Transportation Systems Engineering: Theory and Methods

This chapter deals with the mathematical models simulating transportation supply systems. In broad terms a transportation supply model can be defined as a model, or rather a system of models, simulating the performances and the flows resulting from users’ demand and the technical and organizational aspects of the physical transportation supply. The general structure of a supply model is depicted in Fig. 2.1.1, where several elements (or sub-models) can be distinguished. The graph defines the topology of the connections allowed by the transportation system under study, while the network loading or flow propagation model defines the relationship among path and link flows. The link performance model expresses for each element (link) the relationships between performances, physical and functional characteristics, and flow of users. The impact model simulates the main external impacts of the supply system. Finally, the path performance model defines the relationship between the performances of single elements (links) and those of a whole trip (path) between any origin-destination pair.

Recall from Chapter 1 that transportation demand derives from the need to carry out activities in different locations. Thus, its level and characteristics are influenced by the activity system and the transportation supply in the area.

Models for traffic assignment to transportation networks simulate how demand and supply interact in transportation systems. These models allow the calculation of performance measures and user flows for each supply element (network link), resulting from origin-destination demand flows, path choice behavior, and the reciprocal interactions between supply and demand. Assignment models combine the supply and demand models described in the previous chapters; for this reason they are also referred to as demand-supply interaction models. In fact, as seen in Chapter 4, path choices and flows depend on path generalized costs, futhermore demand flows are generally influenced by path costs in choice dimensions such as mode and destination. Also, as seen in Chapter 2, link and path performance measures and costs may depend on flows due to congestion. There is therefore a circular dependence between demand, flows, and costs, which is represented in assignment models as can be seen in Fig. 5.1.1.

The mathematical models described in the previous chapters are based on the assumptions of intra-period stationariety. This is equivalent to assuming, as stated in Chapter 1, that all significant variables are constant, at least on average, over successive sub-intervals of a reference period long enough to allow the system to reach stationariety condition. This assumption, although acceptable for many applications, does not allow for the satisfactory simulation of some transportation systems such as heavily congested urban road networks or low frequency scheduled services. In the first case, some important phenomena cannot be reproduced by traditional intra-period static models, including demand peaks, temporary capacity variations, temporary over-saturation of supply elements, and formation and dispersion of queues. In the second case, low-frequency services (e.g. two flights per day) may call into question the assumption of intra-period uniform supply and mixed preventive-adaptive users’ choice behavior introduced in the previous chapters. To simulate these aspects, different intra-periodal or within-day dynamic models have recently been developed; these models are usually referred to in the literature as (within-day) Dynamic Traffic Assignment (DTA) models, implying that dynamic assignment models require within-day dynamic demand and supply models.

In Chapter 5 several (within-day static) assignment models were formulated under for various assumptions on users’ behavior and network congestion. Computing link flows and other relevant variables resulting from assignment is computationally for real size networks with thousands of nodes and tens of thousands of links and intensive requires efficient algorithms. This chapter describes the theoretical foundations and the structure of some of the simplest algorithms for solving (within-day) static assignment models (algorithms for within-day dynamic assignment presented in Chapter 6 are still at a reasearch stage). The main emphasis is on presenting simple and effective solution approaches for assignment to large-scale networks, rather than providing an exhaustive analysis of the many existing algorithms.

Analysis and design of transportation systems require, respectively, the estimation of present demand and the forecasting of (hypothetical) future demand. These can be obtained by using different sources of information and statistical procedures.

This chapter outlines a wide range of methods and mathematical models which may assist the transportation systems engineer in designing projects or interventions. It should be stated at the outset that supply design models⁽¹⁾ are not meant to “automate” the complex task of design, especially when the proposed actions can alter significantly the performances of the transportation system. In this case, as we have seen, the project may have structural effects ranging from changes in land use to modifications in the level and structure of travel demand. On the other hand, the elements of the transportation supply to be designed may assume a very large number of possible configurations; circulation directions in an urban road network or the lines and frequencies of a transit system are two cases in point. In these cases it is practically impossible to explore and compare all the feasible configurations to identify the optimum with respect to a given set of objectives and constraints.

Transportation systems engineering can be defined as a discipline aimed at the functional design of physical and/or organizational actions on transportation systems. Each set of coordinated, internally consistent actions is referred to as a project or plan. The transportation system engineer must also evaluate the main potential effects of the project(s) to test their technical suitability and to support intermediate and final decision-makers.