The economic rationale for stochastic urban transport models and travel behaviour: a mathematical programming approach to quantitative analysis with Perth data

Wolfgang Ernst

Research output: ThesisDoctoral Thesis

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Abstract

[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] This thesis reviews, extends and applies to urban traffic analysis the entropy concept of Shannon and Luce's mathematical psychology in a fairly complex and mathematically demanding model of human decision making, if it is solved as a deeply nested structure of logit calculus. Recognising consumers' different preferences and the universal propensity to seek the best choice when going to some desired goal (k), a transparent mathematical program (MP) is developed: the equivalent of a nested multinomial logit model without its inherent computational difficulty. The MP model makes a statistical assessment of individual decisions based on a randomised (measurable) utility within a given choice structure: some path through a diagram (Rk, Dk), designed a priori, of a finite number of sequential choices. The Equivalence Theorem (ET) formalises the process and states a non-linear MP with linear constraints that maximises collective satisfaction: utility plus weighted entropy, where the weight (1/θn) is a behavioural parameter to be calibrated in each case, eg for the Perth CBD. An optimisation subject to feasible routes through the (Rk, Dk) network thus captures the rational behaviour of consumers on their individually different best-choice decision paths towards their respective goals (k). This theory has been applied to urban traffic assignment before: a Stochastic User Equi-librium (SUE). What sets this thesis apart is its focus on MP models that can be solved with standard Operations Research software (eg MINOS), models for which the ET is a conditio sine qua non. A brief list of SUE examples in the literature includes Fisk's logit SUE model in (impractically many) route flows. Dial's STOCH algorithm obviates path enumeration, yet is a logit multi-path assignment procedure, not an MP model; it is nei-ther destination oriented nor an optimisation towards a SUE. A revision of Dial's method is provided, named STOCH[k], that computes primal variables (node and link flows) and Lagrangian duals (the satisfaction difference n→k). Sheffi & Powell presented an unconstrained optimisation problem, but favoured a probit SUE, defying closed formulae and standard OR software. Their model corresponds to the (constrained) dual model here, yet the specifics of our primary MP model and its dual are possible only if one restricts himself to logit SUE models, including the ET, which is logit-specific. A real world application needs decomposition, and the Perth CBD example is iteratively solved by Partial Linearisation, switching from (measured) disutility minimisation to Sheffi & Powell's Method of Successive Averages near the optimum. The methodology is demonstrated on the Perth Central Business District (CBD). To that end, parameter Θ is calibrated on Main Roads' traffic count data over the years 1997/98 and 1998/99. The method is a revision of Liu & Fricker's simultaneous estimation of not only Θ but an appropriate trip matrix also. Our method handles the more difficult variable costs (congestion), incomplete data (missing observations) and observation errors (wrong data). Finally, again based on Main Roads' data (a sub-area trip matrix), a Perth CBD traffic assignment is computed, (a) as a logit SUE and - for comparison - (b) as a DUE (using the PARTAN method of Florian, Guélat and Spiess). The results are only superficially similar. In conclusion, the methodology has the potential to replace current DUE models and to deepen transport policy analysis, taking into account individual behaviour and a money-metric utility that quantifies 'social benefits', for instance in a cost-benefit-analysis.
Original languageEnglish
QualificationDoctor of Philosophy
Publication statusUnpublished - 2003

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