Natale Papola

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.

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.

Schedule-based transit assignment: new dynamic equilibrium model with vehicle capacity constraints

We propose in this paper a new approach for modelling congested transit networks with fixed timetables where it may happen that there is not enough room onboard to allow all users waiting for a given line on the arriving carrier, so that passengers need to queue at the stop until the service becomes actually available to them. The traditional approach to reproduce this phenomenon within the established framework of diachronic graphs, where the supply is represented through a space-time network, is to introduce volume-delay functions for waiting arcs, which are meant to discourage passengers from boarding overcrowded carriers. However, this produces a distortion on the cost pattern, since passengers who achieve boarding do not suffer any additional cost, and may also cause numerical instability. To overcome these limitations we extend to the case of scheduled services an existing Dynamic Traffic Assignment model, allowing for explicit capacity constraints and FIFO queue representation, where the equilibrium is formulated as a fixed point problem in terms of flow temporal profiles. The proposed model propagates time-continuous flows of passengers on the pedestrian network and time-discrete point-packets of passengers on the line network. To this end, the waiting time pattern, corresponding to a given flow temporal profile of pedestrians who reach a stop to ride a certain line, 2 Natale Papola, Francesco Filippi, Guido Gentile, Lorenzo Meschini has a saw-tooth temporal profile such to concentrate passengers on the scheduled runs, while satisfying the constraint that the number of boarding users must not be higher than the onboard residual capacities. An MSA algorithm is also devised, whose efficiency is tested on the regional transit network of Rome.

Maximal bandwidth problems: a new algorithm based on the properties of periodicity of the system

A new approach to arterial progression optimisation, based upon the properties of periodicity in time and space of the system, gives rise to the concept of equivalent systems and module of the system, which allow us to devise a very rapid algorithm for solving a bandwidth maximisation problem. Because inbound speed, outbound speed, and cycle time are synthetically expressed by the module, investigating the dependence of the solution upon these variables is greatly facilitated. The knowledge of the solution as a function of the module makes it possible to determine easily and rapidly the supremum value of the bandwidth, while the availability of a family of maximal bandwidth solutions opens new perspectives in investigating the relationship between bandwidth maximisation and delay and stop minimisation problems.

Bandwidth maximization: Split and unsplit solutions

The mathematical formulation of the problem of maximizing the green band in a two-way street is performed. In so doing, in addition to problems for which the bandwidths are unsplit, we consider cases in which the bandwidths in a single cycle, in one or both directions, are split into two intervals separated by a red time. The expression of the bandwidth as a function of the offset and the distance between a pair of signals is not the same for every possible value of these variables. However, the system is periodic in space as well as in time. It is, moreover, symmetrical with respect to a half-period both in time and in space. These properties made it possible to find, without ambiguity, the different expressions of the bandwidth and the best solution for any given pair of signals. As a result, when the best solution is of the split type, it is, obviously, better than the one of the unsplit type; however, the differences, usually small for a pair of signals, are generally negligible or nil for a sequence of a sufficiently large number of signals.

A New Analytical Model for Traffic Signal Synchronization

In this paper, using some mathematical properties of the maximal bandwidth problem, an analytical formalization in close form expressing travel time and average delay as functions of maximal bandwidth variables has been found out. A calculation procedure has also been carried out and numerical examples are presented. The results exhibit a more than satisfactory efficiency of the procedure which, interestingly, can be extended to more general problems, like global network optimization.

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.

OPTIMAL RESOURCE ALLOCATION TO ELEMENTARY NETWORKS

A wide range of transportation bilevel problems are investigated referring to an elementary network consisting of one origin destination (OD) pair, with a given demand, connected by two links. In this context, it is apparent that these problems, generally non-convex, exhibit several local minima. Most results are supplied in a graphical form and analytical proofs are developed for the Network Design Problem with linear investment functions.