System Optimal Dynamic Traffic Assignment Research Articles

Integration of Environmental Objectives in a System Optimal Dynamic Traffic Assignment Model

Abstract: Maintaining air‐quality standards is a major concern for transportation planners and policy makers in the United States. This necessitates considering nontraditional emission objectives in transportation systems modeling. In this research, we integrate emission‐based objective into the traditional travel time based dynamic assignment framework. Carbon monoxide (CO) emissions from vehicles are computed as functions of space mean speed (determined from an embedded mesoscopic traffic flow model). Different performance metrics (CO emission, system wide travel time, and speed profiles) from the integrated model are compared with traditional dynamic assignment model (with travel time minimization objective). In addition, results indicate changes in route choice behavior of the road users when emission objective is integrated to dynamic assignment framework.

Robust optimization approach for system optimal dynamic traffic assignment with demand uncertainty

This research deals with the path-based system optimal dynamic traffic assignment (SODTA) problem with uncertain demands that are assumed to be bounded by a prescribed uncertainty set. A robust optimization approach is adopted to address this problem. The objective is to minimize the total network travel time under the worst-case scenario defined by a pre-determined demand uncertainty set. We formulate the robust counterpart optimization problem of SODTA for a general uncertainty set and show that solving the robust SODTA problem is not more difficult than solving the deterministic SODTA problem for some specific types of uncertainty set. Moreover, a column generation-based algorithmic framework that embeds a scaled gradient projection algorithm is proposed to solve the SODTA problem. Numerical experiments were conducted to demonstrate the effectiveness of the algorithm and to examine the impact of different types of demand uncertainty set on solution quality.

A Mixed Integer Linear Program for the Single Destination System Optimum Dynamic Traffic Assignment Problem with Physical Queue

In order to solve the system optimum dynamic traffic assignment problem, the whole link model with physical queue is used to formulate the single destination system optimum dynamic traffic assignment problem as a mixed linear program. A relationship between the cumulative curves and the wave speed presented by Newell (1993) is used to present a dynamic network model in considering spillback queue. And nonlinear constrains are relaxed into mixed linear constrains; the linear program software is used to solve the system optimum dynamic traffic assignment problem. A numerical example illustrates the simplicity and applicability of the proposed approach. KEYWORDS: Dynamic System Optimum Traffic Assignment; physical queue; mixed integer linear programming

Dynamic Traffic Assignment under Uncertainty: A Distributional Robust Chance-Constrained Approach

This paper provides a chance-constrained programming approach for transportation planning and operations under uncertainty. The major contribution of this paper is to approximate a joint chance-constrained Cell Transmission Model based System Optimum Dynamic Traffic Assignment with only partial distributional information about uncertainty as a linear program which is computationally efficient. Numerical experiments have been conducted to show the performance of the proposed approach compared with other two workable approaches based on a cumulative distribution function and a sampling method. This new approach can be used as a pragmatic tool for system optimum dynamic traffic control and management.

A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem

The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicle-holding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP.

Enhancing Realism in Modeling Merge Junctions in Analytical Models for System-Optimal Dynamic Traffic Assignment

The existing analytical system-optimal dynamic traffic assignment (SO-DTA) model formulated with the linear programming (LP) approach usually assumes system control over vehicles in the entire network. This property would give rise to unreasonable priorities at merge junctions that are sometimes physically impossible to realize for the given roadway configuration. In this paper, we demonstrate that models with and without considering the merge-priority ratio would exhibit very different traffic patterns and route-choice behavior. To realistically model traffic flow on a transportation network, one should properly distinguish the level of control by drivers, roadway geometry, and system providers. This paper also attempts to develop an LP module that explicitly considers the merge-priority ratio of a merge junction and can potentially be incorporated into the existing LP formulation of the SO-DTA problem based on the cell-transmission model. By more realistically modelling the behavior of vehicles at merge junctions, the obtained solution can be used as a benchmark to compare control strategies developed without explicitly considering the merge-priority ratio at merge junctions or strategies developed with heuristic approaches.

Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains

This paper proposes a methodology to generate a robust logistics plan that can mitigate demand uncertainty in humanitarian relief supply chains. More specifically, we apply robust optimization (RO) for dynamically assigning emergency response and evacuation traffic flow problems with time dependent demand uncertainty. This paper studies a Cell Transmission Model (CTM) based system optimum dynamic traffic assignment model. We adopt a min–max criterion and apply an extension of the RO method adjusted to dynamic optimization problems, an affinely adjustable robust counterpart (AARC) approach. Simulation experiments show that the AARC solution provides excellent results when compared to deterministic solution and sampling based stochastic programming solution. General insights of RO and transportation that may have wider applicability in humanitarian relief supply chains are provided.

A cell-based Merchant–Nemhauser model for the system optimum dynamic traffic assignment problem

A cell-based variant of the Merchant–Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop’s second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.

