SIMULATION AND MATHEMATICAL MODELING TO SUPPORT COMMUNITY-WIDE EVACUATION DECISIONS FOR MULTIPLE POPULATION GROUPS

Evacuating a large population from an at-risk area has been the subject of extensive research over the past few decades. In order to measure trip completion and total evacuation times accurately, most researchers have implemented some combination of simulation and optimization methods to provide vehicular flow and congestion data. While the general at-risk population comprises the majority of travelers on the road network, there are often specific groups to consider when assessing the ability to evacuate an entire population. In particular, healthcare facilities (e.g., hospitals) may require evacuation, and the trip times may become an important health issue for patients being evacuated. Emergency vehicles from these facilities will share the same roadways and exit paths that are used by the local community, and it becomes increasingly important to minimize long travel times when patient care must be provided during transport. As the size of the area to model grows larger, predicting individual vehicle performance becomes more difficult. Standard transportation-specific micro-simulation, which models vehicle interactions and driver behaviors in detail, may perform very well on road networks that are smaller in size. In this research, a novel modeling approach, based on cell transmission and a speed-flow relationship, is proposed that combines the \u27micro\u27 and \u27meso\u27 approaches of simulation modeling. The model is developed using a general purpose simulation software package. This allows for an analysis at each vehicle level in the travel network. In addition, using these method and approaches, we can carry out dynamic trip planning where evacuees decide their route according to current road and traffic conditions. By translating this concept to an actual implementation, a traffic management center could identify current best travel routes between several origins and destinations, while continuing to update this list periodically. The model could suggest routings that favor either a user-optimal or system-optimal objective. This research also extended the concept of dynamic traffic assignment while modeling evacuation traffic. This extension includes the utilization of Wardrop\u27s System Optimum theory, where flow throughout the network is controlled in order to lower the risk of traffic congestion. Within this framework traffic flow is optimized to provide a route assignment under dynamic traffic conditions. This dissertation provides a practical and effective solution for a comprehensive evacuation analysis of a large, metropolitan area and the evacuation routes extending over 100 miles. Using the methodologies in this dissertation, we were able to create evacuation input data for general as well as special needs populations. These data were fed into the tailored simulation model to determine critical evacuation start times and evacuation windows for both the community-wide evacuation. Moreover, our analysis suggested that a hospital evacuation would need to precede a community-wide evacuation if the community-wide evacuation does not begin more than 24 hours before a hurricane landfall. To provide a more proactive approach, we further suggested a routing strategy, through a dynamic traffic assignment framework, for supporting an optimal flow of traffic during an evacuation. The dynamic traffic assignment approach also provides a mechanism for recommending specific time intervals when traffic should be diverted in order to reduce traffic congestion

Traffic Control and Route Choice; Capacity Maximization and Stability

Peer reviewedPublisher PD

Dynamic User Equilibrium (DUE)

The quantitative analysis of road network traffic performed through static assignment models yields the transport demand-supply equilibrium under the assumption of within-day stationarity. This implies that the relevant variables of the system (i.e. user flows, travel times, costs) are assumed to be constant over time within the reference period. Although static assignment models satisfactorily reproduce congestion effects on traffic flow and cost patterns, they do not allow to represent the variation over time of the demand flows (i.e. around the rush hour) and of the network performances (i.e. in presence of time varying tolls, lane usage, signal plans, link usage permission); most importantly, they cannot reproduce some important dynamic phenomena, such as the formation and dispersion of vehicle queues due to the temporary over-saturation of road sections, and the spillback, that is queues propagation towards upstream roads

A splitting rate model of traffic re-routeing and traffic control

Non peer reviewedPublisher PD

Using the general link transmission model in a dynamic traffic assignment to simulate congestion on urban networks

