To evaluate the traffic state over time and space, several models can be used. A typical model for estimating the state of the traffic for a stretch of road or a road network is the cell transmission model, which is a form of state space model. This kind of model typically needs to be calibrated since the different roads have different properties. This thesis will present a calibration framework for the velocity based cell transmission model, the CTM-v. The cell transmission model for velocity is a discrete time dynamical system that can model the evolution of the velocity field on highways. Such a model can be fused with an ensemble Kalman filter update algorithm for the purpose of velocity data assimilation. Indeed, enabling velocity data assimilation was the purpose for ever developing the model in the first place and it is an essential part of the Mobile Millennium research project. Therefore a systematic methodology for calibrating the cell transmission is needed. This thesis presents a framework for calibration of the velocity based cell transmission model that is combined with the ensemble Kalman filter. The framework consists of two separate methods, one is a statistical approach to calibration of the fundamental diagram. The other is a black box optimization method, a simplification of the complex method that can solve inequality constrained optimization problems with non-differentiable objective functions. Both of these methods are integrated with the existing system, yielding a calibration framework, in particular highways were stationary detectors are part of the infrastructure. The output produced by the above mentioned system is highly dependent on the values of its characterising parameters. Such parameters need to be calibrated so as to make the model a valid representation of reality. Model calibration and validation is a process of its own, most often tailored for the researchers models and purposes. The combination of the two methods are tested in a suit of experiments for two separate highway models of Interstates 880 and 15, CA which are evaluated against travel time and space mean speed estimates given by Bluetooth detectors with an error between 7.4 and 13.4 % for the validation time periods depending on the parameter set and model.

The cell transmission model (CTM) based single destination system optimal dynamic traffic assignment (SD-SO-DTA) model has been widely applied to situations such as mass evacuations on a transportation network. Although formulated as a linear programming (LP) model, embedded multi-period cell network representation yields an extremely large model for real-size networks. As a result, most of these models are not solvable using existing LP solvers. Solutions obtained by LP also involve holding vehicles at certain locations, violating CTM flow dynamics. This doctoral research is aimed at developing innovative algorithms that overcome both computational efficiency and solution realism issues. We first prove that the LP formulation of the SD-SO-DTA problem is equivalent to the earliest arrival flow (EAF), and then develop efficient algorithms to solve EAF. Two variants of the algorithm are developed under different model assumptions and network operating conditions. For the case of time-varying network parameters, we develop a network flow algorithm on a time-expanded network. The main challenge in this approach is to address the issue of having backward wave speed lower than forward wave speed. This situation leads to non-typical constraints involving coefficients with value of less than 1. In this dissertation we develop a new network algorithm to solve this problem in optimal, even with coefficients of value less than 1. Additionally, the developed approach solves for optimal flows that exhibit non-vehicle-holding properties, which is a major breakthrough compared to all existing solution techniques for SD-SODTA. For the case of time-invariant network parameters, we reduce the SD-SO-DTA to a standard EAF problem on a dynamic network, which is constructed on the original roadway network without dividing it into cells. We prove that the EAF under free flow status is one of the optimal solutions of SD-SO-DTA, if cell properties follow a trapezoidal/triangular fundamental diagram. We use chain flows obtained on a static network to induce dynamic flows, an approach applicable to large-scale networks. Another contribution of this research is to provide a simple and practical algorithm solving the EAF with multiple sources, which has been an active research area for many years. Most existing studies involve submodular function optimization as subroutines, and thus are not practical for real-life implementation. This study’s contribution in this regard is the development of a practical algorithm that avoids submodular function optimization. The main body of the given method is comprised of |S⁺| iterations of earliest arrival s - t flow computations, where |S⁺| is the number of sources. Numerical results show that our multi-source EAF algorithm solves the SD-SO-DTA problem with time-invariant parameters to optimum.

