A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks. These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or, the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks

Smart Procurement of Naturally Generated Energy (SPONGE) for Plug-in Hybrid Electric Buses

We discuss a recently introduced ECO-driving concept known as SPONGE in the context of Plug-in Hybrid Electric Buses (PHEB)'s.Examples are given to illustrate the benefits of this approach to ECO-driving. Finally, distributed algorithms to realise SPONGE are discussed, paying attention to the privacy implications of the underlying optimisation problems.Comment: This paper is recently submitted to the IEEE Transactions on Automation Science and Engineerin

Tolling, Capacity Selection and Equilibrium Problems with Equilibrium Constraints

An Equilibrium problem with an equilibrium constraint is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium regarding competition in toll pricing on a network utilising 2 alternative algorithms. In the first algorithm, we utilise a Gauss Siedel fixed point approach based on the cutting constraint algorithm for toll pricing. In the second algorithm, we extend an existing sequential linear complementarity approach for finding Nash equilibrium subject to Wardrop Equilibrium constraints. Finally we consider how the equilibrium may change between the Nash competitive equilibrium and a collusive equilibrium where the two players co-operate to form the equivalent of a monopoly operation

Second best toll and capacity optimisation in network: solution algorithm and policy implications

This paper looks at the first and second-best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second-best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second-best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported

Innovative systems for the transportation disadvantaged: towards more efficient and operationally usable planning tools

When considering innovative forms of public transport for specific groups, such as demand responsive services, the challenge is to find a good balance between operational efficiency and 'user friendliness' of the scheduling algorithm even when specialized skills are not available. Regret insertion-based processes have shown their effectiveness in addressing this specific concern. We introduce a new class of hybrid regret measures to understand better why the behaviour of this kind of heuristic is superior to that of other insertion rules. Our analyses show the importance of keeping a good balance between short- and long-term strategies during the solution process. We also use this methodology to investigate the relationship between the number of vehicles needed and total distance covered - the key point of any cost analysis striving for greater efficiency. Against expectations, in most cases decreasing fleet size leads to savings in vehicle mileage, since the heuristic solution is still far from optimality

Modelling single line train operations

Scheduling of trains on a single line involves using train priorities for the resolution of conflicts. The mathematical programming model described in the first part of this paper schedules trains over a single line track when the priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay. This priority is used in a branch and bound procedure to allow the determination of optimal solutions quickly. This is demonstrated with the use of an example. Rail operations over a single line track require the existence of a set of sidings at which trains can cross and/ or overtake each other. Investment decisions on upgrading the number and location of these sidings can have a significant impact on both customer service and rail profitability. Sidings located at insufficient positions may lead to high operating costs and congestion. The second part of this paper puts forward a model to determine the optimal position of a set of sidings on a single track rail corridor. The sidings are positioned to minimise the total delay and train operating costs of a given cyclic train schedule. The key feature of the model is the allowance of non-constant train velocities and non-uniform departure times

Two-echelon freight transport optimisation: unifying concepts via a systematic review

Multi-echelon distribution schemes are one of the most common strategies adopted by the transport companies in an aim of cost reduction, but their identification in scientific literature is not always easy due to a lack of unification. This paper presents the main concepts of two-echelon distribution via a systematic review, in the specific a meta-narrative analysis, in order to identify and unify the main concepts, issues and methods that can be helpful for scientists and transport practitioners. The problem of system cost optimisation in two-echelon freight transport systems is defined. Moreover, the main variants are synthetically presented and discussed. Finally, future research directions are proposed.location-routing problems, multi-echelon distribution, cross-docking, combinatorial optimisation, systematic review.