This paper develops a novel linear programming formulation for autonomous intersection control (LPAIC) accounting for traffic dynamics within a connected vehicle environment. Firstly, a lane based bi-level optimization model is introduced to propagate traffic flows in the network, accounting for dynamic departure time, dynamic route choice, and autonomous intersection control in the context of system optimum network model. Then the bi-level optimization model is transformed to the linear programming formulation by relaxing the nonlinear constraints with a set of linear inequalities. One special feature of the LPAIC formulation is that the entries of the constraint matrix has only {−1, 0, 1} values. Moreover, it is proved that the constraint matrix is totally unimodular, the optimal solution exists and contains only integer values. It is also shown that the traffic flows from different lanes pass through the conflict points of the intersection safely and there are no holding flows in the solution. Three numerical case studies are conducted to demonstrate the properties and effectiveness of the LPAIC formulation to solve autonomous intersection control.

A linear programming formulation for autonomous intersection control within a dynamic traffic assignment and connected vehicle environment

Morning commuters choose their departure times based on a combination of factors—the chances of running into bottleneck congestion, the likely schedule delays, and parking space availability. This study investigates the morning commute problem with both bottleneck congestion and parking space constraints. In particular, it considers the situation when some commuters have reserved parking spots while others have to compete for public ones on a first-come-first-served basis. Unlike the traditional pure bottleneck model, the rush-hour dynamic traffic pattern with a binding parking capacity constraint varies with the relative proportions of the two classes of commuters. It is found that an appropriate combination of reserved and unreserved parking spots can temporally relieve traffic congestion at the bottleneck and hence reduce the total system cost, because commuters without a reserved parking spot are compelled to leave home earlier in order to secure a public parking spot. System performance is quantified in terms of the relative proportions of the two classes of commuters and is compared with those in the extreme cases when all auto commuters have to compete for parking and when none of them have to compete for one.

On the morning commute problem with bottleneck congestion and parking space constraints

https://opus.lib.uts.edu.au/bitstream/10453/44134/1/IS-survey.pdf

Multilevel decision-making

When total parking supply in an urban downtown area is insufficient, morning commuters would choose their departure times not only to trade off bottleneck congestion and schedule delays, but also to secure a parking space. Recent studies found that an appropriate combination of reserved and unreserved parking spaces can spread the departures of those morning commuters and hence reduce their total travel cost. To further mitigate both traffic congestion and social cost from competition for parking, this study considers a parking reservation scheme with expiration times, where commuters with a parking reservation have to arrive at parking spaces for the reservation before a predetermined expiration time. We first show that if all parking reservations have the same expiration time, it is socially preferable to set the reservations to be non-expirable, i.e., without expiration time. However, if differentiated expiration times are properly designed, the total travel cost can be further reduced as compared with the reservation scheme without expiration time, since the peak will be further smoothed out. We explore socially desirable equilibrium flow patterns under the parking reservation scheme with differentiated expiration times. Finally, efficiencies of the reservation schemes are examined.

Expirable parking reservations for managing morning commute with parking space constraints

It is explained why the set of the fundamental empirical features of traffic breakdown (a transition from free flow to congested traffic) should be the empirical basis for any traffic and transportation theory that can be reliably used for control and optimization in traffic networks. It is shown that the generally accepted fundamentals and methodologies of the traffic and transportation theory are not consistent with the set of the fundamental empirical features of traffic breakdown at a highway bottleneck. To these fundamentals and methodologies of the traffic and transportation theory belong (i) Lighthill–Whitham–Richards (LWR) theory, (ii) the General Motors (GM) model class (for example, Herman, Gazis et al. GM model, Gipps’s model, Payne’s model, Newell’s optimal velocity (OV) model, Wiedemann’s model, Bando et al. OV model, Treiber’s IDM, Kraus’s model), (iii) the understanding of highway capacity as a particular (fixed or stochastic) value, and (iv) principles for traffic and transportation network optimization and control (for example, Wardrop’s user equilibrium (UE) and system optimum (SO) principles). Alternatively to these generally accepted fundamentals and methodologies of the traffic and transportation theory, we discuss the three-phase traffic theory as the basis for traffic flow modeling as well as briefly consider the network breakdown minimization (BM) principle for the optimization of traffic and transportation networks with road bottlenecks.

Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: A brief review

This paper develops a formulation for the network level dynamic traffic equilibrium model with departure time choice and route choice. The embedded network loading procedure follows the cell transmission model without the holding-back issues by using detailed representations of flows at merges and diverges. The problem is modeled using a complementarity approach. The existence of the equilibrium solution is discussed using techniques from generalized variational inequalities. Computational results are performed using state of the art solvers. Since these solvers fail to solve any reasonable size networks, a specialized projection algorithm is developed to solve the problem. Numerical results are presented to demonstrate the performance of the algorithm in various starting with simple networks and extending to reasonable size networks with different traffic parameters. It is shown that the solution procedure produces good dynamic equilibrium solutions for general transportation networks.

Dynamic user equilibrium with a path based cell transmission model for general traffic networks

In this paper we formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand. The formulation is based on ideas from complementarity theory. The travel time is estimated based on two methods which have different transportation applications: (1) maximum travel time and (2) average travel time. These travel time functions result in linear and non-linear complementarity formulations respectively. Solution existence and the properties of the formulations are rigorously analyzed. Extensive computational experiments are conducted to demonstrate the benefits of the proposed formulations on various test networks.

Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

Traffic holding-back is considered an undesirable issue in dynamic traffic assignment since the vehicles are artificially held back on links in spite of the availability of downstream capacity. Holding-back occurs naturally in some system optimal dynamic traffic assignment models. In this paper, we focus on the holding back issue in the cell transmission based models and review the current methods of solving holding-back to understand their advantages and drawbacks. Then, we propose improvements to overcome the drawbacks of the current models. Finally, we propose a novel model which completely eliminates holding-back in a system optimal dynamic traffic assignment for traffic networks with multiple O–D pairs. Rigorous numerical results illustrate the benefits of using the proposed models.

On the holding-back problem in the cell transmission based dynamic traffic assignment models

A Bi-level Formulation for the Combined Dynamic Equilibrium based Traffic Signal Control

Household behavior and dynamic traffic flows are the two most important aspects of hurricane evacuations. However, current evacuation models largely overlook the complexity of household behavior leading to oversimplified traffic assignments and, as a result, inaccurate evacuation clearance times in the network. In this paper, we present a high fidelity multi-agent simulation model called A-RESCUE (Agent-based Regional Evacuation Simulator Coupled with User Enriched behavior) that integrates the rich activity behavior of the evacuating households with the network level assignment to predict and evaluate evacuation clearance times. The simulator can generate evacuation demand on the fly, truly capturing the dynamic nature of a hurricane evacuation. The simulator consists of two major components: household decision-making module and traffic flow module. In the simulation, each household is an agent making various evacuation related decisions based on advanced behavioral models. From household decisions, a number of vehicles are generated and entered in the evacuation transportation network at different time intervals. An adaptive routing strategy that can achieve efficient network-wide traffic measurements is proposed. Computational results are presented based on simulations over the Miami-Dade network with detailed representation of the road network geometry. The simulation results demonstrate the evolution of traffic congestion as a function of the household decision-making, the variance of the congestion across different areas relative to the storm path and the most congested O-D pairs in the network. The simulation tool can be used as a planning tool to make decisions related to how traffic information should be communicated and in the design of traffic management policies such as contra-flow strategies during evacuations.

Kien Doan

Papers

Dynamic user equilibrium with a path based cell transmission model for general traffic networks

Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

On the holding-back problem in the cell transmission based dynamic traffic assignment models

A Bi-level Formulation for the Combined Dynamic Equilibrium based Traffic Signal Control

A-RESCUE: An Agent based Regional Evacuation Simulator Coupled with User Enriched Behavior