Evacuation Network Modeling via Dynamic Traffic Assignment with Probabilistic Demand and Capacity Constraints

Two major sources of uncertainty in evacuation modeling are randomness in evacuation demand and roadway capacity. This paper takes these two sources of uncertainty into account in proposing an analytical system-optimal dynamic traffic assignment model with probabilistic demand and capacity constraints. The problem is modeled on the basis of two stochastic modeling approaches considering the problem's constraints, namely, individual chance constraints and joint chance constraints. The probability distributions of random demands and capacities are assumed to be discrete. A solution method customized for stochastic programming models with random discrete right-hand sides is used. The differences in reliability between the two models are discussed with the help of a numerical example. Although use of the proposed stochastic dynamic traffic assignment is not confined to evacuation modeling, it provides an important probabilistic modeling and analysis framework for evacuation modeling in which the demand and capacity uncertainties are vital. Overall, the proposed model enables evacuation planners to obtain results that can be interpreted through well-understood reliability measures instead of deterministic point estimates of the highly stochastic evacuation process.

Evacuation Modelling in the United States: Does the Demand Model Choice Matter?

This paper reviews the literature on the evacuation demand problem, with an emphasis on the impact of various modelling approaches on network‐wide evacuation performance measures. First, a number of important factors that affect evacuee behaviour are summarized. Evacuation software packages and tools are also investigated in terms of the demand generation model they use. The most widely used models are then selected for performing sensitivity analysis. Next, a cell‐transmission‐based system optimal dynamic traffic assignment (SO‐DTA) model is employed to assess the effects of the demand model choice on the clearance time and average travel time. It is concluded that evacuation demand models should be selected with care, and policy makers should make sure the selected demand curve can replicate real‐life conditions with relatively high fidelity for the study region to be able to develop reliable and realistic evacuation plans.

What Do Different Traffic Flow Models Mean for System-Optimal Dynamic Traffic Assignment in a Many-to-One Network?

A variety of macroscopic traffic flow models have been applied to formulate the link-based system optimal dynamic traffic assignment (SO-DTA) problem in a many-to-one network. It is expected that SO-DTA models based on various traffic flow models usually result in different optimal link traffic evolution patterns, but whether and how traffic flow models affect the minimal system cost and the corresponding optimal arrival pattern at the destination is unclear. Three traffic flow models–point-queue, spatial-queue, and cell-transmission–are examined, and their resulted minimal system cost in many-to-one networks is compared. It is proved that for three simple networks–a linear network with two sequential bottlenecks, a two-in-one-out merge network, and a one-in-two-out diverge network–the minimal system costs for the SO-DTA models based on these three traffic flow models are identical. Numerical experiments show that this property appears to be held for general many-to-one networks. The reason may be that all three traffic flow models propagate the uncongested flows at the same speed and release the congested flows always at the link capacity. In SO-DTA applications where only the minimal system cost or arrival pattern at the destination is of major interest, the findings can be utilized to substantially expedite the solution procedure.

Heuristic Framework for Optimizing Hurricane Evacuation Operations

In this research, an optimization framework is proposed to find the system-optimal solution for the emergency evacuation planning problem. The model simultaneously solves for the choice of destination (shelter), evacuation route, and departure time for all evacuees from given origins (endangered zones). Heuristic algorithms are proposed to find the system-optimal dynamic traffic assignment during an iterative procedure. A mesoscopic traffic simulator is embedded in the optimization modules to find travel time marginals and obtain required performance measures in every iteration. Implementing the proposed algorithm brings about dramatic improvements in network performance measures such as total travel time and network clearance time in a case study of Ocean City, Maryland.

Dynamic Network Simplex Method for Designing Emergency Evacuation Plans

The cell-based system optimal dynamic traffic assignment (SO-DTA) model has recently been applied to study emergency evacuation by a handful of authors. It is recognized that an optimal solution to this model may contain a phenomenon called traffic holding, which discharges flow at a lower rate than what can be achieved under the given traffic conditions. Mathematically, this is caused by the relaxation of traffic flow propagation constraints. In this paper, an optimal traffic pattern that contains no holding is always proved to exist in the context of evacuation planning. An optimal traffic pattern without holding is much easier and less costly to implement in emergency response. A dynamic network simplex method for solving the simplified SO-DTA model that represents traffic flow propagation by a point-queue model is proposed. By making full use of the network structure, the algorithm is able to identify an optimal solution without holding. For the original cell-based SO-DTA, an iterative procedure is suggested that can effectively eliminate holding in a solution obtained from a conventional linear programming algorithm.

Modeling no-notice mass evacuation using a dynamic traffic flow optimization model

This paper presents a network transformation and demand specification approach for no-notice evacuation modeling. The research is aimed at formulating the Joint Evacuation Destination–Route-Flow-Departure (JEDRFD) problem of a no-notice mass evacuation into a system optimal dynamic traffic assignment model. The proposed network transformation technique permits the conversion of a typical transportation planning network to an evacuation network configuration in which a hot zone, evacuation destinations, virtual super-safe node and connectors are established. Combined with a demand specification method, the JEDRFD problem is formulated as a single-destination cell-transmission-model-based linear programming model. The advantage of the proposed model compared with prior studies in the literature is that the multi-dimensional evacuation operation decisions are jointly obtained at the optimum of the JEDRFD model. The linear single-destination structure of the proposed model implies another advantage in computational efficiency. A numerical example is given to illustrate the modeling procedure and solution properties. Real-time operational issues and data requirements are also discussed.