Road traffic increases constantly and the negative consequences in the form of traffic jams can be realized especially in urban areas. In order to provide real time traffic information to road users and traffic managers, accurate computer models gain relevance. A software called Mobile Millennium Stockholm (MMS) was developed to estimate and predict travel times and has been implemented on a 7km test stretch in the north of Stockholm. The core of the software is the cell transmission model (CTM) which is a macroscopic traffic flow model based on aggregated speed observations. This thesis focuses on different calibration techniques of the so called fundamental diagram as an important input factor to the CTM. The diagrams illustrate the mathematical function which defines the relation between traffic flow, density and speed. The calibration is performed in different scenarios based on the least square (LS) and total least square (TLS) error minimization. Furthermore, sources, representing the traffic demand, and sinks, representing the surrounding of the modeled network, are implemented as dynamic parameters to model the change in traffic behavior throughout the day. Split ratios, as a representation of the drivers‘ route choice in the CTM are estimated and implemented as well. For the framework of this work, the MMS software is run in a pure prediction mode. The CTM is based on the source, sink, split and fundamental diagram parameters only and run forward in time. For each fundamental diagram calibration scenario an independent model run is performed. The evaluation of the scenarios is based on the output of the model. The results are compared to existing Bluetooth travel time measurements for the test stretch, which are used as ground truth observations, and a mean average percentage error (MAPE) is calculated. This leads to a most reasonable technique for the fundamental diagram calibration – the total least square error minimization.

Traffic problems caused by congestion are increasing in cities all over the world. As a traffic management tool traffic predictions can be used in order to make prevention actions against traffic congestion. There is one software for traffic state estimations called Mobile Millennium Stockholm (MMS) that are a part of a project for estimate real-time traffic information.In this thesis a framework for running traffic predictions in the MMS software have been implemented and tested on a stretch north of Stockholm. The thesis is focusing on the implementation and evaluation of traffic prediction by running a cell transmission model (CTM) forward in time.This method gives reliable predictions for a prediction horizon of up to 5 minutes. In order to improve the results for traffic predictions, a framework for dynamic inputs of demand and sink capacity has been implemented in the MMS system. The third part of the master thesis presents a model which adjusts the split ratios in a macroscopic traffic model based on driver behavior during congestion.

Urban transportation networks are vulnerable to various incidents. In order to combat the negative effects due to incident-related congestion, various mitigation strategies have been proposed and implemented. The effectiveness of these congestion mitigation strategies for incident conditions largely depends on the accuracy of information regarding network conditions. Therefore, an efficient and accurate procedure to determine the link states, reflected by flows and density over time, is essential to incident management. This thesis presents a user equilibrium Dynamic Traffic Assignment (DTA) model that incorporates the Cell Transmission Model (CTM) to evaluate the temporal variation of flow and density over links, which reflect the link states of a transportation network. Encapsulation of the CTM equips the model with the capability of accepting inputs of incidents like duration and capacity reduction. Moreover, the proposed model is capable of handling multiple origin-destination (OD) pairs. By using this model, the temporal variation of flows over links can be readily evaluated. The visualized prediction of link density variations is used to investigate the link state relationships. By isolating the effects of an incident, the parallel routes of a specific OD pair display the relationship of substituting for each other, which is consistent with the general expectation regarding such parallel routes. A closer examination of the density variations confirms the existence of a substitution relationship between the unshared links of the two parallel routes. This information regarding link state relationship can be used as general guidance for incident management purposes. / Master of Science

This dissertation addresses the development and analysis of optimization models for evacuation planning. Specifically we consider the cases of large-scale regional evacuation using household vehicles and hospital evacuation. Since it is difficult to estimate the exact number of people evacuating, we first consider the case where the population size is uncertain. We review the methods studied in the literature, mainly the strategy of using a deterministic counterpart, i.e., a single deterministic parameter to represent the uncertain population, and we show that these methods are not very effective in generating a good traffic management strategy. We provide alternatives, where we describe some networks where an optimal policy exist independent of the demand realization and we propose some simple heuristics for more complex ones. Next we consider the traffic management tools that can be generated from an evacuation plan. We start by introducing the cell transmission model with flow reduction. This model captures the flow reduction after the onset of congestion. We then discuss the management tools that can be extracted from this model. We also propose some simplification to the model formulation to enhance its tractability. A heuristic for generating a solution is also proposed, and its solution quality is analyzed. Finally, we discuss the hospital evacuation problem where we develop an integer programming model that integrates the building evacuation with the transportation of patients. The impact of building evacuation capabilities on the transportation plan is investigated through the case of a large regional hospital case study. We also propose a decomposition scheme to improve the tractability of the integer program. / Ph. D.