This article presents two new models of Dynamic User Equilibrium that are particularly suited for ITS applications, where the evolution of vehicle flows and travel times must be simulated on large road networks, possibly in real-time. The key feature of the proposed models is the detail representation of the main congestion phenomena occurring at nodes of urban networks, such as vehicle queues and their spillback, as well as flow conflicts in mergins and diversions. Compared to the simple word of static assignment, where only the congestion along the arc is typically reproduced through a separable relation between vehicle flow and travel time, this type of DTA models are much more complex, as the above relation becomes non-separable, both in time and space. Traffic simulation is here attained through a macroscopic flow model, that extends the theory of kinematic waves to urban networks and non-linear fundamental diagrams: the General Link Transmission Model. The sub-models of the GLTM, namely the Node Intersection Model, the Forward Propagation Model of vehicles and the Backward Propagation Model of spaces, can be combined in two different ways to produce arc travel times starting from turn flows. The first approach is to consider short time intervals of a few seconds and process all nodes for each temporal layer in chronological order. The second approach allows to consider long time intervals of a few minutes and for each sub-model requires to process the whole temporal profile of involved variables. The two resulting DTA models are here analyzed and compared with the aim of identifying their possible use cases. A rigorous mathematical formulation is out of the scope of this paper, as well as a detailed explanation of the solution algorithm. The dynamic equilibrium is anyhow sought through a new method based on Gradient Projection, which is capable to solve both proposed models with any desired precision in a reasonable number of iterations. Its fast convergence is essential to show that the two proposed models for network congestion actually converge at equilibrium to nearly identical solutions in terms of arc flows and travel times, despite their two diametrical approaches wrt the dynamic nature of the problem, as shown in the numerical tests presented here

System optimizing flow and externalities in time-dependent road networks

This paper develops a framework for analysing and calculating system optimizing flow and externalities in time-dependent road networks. The externalities are derived by using a novel sensitivity analysis of traffic models. The optimal network flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. This control theoretic formulation can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models. The analysis in this paper is more general and is applied to calculate the system optimizing flow for Friesz’s whole link traffic model. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

Analysis of dynamic system optimal assignment with departure time choice

Most analyses on dynamic system optimal (DSO) assignment are done by using the control theory with an outflow traffic model. On the one hand, this control theoretical formulation provides some attractive mathematical properties for analysis. On the other hand, however, this kind of formulation often ignores the importance of ensuring proper flow propagation. Moreover, the outflow models have also been extensively criticized for their implausible traffic behaviour. This paper aims to provide another framework for analysing a DSO assignment problem based upon sound traffic models. The assignment problem we considered aims to minimize the total system cost in a network by seeking an optimal inflow profile within a fixed planning horizon. This paper first summarizes the requirements on a plausible traffic model and reviews three common traffic models. The necessary conditions for the optimization problem are then derived using a calculus of variations technique. Finally, a simple working example and some concluding remarks are given

User equilibrium, system optimum, and externalities in time-dependent road networks

This paper develops a comprehensive framework for analysing and calculating user equilibrium, system optimum, and externalities in time-dependent road networks. Under dynamic user equilibrium, traffic is assigned such that for each origin-destination pair in the network, the individual travel costs experienced by each traveller, no matter which combination of travel route and departure time he/she chooses, are equal and minimal. The system optimal flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. The externalities are derived by using a novel sensitivity analysis. The analyses developed in this paper can work with general travel cost functions. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given

Traffic models for dynamic system optimal assignment

Most analyses on dynamic system optimal (DSO) assignment are done by using a control theory with an outflow traffic model. On the one hand, this control theoretical formulation provides some attractive mathematical properties for analysis. On the other hand, however, this kind of formulation often ignores the importance of ensuring proper flow propagation. Moreover, the outflow models have also been extensively criticized for their implausible traffic behaviour. This paper aims to provide another framework for analysing a DSO assignment problem based upon sound traffic models. The assignment problem we considered aims to minimize the total system cost in a network by seeking an optimal inflow profile within a fixed planning horizon. This paper first summarizes the requirements on a plausible traffic model and reviews three common traffic models. The necessary conditions for the optimization problem are then derived using a calculus of variations technique. Finally, a simple working example and concluding remarks are given