be fed back onto earlier stages and the sub-models run again until the costs from assignment become stable and an overall system equilibrium is reached.
The classic models were developed originally to assist transport planning, mostly in urban areas. They are good for comparing two alternative plans or projects. Of course, information about the future characteristics of the network and the location of population and economic activities is required to produce projections of traffic and associated delay under future alternative plans.
Forecasting toll road traffic
The classic models were developed originally to assist transport planning, mostly in urban areas. They are good for comparing two alternative plans or projects. Of course, information about the future characteristics of the network and the location of population and economic activities is required to produce projections of traffic and associated delay under future alternative plans. The plans would then be compared on the basis of future levels of congestion, time spent on the network, fuel consumption, environmental conditions (emissions, noise, accidents) and accessibility to jobs and services.
If the classic model is good enough to compare alternative plans or schemes, it is less good to estimate traffic and revenue projections for toll roads and other concessions, for example Metro or Rail. Toll road traffic and revenue projections require much closer attention to two key issues that are oversimplified in the classic model. The first one is willingness to pay and the second, the handling of risk and uncertainty.
Willingness to pay tolls
A successful toll road must provide a useful advantage over the use of alternative, untolled, routes. The most important of these is a saving in time spent travelling. Drivers will then consider this time saving and compare it against the cost of the toll and decide whether they are willing to pay for it. Some drivers will have a high willingness to pay where others will prefer to save the money and incur in additional travel time. Willingness to pay is closely linked to two factors: how important it is to save time and personal or family income. The more valuable the time saving or the higher the income, the greater the willingness to pay. In some cases, the company will pay the tolls incurred by their employees, especially when travelling as part of their job; this increases their willingness to pay significantly.
Consider two routes, one untolled and one with a toll and a shorter time. For those using the tolled route, and ignoring distance related costs, it is possible to write the following relationship:
Dividing this relationship by cwe get:
This relationship is all expressed in monetary units. The ratio a/c is usually referred to as the ?Value of Time? or more precisely, the ?Value of Travel Time Savings? (VTTS) and reflects the willingness of an individual to pay. It is expressed in monetary units per minute or per hour ($/hr). This key parameter in demand modelling deserves careful attention and countries spend considerable resources estimating and updating the values for different socio-economic groups and trip purposes. Sometimes, a distinction is made for VTTS for short and long trips and whether these are undertaken under free-flow or interrupted flow conditions (traffic lights, roundabouts, congestion) is also considered.
A consultancy estimating traffic and revenue for a toll road will also spend significant time and effort in ascertaining the most accurate values for VTTS. Good modelling work will require representation of different values of time for different types of users, ?user classes? in modelling terminology. Best practice requires the disaggregation of demand in at least six car user classes and at least four for trucks as they generally value savings higher. Errors in these parameters will result in under or over estimation of future traffic.
Software
There are four commercial software packages that are accepted internationally as suitable for this kind of work: CUBE Voyager (Citilabs), EMME (INRO), VISUM (ptv) and TransCAD (Caliper). Although they have slightly different features, they can satisfy the requirements of transport planning and toll modelling. The accuracy and reliability of the model, however, depends more on the technical skills, attention to detail and experience of the modeller, han the choice of software. Quality Assurance is an important component of good modelling practice, ?quick and dirty? jobs result in very expensive mistakes.
Dr Luis Willumsen
Director of Luis Willumsen Consultancy
Visiting Professor, University College, London
(Dr Willumsen is an internationally recognised authority in transport demand modelling and planning who has worked in 30 countries. He has a distinguished academic career and extensive experience as a consultant for over 20 years. He has made major contributions to modelling techniques and the estimation of future traffic and revenue projections for Toll Roads, Mass Transit and Rail concessions).