In the past, the study of Emergency Vehicle (EV) signal preemption has been mostly done using field studies. None of the simulation models that are currently commercially available have the capability to model the presence of EVs and simulate the traffic dynamics of the vehicles surrounding them. This study presents a macroscopic traffic model for examining the effect of signal preemption for EVs on traffic control measures, roadway capacity, and delays incurred to the vehicles on the side streets. The model is based on the cell transmission model, which is consistent with the hydrodynamic theory of traffic flow. A special component, in the form of a moving bottleneck that handles the traffic dynamics associated with the presence of EVs, was developed in the model. Several test scenarios were constructed to demonstrate the capabilities of the model for studying the impact of signal preemption on an arterial with multiple intersections under various traffic demand levels and varying frequencies of the arrival of EVs. Performance measures, such as average vehicle delay, maximum delay, and standard deviation of delay to traffic on all approaches, were obtained. An additional advantage of the model, apart from the capability to model EVs, is that the state-space equations used in the model can be easily incorporated into a mathematical programming problem. By coupling with a desired objective function, the model can be solved analytically. Optimal solutions can be generated to obtain insights into the development of traffic control strategies in the presence of EVs. / Master of Science

Recent natural disasters have highlighted the need to evacuate people as quickly as possible. During hurricane Rita in 2005, people were stuck in queue buildups and large scale congestions, due to improper use of capacity, planning and inadequate response to vehicle breakdown, flooding and accidents. Every minute is precious in situation of such disaster scenarios. Understanding evacuation demand loading is an essential part of any evacuation planning. One of the factors often understood to effect evacuation, but not modeled has been the effect of a previous hurricane. This has also been termed as the 'Katrina Effect', where, due to the devastation caused by hurricane Katrina, large number of people decided to evacuate during Hurricane Rita, which hit Texas three weeks after Katrina hit Louisiana. An important aspect influencing the rate of evacuation loading is Evacuation Preparation Time also referred to as 'Mobilization time' in literature. A methodology to model the effect of a recent past hurricane on the mobilization times for evacuees in an evacuation has been presented utilizing simultaneous estimation techniques. The errors for the two simultaneously estimated models were significantly correlated, confirming the idea that a previous hurricane does significantly affect evacuation during a subsequent hurricane. The results show that the home ownership, number of individuals in the household, income levels, and level/risk of surge were significant in the model explaining the mobilization times for the households. Pet ownership and number of kids in the households, known to increase the mobilization times during isolated hurricanes, were not found to be significant in the model. Evacuation operations are marred by unexpected blockages, breakdown of vehicles and sudden flooding of transportation infrastructure. A fast and accurate simulation model to incorporate flexibility into the evacuation planning procedure is required to react to such situations. Presently evacuation guidelines are prepared by the local emergency management, by testing various scenarios utilizing micro-simulation, which is extremely time consuming and do not provide flexibility to evacuation plans. To gain computational speed there is a need to move away from the level of detail of a micro-simulation to more aggregated simulation models. The Cell Transmission Model which is a mesoscopic simulation model is considered, and compared with VISSIM a microscopic simulation model. It was observed that the Cell Transmission Model was significantly faster compared to VISSIM, and was found to be accurate. The Cell Transmission model has a nice linear structure, which is utilized to construct Linear Programming Problems to determine optimal strategies. Optimization models were developed to determine strategies for optimal scheduling of evacuation orders and optimal crossover locations for contraflow operations on freeways. A new strategy termed as 'Dynamic Crossovers Strategy' is proposed to alleviate congestion due to lane blockages (due to vehicle breakdowns, incidents etc.). This research finds that the strategy of implementing dynamic crossovers in the event of lane blockages does improve evacuation operations. The optimization model provides a framework within which optimal strategies are determined quickly, without the need to test multiple scenarios using simulation. Destination networks are the cause of the main bottlenecks for evacuation routes, such aspects of transportation networks are rarely studied as part of evacuation operations. This research studies destination networks from a macroscopic perspective. Various relationships between network level macroscopic variables (Average Flow, Average Density and Average speed) over the network were studied. Utilizing these relationships, a "Network Breathing Strategy" was proposed to improve dissipation of evacuating traffic into the destination networks. The network breathing strategy is a cyclic process of allowing vehicles to enter the network till the network reaches congestion, which is followed by closure of their entry into the network until the network reaches an acceptable state. After which entrance into the network is allowed again. The intuitive motivation behind this methodology is to ensure that the network does not remain in congested conditions. The term 'Network Breathing' was coined due to the analogy seen between this strategy to the process of breathing, where vehicles are inhaled by the network (vehicles allowed in) and dissipated by the network (vehicles are not allowed in). It is shown that the network breathing improves the dissipation of vehicle into the destination network. Evacuation operations can be divided into three main levels: at the origin (region at risk), routes and destination. This research encompasses all the three aspects and proposes a framework to assess the whole system in its entirety. At the Origin the demand dictates when to schedule evacuation orders, it also dictates the capacity required on different routes. These breakthroughs will provide a framework for a real time Decision Support System which will help emergency management official make decisions faster and on the fly.

