The reliability-based stochastic transit assignment problem with elastic demand

This paper examines the reliability-based stochastic transit assignment problem with elastic demand. A Variational Inequality (VI) model for this problem is developed. The VI model considers capacity, waiting time and in-vehicle travel time as stochastic variables, and includes Spiess and Florian’s (1989) and de Cea and Fernández’s (1993) models as special cases. A reliability-based stochastic user equilibrium condition is defined to capture the route choice behavior of passengers. To illustrate the properties of the VI model, numerical studies were conducted on de Cea and Fernández’s (1993) network. The studies also show that Spiess and Florian’s and de Cea and Fernández’s models can overestimate the system performance substantially.postprin

Reliable network design under supply uncertainty with probabilistic guarantees

This paper proposes a bi-level risk-averse network design model for transportation networks with heterogeneous link travel time distributions. The objective of the network design is to minimise the total system travel time (TSTT) budget (TSTTB), which consists of the mean TSTT and a safety margin. The design is achieved by selecting optimal link capacity expansions subject to a fixed expansion budget. Users’ selfish behaviour and risk attitude are captured in the lower level traffic assignment constraints, in which travellers select routes to minimise their own path travel time budget. The properties of the design problem are analysed analytically and numerically. The analysis shows that despite the lack of knowledge of travel time distributions, the probabilities that the actual TSTT and the actual path travel time are, respectively, within the optimal TSTTB and the minimum path travel time budget under optimal design have lower bounds. The lower bounds are related to the system manager's and travellers’ risk aversion. The optimal TSTTB is proven to be bounded below even when the link expansion budget is unlimited.postprin

Modeling Choice Problems with Heterogeneous User Preferences in the Transportation Network

Users of transportation systems need to make a variety of different decisions for their trips in the network, while their objective is to keep the generalized costs of their own trips minimized. In the transportation network, there is a diversity of different factors that can influence the decisions of the users, while the relative importance of these factors varies among the heterogeneous users with different trip purposes. Nonetheless, the cumulative result of the individual decisions of the users seeking to minimize their costs according to their own preferences leads to the user equilibrium condition in which no one can reduce his/her cost by changing his/her decision. In this research, we adapt the concept of the efficient frontier from portfolio theory (Markowitz, 1952) in finance in order to model the bicriterion choice behavior of users with heterogeneous preferences in transportation networks. We show that the efficient frontier has a set of primary properties that remains general in different problems. Thus, the primary properties of the efficient frontier can be employed to analytically model and solve different bicriterion choice problems in transportation. For the first application, we use these properties to propose an analytical model for the morning commute problem when there is a heterogeneity associated with preferences of the users (Vickrey, 1969; Daganzo, 1985). A dynamic pricing strategy is also proposed to optimize the bottleneck by minimizing the total cost for users. In addition to the morning commute problem, Vickrey’s congestion theory is also shown to have applications in modeling and optimizing the operation of the demand responsive transit (DRT) system with time-dependent demand and state-dependent capacity as queueing systems. The efficiency of the DRT system can be improved by implementing a dynamic pricing strategy. The analytical solution of the morning commute problem can be also extended for modeling and pricing the DRT system when there is a heterogeneity associated with the preferences of the DRT service users. For another application of the efficient frontier in modeling choice problems in transportation, we propose a traffic assignment model to account for the heterogeneity in sensitivity of the users to travel time reliability in a network under travel time variability. However, the proposed model can have wide applications in modeling the equilibrium condition of different multicriterion choice problems in transportation

Models and Solution Algorithms for Asymmetric Traffic and Transit Assignment Problems

Modeling the transportation system is important because it provides a “common ground” for discussing policy and examining the future transportation plan required in practices. Generally, modeling is a simplified representation of the real world; however, this research added value to the modeling practice by investigating the asymmetric interactions observed in the real world in order to explore potential improvements of the transportation modeling. The Asymmetric Transportation Equilibrium Problem (ATEP) is designed to precisely model actual transportation systems by considering asymmetric interactions of flows. The enhanced representation of the transportation system by the ATEP is promising because there are various asymmetric interactions in real transportation such as intersections, highway ramps, and toll roads and in the structure of the transit fares. This dissertation characterizes the ATEP with an appropriate solution algorithm and its applications. First, the research investigates the factors affecting the convergence of the ATEP. The double projection method is applied to various asymmetric types and complexities in the different sizes of networks in order to identify the influential factors including demand intensities, network configuration, route composition between modes, and sensitivity of the cost function. Secondly, the research develops an enhancement strategy for improvement in computational speed for the double projection method. The structural characteristics of the ATEP are used to develop the convergence enhancement strategy that significantly reduces the computational burdens. For the application side, instances of asymmetric interactions observed in in-vehicle crowding and the transit fare structure are modeled to provide a suggestion on policy approach for a transit agency. The direct application of the crowding model into the real network indicates that crowd modeling with multi user classes could influence the public transportation system planning and the revenue achievement of transit agencies. Moreover, addition of the disutility factor, crowding, not always causes the increase of disutility from the transit uses. The application of the non-additive fare structure in the Utah Transit Authority (UTA) network addresses the potential of the distance-based fare structure should the UTA make a transition to this fare structure from their current fare model. The analysis finds that the zero base fare has the highest potential for increasing the transit demand. However, collecting less than $0.50 with a certain buffer distance for the first boarding has potential for attracting the users to UTA\u27s transit market upon the fare structure change

Development of an Optimisation Model for Scheduling of Street Works Schemes

The coordination of street works activities in urban networks has been highlighted by the Government as one of the most important aspects of street works practice, benefiting street authorities, undertakers and road users alike (Department for Transport, 2012c). The present research aims to develop an optimisation model for minimising the overall costs and disruptions incurred by all stakeholders as a result of implementing a number of street works schemes in an urban traffic network. The output of the optimisation model consists of optimum values for the underlying decision variables of the model such as start time of each street works scheme, type of traffic management strategy for each link, sequence of link closures and the level of resources allocated to undertake each scheme. The following two distinct objective functions, which are subject to minimisation by the optimisation model, have been developed: A primary objective function which captures the monetised effects of street works schemes such as cost of delays to road users, and cost of undertaking street works schemes. A secondary objective function (developed as a fuzzy inference system) to capture the non-monetised disruptive effects of street works schemes. The fuzzy variables of this inference system correspond to the level of ‘accessibility degradation’ of the network links, ‘connectivity degradation’ of the origin-destinations of the network, and ‘time sensitivity’ of the disruptive events (i.e. street works schemes). Next the street works optimisation problem was mathematically formulated as a bi-level optimisation programming problem, where the higher level problem is associated with minimising the aforementioned objective functions, and the lower level problem deals with predicting traffic flows, and thus the amount of delays incurred by the road users. Subsequently this study developed a genetic algorithm solution method to solve the resulting non-convex and NP-hard optimisation problem with integer or mixed type variables. Finally the performance of the optimisation algorithm was verified by a number of experimental tests on a small hypothetical network for three street works schemes