published_or_final_version / Civil Engineering / Master / Master of Philosophy

published_or_final_version / abstract / Civil Engineering / Master / Master of Philosophy

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Alfred P. Sloan School of Management. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND DEWEY. / Bibliography: leaves 148-149. / M.S.

Researchers in multiple areas have shown that characterizing and accounting for the uncertainty inherent in decision support models is critical for developing more efficient planning and operational strategies. This is particularly applicable for the transportation engineering domain as most strategic decisions involve a significant investment of money and resources across multiple stakeholders and has a considerable impact on the society. Moreover, most inputs to transportation models such as travel demand depend on a number of social, economic and political factors and cannot be predicted with certainty. Therefore, in recent times there has been an increasing emphasis being placed on identifying and quantifying this uncertainty and developing models which account for the same. This dissertation contributes to the growing body of literature in tackling uncertainty in transportation models by developing methodologies which address the uncertainty in input parameters in traffic assignment models. One of the primary sources of uncertainty in traffic assignment models is uncertainty in origin destination demand. This uncertainty can be classified into long term and short term demand uncertainty. Accounting for long term demand uncertainty is vital when traffic assignment models are used to make planning decisions like where to add capacity. This dissertation quantifies the impact of long term demand uncertainty by assigning multi-variate probability distributions to the demand. In order to arrive at accurate estimates of the expected future system performance, several statistical sampling techniques are then compared through extensive numerical testing to determine the most "efficient" sampling techniques for network assignment models. Two applications of assignment models, network design and network pricing are studied to illustrate the importance of considering long term demand uncertainty in transportation networks. Short term demand uncertainty such as the day-to-day variation in demand affect traffic assignment models when used to make operational decisions like tolling. This dissertation presents a novel new definition of equilibrium when the short term demand is assumed to follow a probability distribution. Various properties of the equilibrium such as existence, uniqueness and presence of a mathematical programming formulation are investigated. Apart from demand uncertainty, operating capacity in real world networks can also vary from day to day depending on various factors like weather conditions and incidents. With increasing deployment of Intelligent Transportation Systems, users get information about the impact of capacity or the state of the roads through various dissemination devices like dynamic message signs. This dissertation presents a new equilibrium formulation termed user equilibrium with recourse to model information provision and capacity uncertainty, where users learn the state or capacity of the link when they arrive at the upstream node of that link. Depending on the information received about the state of the upstream links, users make different route choice decisions. In this work, the capacity of the links in the network is assumed to follow a discrete probability distribution. A mathematical programming formulation of the user equilibrium with recourse model is presented along with solution algorithm. This model can be extended to analytically model network flows under information provision where the arcs have different cost functional form depending on the state of the arc. The corresponding system optimal with recourse model is also presented where the objective is minimize the total system cost. The network design problem where users are routed according to the user equilibrium with recourse principle is studied. The focus of this study is to show that planning decisions for networks users have access to information is significantly different from the no-information scenario. / text

[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.

[Truncated abstract] In an urban network, any change to the capacity of a road or an intersection will generally result in some traffic changing its route. In addition the presence of intersections creates the need for frequent stops. These stops increase the fuel consumption by anywhere between thirty to fifty percent as evidenced by published standardised vehicle fuel consumption figures for urban and for country driving. Other components of vehicle operating costs such as tyre and brake wear and time costs will also be increased by varying amounts. Yet almost all methods in use for economic evaluation of urban road projects use open road vehicle operating costs (sometimes factored to represent an average allowance for stopping at intersections) for one year or sometimes two years in the analysis period and then make assumptions about how the year by year road user benefits may change throughout the period in order to complete the analysis. This thesis will describe a system for estimating road user costs in an urban network that calculates intersection effects separately and then adds these effects to the travel costs of moving between intersections. Daily traffic estimates are used with a distribution of the flow rate throughout the twenty-four hours giving variable speed of travel according to the level of congestion at different times of the day. For each link, estimates of traffic flow at two points in time are used to estimate the year-by-year traffic flow throughout the analysis period by linear interpolation or extrapolation. The annual road user costs are then calculated from these estimates. Annual road user benefits are obtained by subtracting the annual road user costs for a modified network from the annual road user costs for an unmodified network. The change in the road network maintenance costs are estimated by applying an annual per lane maintenance cost to the change in lane-kilometres of road in the two networks. The Benefit Cost Ratio is calculated for three discount rates. An estimate of the likely range of error in the Benefit Cost Ratio is also calculated