Solving a discrete multimodal transportation network design problem

This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.     

Optimal selection of build-operate-transfer projects on transportation networks

This paper considers the problem of how to select highway projects for the build-operate-transfer (BOT) development with the objective of improving the social benefit while ensuring the marketability of those selected. The problem can be viewed as a tri-level leader-follower game and is formulated as a mixed integer program with equilibrium constraints. Without solving the associated problem, we show that optimal tolls and travel times on selected BOT highways can be determined from their attributes under mild assumptions. This leads to an efficient heuristic algorithm for solving the project selection problem.     

Multi-fleet ferry service network design with passenger preferences for differential services

This paper investigates a multi-fleet ferry routing and scheduling problem that takes into account ferry services with different operation characteristics and passengers with different preferred arrival time windows. The logit model is used to represent passengers’ service choices. The full problem is formulated as a mixed integer nonlinear programming problem and solved with a heuristic procedure that first fixes the demand and then decomposes the resultant model by ferry services. At each iteration of the algorithm, the demand is updated and the relaxed problem is re-solved. Numerical results for the case of ferry service network design in Hong Kong are provided to illustrate the properties of the model and the performance of the heuristic.     

Optimization of transport investment and pricing policies: the role of transport pricing in network design

This paper investigates the role of transport pricing in network design and describes two facts about flow pattern in a transportation system. The first, illustrated by an example of Braess paradox, is that adding a new link to the network does not necessarily minimize the total travel time. The second is that introducing of appropriate toll pricing may reduce not only the total network time but also the travel time for each individual traveller. It follows with the investigations of different system objectives and different pricing policies (only toll pricing and distance‐based pricing are considered), and shows how they affect the system performance and flow pattern. Lastly, a systematic optimization process is proposed for integrated planning of transport network and pricing policies.     

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.     

Bounded rationality and irreversible network change

A network change is said to be irreversible if the initial network equilibrium cannot be restored by revoking the change. The phenomenon of irreversible network change has been observed in reality. To model this phenomenon, we develop a day-to-day dynamic model whose fixed point is a boundedly rational user equilibrium (BRUE) flow. Our BRUE based approach to modeling irreversible network change has two advantages over other methods based on Wardrop user equilibrium (UE) or stochastic user equilibrium (SUE). First, the existence of multiple network equilibria is necessary for modeling irreversible network change. Unlike UE or SUE, the BRUE multiple equilibria do not rely on non-separable link cost functions, which makes our model applicable to real-world large-scale networks, where well-calibrated non-separable link cost functions are generally not available. Second, travelers’ boundedly rational behavior in route choice is explicitly considered in our model. The proposed model is applied to the Twin Cities network to model the flow evolution during the collapse and reopening of the I-35 W Bridge. The results show that our model can to a reasonable level reproduce the observed phenomenon of irreversible network change.