Impact of Probabilistic Road Capacity Constraints on the Spatial Distribution of Hurricane Evacuation Shelter Capacities

The focus of this study is on determining the change in capacity requirements and desirable shelter locations as a result of link capacity changes during evacuation. A cell transmission-based system optimal dynamic traffic assignment (SO-DTA) formulation first proposed by Ziliaskopoulos is extended by introducing probabilistic capacity constraints. The p-level efficient points method first proposed by Prékopa is used to deal with probabilistic capacity constraints of the proposed stochastic SO-DTA model. The model captures the probabilistic nature of link capacities that change in response to the impacts of events such as hurricanes and earthquakes that can destroy or damage highway links. First, a simple single-destination example network is studied to show the effectiveness of the proposed model. Then the impact of using stochastic and deterministic link capacities is also analyzed with a simplified multiple-origin, multiple-destination version of the Cape May, New Jersey, network. Desirable shelter locations are evaluated by letting the stochastic SO-DTA model assign flows generating the minimum systemwide travel time. The results indicate that introducing probabilistic link capacities can adjust the overall flow in the network as well as shelter utilization. Thus, if planners consider the predictions of the deterministic model, they may face the risk of not having sufficient food, medicine, and other emergency supplies in shelters. This paper suggests a more realistic approach to evacuation planning to avoid the inefficiencies that created problems after such recent major disasters as Hurricane Katrina and the tsunami in Southeast Asia.

A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).

Discrete-time dynamic traffic assignment models with periodic planning horizon: system optimum

This paper proposes a system optimal dynamic traffic assignment model that does not require the network to be empty at the beginning or at the end of the planning horizon. The model assumes that link travel times depend on traffic densities and uses a discretized planning horizon. The resulting formulation is a nonlinear program with binary variables and a time-expanded network structure. Under a relatively mild condition, the nonlinear program has a feasible solution. When necessary, constraints can be added to ensure that the solution satisfies the First-In-First-Out condition. Also included are approximation schemes based on linear integer programs that can provide solutions arbitrarily close to that of the original nonlinear problem.

System Optimal Signal Optimization Formulation

A mixed-integer linear programming formulation is proposed to solve the combined system optimal dynamic traffic assignment and signal optimization problem. Traffic conditions are modeled with the cell transmission model, a convergent numerical approximation to the hydrodynamic model of traffic flow. The formulation is suited to respond to oversaturated traffic conditions. It also can be adapted to account for turning movements, protected and permissive phases (gap acceptance), and multiple signal controller types: dynamic (traffic adaptive) and pretimed. Trials with a test network validated the formulation and achieved promising results. Specifically, dynamic signal control proved to be substantially more effective than pretimed control for incident conditions. In addition, potential benefits of rerouting vehicles in both directions of a roadway were revealed even when only one direction is closed.

System Optimal Signal Optimization Formulation

A mixed-integer linear programming formulation is proposed to solve the combined system optimal dynamic traffic assignment and signal optimization problem. Traffic conditions are modeled with the cell transmission model, a convergent numerical approximation to the hydrodynamic model of traffic flow. The formulation is suited to respond to oversaturated traffic conditions. It also can be adapted to account for turning movements, protected and permissive phases (gap acceptance), and multiple signal controller types: dynamic (traffic adaptive) and pretimed. Trials with a test network validated the formulation and achieved promising results. Specifically, dynamic signal control proved to be substantially more effective than pretimed control for incident conditions. In addition, potential benefits of rerouting vehicles in both directions of a roadway were revealed even when only one direction is closed.

Optimal Scheduling of Evacuation Operations

Evacuations necessitated by extreme events are usually envisioned as taking place with all people evacuating simultaneously; this leads to premature congestion on the surface streets and excessive delays. With the evacuating load onto the network staggered, the onset of congestion may be delayed, and people can evacuate more quickly. In this study, the problem of scheduling evacuation trips between a selected set of origin nodes and (safety) destinations was considered, with the objective of minimizing network clearance time. A modified system-optimal dynamic traffic assignment formulation is proposed; in it the total system evacuation time, as opposed to the total system trip time, is minimized. An iterative heuristic procedure is used to solve this problem: the method of successive averages is used to find the flow assignments for the next iteration; a traffic simulator, DYNASMART-P, is used to propagate the vehicles on their prescribed paths and determine the state of the system. Therefore, the simulator serves as a tool to satisfy the dynamic traffic assignment constraints implicitly while evaluating the objective function. The output of this model will be the departure time, route, and destination choices for each evacuee. The output is then aggregated to produce a time-dependent staging policy for each selected origin.