Guido Gentile

Route Choice on Transit Networks with Online Information at Stops

Passengers on a transit network with common lines are often faced with the problem of choosing between either to board the arriving bus or to wait for a faster one. Many assignment models are based on the classical assumption that at a given stop passengers board the first arriving carrier of a certain subset of the available lines, often referred to as the attractive set. In this case, it has been shown that, if the headway distributions are exponential, then an optimal subset of lines minimizing the passenger travel time can be easily determined. However, when online information on future arrivals of buses are posted at the stop, it is unlikely that the above classical assumption holds. In this case, passengers may choose to board a line that offers the best combination of displayed waiting time and expected travel time to their destination once boarded. In this paper, we propose a general framework for determining the probability of boarding each line available at a stop when online information on bus waiting times is provided to passengers. We will also show that the classical model without online information may be interpreted as a particular instance of the proposed framework, this way achieving an extension to general headway distributions. The impact of the availability of information regarding bus arrivals and that of the regularity of transit lines on the network loads, as well as on the passenger travel times, will be illustrated with small numerical examples.

Network pricing optimization in multi-user and multimodal context with elastic demand

Abstract Network Pricing Optimization (NPO) is formulated first as a Network Design Problem (NDP) where the design variables are tolls, the objective function is the Social Surplus and the equilibrium constraint is any current multi-user multimodal stochastic traffic assignment model with elastic demand up to trip generation and asymmetric arc cost function Jacobian. NPO is then formulated also as an Efficient Allocation Problem (EAP), where an optimal flow pattern, the System Optimum (SO), is sought and tolls are consistently determined. Necessary and sufficient conditions for the solutions to both problems are stated, showing the validity of the marginal pricing principle in the context considered.

The General Link Transmission Model for Dynamic Network Loading and a Comparison with the DUE Algorithm

This chapter will present the General Link Transmission Model (GLTM) that is the extension of the link transmission model (LTM) to any concave fundamental diagram and node topology and compare it with the dynamic user equilibrium (DUE) algorithm. This assignment method has been employed successfully (1) as a simulation engine in the solution of a signal synchronization problem based on a genetic algorithm, which by its nature requires many fast runs of the black box, and (2) to extend in space and time the traffic measured by probe vehicles in a travel time estimation problem, which requires short-term predictions on large congested networks. The model proved to be flexible, reliable, and easy to calibrate, as well as efficient in the use of memory and CPU. It is recommended when route choice is not crucial or elastic, otherwise DUE is preferable since it is specifically designed for the equilibrium problem. However, in the later case it is also very useful to run the GLTM at the end of DUE based on the equilibrium splitting rates, so a s to achieve a fine-grained solution of the resulting continuous dynamic network loading (CDNL)

Local User Cost Equilibrium: a bush-based algorithm for traffic assignment

This article presents a new algorithm for traffic assignment, called Local User Cost Equilibrium (LUCE), which iteratively solves a sequence of user-equilibrium problems associated with flows exiting from a node. The method is based on the idea of assigning users directed towards each destination separately; these flows form a bush, i.e. an acyclic sub-graph that connects every node to that destination. For each node, the algorithm considers the arcs of its forward star as the set of travel alternatives available to users and seeks a deterministic equilibrium of flows towards the same destination. The cost function associated with each of these local route choices expresses the average impedance to reaching the destination if a user continues the trip on a particular arc. The method is ‘local’ in an analytical sense, because the cost function is linearised at the current flow pattern, as if it was independent from the other splitting rates of the same node. The method is also ‘local’ in a topological sense, as nodes are processed through a polynomial visit of the current bush, inspired by dynamic programming. The node problem is formulated as a quadratic program in terms of destination-specific flows. We prove that its solution recursively applied in topological order provides a descent direction with respect to the sum-integral objective function of traffic assignment. The local equilibrium problem at nodes is solved through a greedy algorithm resembling the ad-hoc method used to compute shortest hyperpaths in transit assignment. The latter is the main contribution of this article. The main advantage of LUCE is to achieve a fast convergence rate that compares favourably with the existing methods, and to implicitly assign the demand flow of each origin-destination pair on several paths at once.

