Graph Orientation and Flows Over Time

Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -- streets, tracks, etc. -- are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus the question arises, what influence the orientation of the network has on the network flow over time problem that is being solved on the oriented network. In the literature, this is also referred to as the contraflow or lane reversal problem. We introduce and analyze the price of orientation: How much flow is lost in any orientation of the network if the time horizon remains fixed? We prove that there is always an orientation where we can still send $\frac{1}{3}$ of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is $\frac12$ which is again tight. We present more results of similar flavor and also show non-approximability results for finding the best orientation for single and multicommodity maximum flows over time

Maximum Contraflow Evacuation Planning Problems On Multi-network

Contraflow approach for the evacuation planning problem increases outbound capacity of the evacuation routes by the reversal of anti-parallel arcs, if such arcs exist. The existing literature focuses on network contraflow problems that allow only anti-parallel arcs with equal transit time. However, the problems modeled on multi-network, allowing parallel as well as anti-parallel arcs with not necessarily equal transit time, seem more realistic. In this paper, we study the maximum dynamic contraflow problem for multi-network and propose efficient solution techniques to them with discrete as well as continuous time settings. We also extend the results to solve earliest version of the problem for two terminal series parallel (TTSP) multi-network

A Framework for Developing and Integrating Effective Routing Strategies Within the Emergency Management Decision-Support System, Research Report 11-12

This report describes the modeling, calibration, and validation of a VISSIM traffic-flow simulation of the San José, California, downtown network and examines various evacuation scenarios and first-responder routings to assess strategies that would be effective in the event of a no-notice disaster. The modeled network required a large amount of data on network geometry, signal timings, signal coordination schemes, and turning-movement volumes. Turning-movement counts at intersections were used to validate the network with the empirical formula-based measure known as the GEH statistic. Once the base network was tested and validated, various scenarios were modeled to estimate evacuation and emergency vehicle arrival times. Based on these scenarios, a variety of emergency plans for San José’s downtown traffic circulation were tested and validated. The model could be used to evaluate scenarios in other communities by entering their community-specific data

An Integrated Road Construction and Resource Planning Approach to the Evacuation of Victims From Single Source to Multiple Destinations

This paper presents our study on the emergency resource-planning problem, particularly on the development of a new approach to resource planning through contraflow techniques with consideration of the repair of damaged infrastructures. The contraflow technique is aimed at reversing traffic flows in one or more inbound lanes of a divided highway for the outbound direction. As opposed to the current literature, our approach has the following salient points: (1) simultaneous consideration of contraflow and repair of repair of roads; (2) classification of victims in terms of their problems and urgency in sending them to a safe place or place to be treated; and (3) consideration of multiple destinations for victims. A simulated experiment is also described by comparing our approach with some variations of our approach. The experimental results show that our approach can lead to a reduction in evacuation time by more than 50%, as opposed to the original resource operation on the damaged transportation network, and by about 20%, as opposed to the approach with resource replanning (only) on the damaged network. In addition, the multiobjective optimization algorithm to solve our model can be generalized to other network resource-planning problems under infrastructure damage

Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

Modeling Lane-based Traffic Flow In Emergency Situations In The Presence Of Multiple Heterogeneous Flows

In recent years, natural, man-made and technological disasters have been increasing in magnitude and frequency of occurrence. Terrorist attacks have increased after the September 11, 2001. Some authorities suggest that global warming is partly the blame for the increase in frequency of natural disasters, such as the series of hurricanes in the early-2000\u27s. Furthermore, there has been noticeable growth in population within many metropolitan areas not only in the US but also worldwide. These and other facts motivate the need for better emergency evacuation route planning (EERP) approaches in order to minimize the loss of human lives and property. This research considers aspects of evacuation routing never before considered in research and, more importantly, in practice. Previous EERP models only either consider unidirectional evacuee flow from the source of a hazard to destinations of safety or unidirectional emergency first responder flow to the hazard source. However, in real-life emergency situations, these heterogeneous, incompatible flows occur simultaneously over a bi-directional capacitated lane-based travel network, especially in unanticipated emergencies. By incompatible, it is meant that the two different flows cannot occupy a given lane and merge or crossing point in the travel network at the same time. In addition, in large-scale evacuations, travel lane normal flow directions can be reversed dynamically to their contraflow directions depending upon the degree of the emergency. These characteristics provide the basis for this investigation. This research considers the multiple flow EERP problem where the network travel lanes can be reconfigured using contraflow lane reversals. The first flow is vehicular flow of evacuees from the source of a hazard to destinations of safety, and the second flow is the emergency first responders to the hazard source. After presenting a review of the work related to the multiple flow EERP problem, mathematical formulations are proposed for three variations of the EERP problem where the objective for each problem is to identify an evacuation plan (i.e., a flow schedule and network contraflow lane configuration) that minimizes network clearance time. Before the proposed formulations, the evacuation problem that considers only the flow of evacuees out of the network, which is viewed as a maximum flow problem, is formulated as an integer linear program. Then, the first proposed model formulation, which addresses the problem that considers the flow of evacuees under contraflow conditions, is presented. Next, the proposed formulation is expanded to consider the flow of evacuees and responders through the network but under normal flow conditions. Lastly, the two-flow problem of evacuees and responders under contraflow conditions is formulated. Using real-world population and travel network data, the EERP problems are each solved to optimality; however, the time required to solve the problems increases exponentially as the problem grows in size and complexity. Due to the intractable nature of the problems as the size of the network increases, a genetic-based heuristic solution procedure that generates evacuation network configurations of reasonable quality is proposed. The proposed heuristic solution approach generates evacuation plans in the order of minutes, which is desirable in emergency situations and needed to allow for immediate evacuation routing plan dissemination and implementation in the targeted areas

An Integrated Contraflow Strategy for Multimodal Evacuation

To improve the efficiency of multimodal evacuation, a network aggregation method and an integrated contraflow strategy are proposed in this paper. The network aggregation method indicates the uncertain evacuation demand on the arterial subnetwork and balances accuracy and efficiency by refining the local road subnetworks. The integrated contraflow strategy contains three arterial configurations: noncontraflow to shorten the strategy setup time, full-lane contraflow to maximize the evacuation network capacity, and bus contraflow to realize the transit cycle operation. The application of this strategy takes two steps to provide transit priority during evacuation: solve the transit-based evacuation problem with a minimum-cost flow model, firstly, and then address the auto-based evacuation problem with a bilevel network flow model. The numerical results from optimizing an evacuation network for a super typhoon justify the validness and usefulness of the network aggregation method and the integrated contraflow strategy