A demand model with departure time choice for within-day dynamic traffic assignment

A within-day dynamic demand model is formulated, embodying, in addition to the classic generation, distribution and modal split stages, an actual demand model taking into account departure time choice. The work focuses on this last stage, represented through an extension of the discrete choice framework to a continuous choice set. The dynamic multimodal supply and equilibrium model based on implicit path enumeration, which have been developed in previous work are outlined here, to define within-day dynamic elastic demand stochastic multimodal equilibrium as a fixed point problem on users flows and transit line frequencies. A MSA algorithm capable, in the case of Logit route choice models, of supplying equilibrium flows and frequencies on real dimension networks, is presented, as well as the specific procedures implementing the departure time choice and actual demand models. Finally, the results obtained on a test network are presented and conclusions are drawn.

Tolls and transit frequencies optimization

In this paper a tolls and transit frequencies optimization problem has been reduced to a specific equivalent equilibrium assignment problem and its local solution conditions have been stated. A specific fixed-point approach algorithm has also been devised, introducing a hyper-network consisting of a multi-modal transportation network combined with a specific investment network. Based on a test network, a numerical example concerning different scenarios is presented, exhibiting encouraging results.

A dynamic route choice model for public transport networks with boarding queues

Abstract The concepts of optimal strategy and hyperpath were born within the framework of static frequency-based public transport assignment, where it is assumed that travel times and frequencies do not change over time and no overcrowding occurs. However, the formation of queues at public transport stops can prevent passengers from boarding the first vehicle approaching and can thus lead to additional delays in their trip. Assuming that passengers know from previous experience that for certain stops/lines they will have to wait for the arrival of the 2nd, 3rd, …, k-th vehicle, they may alter their route choices, thus resulting in a different assignment of flows across the network. The aim of this paper is to investigate route choice behaviour changes as a result of the formation and dispersion of queues at stops within the framework of optimal travel strategies. A new model is developed, based on modifications of existing algorithms.

Dynamic User Equilibrium in Public Transport Networks with Passenger Congestion and Hyperpaths

This paper presents a Dynamic User Equilibrium for bus networks where recurrent overcrowding results in queues at stops. The route choice model embedded in the dynamic assignment explicitly considers common lines and strategies with alternative routes. As such, the shortest hyperpath problem is extended to a dynamic scenario with capacity constraints where the diversion probabilities depend on the time the stop is reached and on the expected congestion level at that time. In order to reproduce congestion for all the lines sharing a stop, the Bottleneck Queue model with time-varying exit capacity, introduced in Meschini et al. (2007), is extended. The above is applied to separate queues for each line in order to satisfy the First-In-First-Out principle within every attractive set, while allowing overtaking among passengers having different attractive sets but queuing single file.

New Formulations of the Stochastic User Equilibrium with Logit Route Choice as an Extension of the Deterministic Model

This paper addresses the stochastic user equilibrium (SUE) in the case where the route choice is the multinomial logit model (MNL). Our main finding is that MNL SUE can be formulated and solved as ...

TOLL CORDON DESIGN

Pricing is one of the best tools to improve the efficiency of highly congested transportation networks. It has been shown that an optimal toll pattern can be determined by applying the welfare-economics principle of marginal pricing. Because implementing the marginal pricing solution to the toll optimization problem requires charging each arc of the network any real valued toll, which is not realistic, then it is worth addressing the problem with reference to specific pricing schemes. This paper discusses the case where the use of private vehicles traveling into a distinct area of the city are charged tolls. The aim of the work is to define a methodology capable of determining the optimal shape of the cordon delimiting such a charged-access area, while the toll is assumed to be given and constant.