This research contributes to the state of the art and state of the practice in solving a very important and computationally challenging problem in the areas of urban transportation systems, operations research, disaster management, and public policy. Being a very active topic of research during the past few decades, the problem of developing an efficient and practical strategy for evacuation of real-sized urban traffic networks in case of disasters from different causes, quickly enough to be employed in immediate disaster management scenarios, has been identified as one of the most challenging and yet vital problems by many researchers. More specifically, this research develops fast methods to find the optimal integrated strategy for traffic routing and traffic signal control to evacuate real-sized urban networks in the most efficient manner. In this research a solution framework is proposed, developed and tested which is capable of solving these problems in very short computational time. An efficient relaxation-based decomposition method is proposed, implemented for two evacuation integrated routing and signal control model formulations, proven to be optimal for both formulations, and verified to reduce the computational complexity of the optimal integrated routing and signal control problem. The efficiency of the proposed decomposition method is gained by reducing the integrated optimal routing and signal control problem into a relaxed optimal routing problem. This has been achieved through an insight into intersection flows in the optimal routing solution: in at least one of the optimal solutions of the routing problem, each street during each time interval only carries vehicles in at most one direction. This property, being essential to the proposed decomposition method, is called "unidirectionality" in this dissertation. The conditions under which this property exists in the optimal evacuation routing solution are identified, and the existence of unidirectionality is proven for: (1) the common Single-Destination System-Optimal Dynamic Traffic Assignment (SD-SODTA) problem, with the objective to minimize the total time spent in the threat area; and, (2) for the single-destination evacuation problem with varying threat levels, with traffic models that have no spatial queue propagation. The proposed decomposition method has been implemented in compliance with two widely-accepted traffic flow models, the Cell Transmission Model (CTM) and the Point Queue (PQ) model. In each case, the decomposition method finds the optimal solution for the integrated routing and signal control problem. Both traffic models have been coded and applied to a realistic real-size evacuation scenario with promising results. One important feature that is explored is the incorporation of evacuation safety aspects in the optimization model. An index of the threat level is associated with each link that reflects the adverse effects of traveling in a given threat zone on the safety and health of evacuees during the process of evacuation. The optimization problem is then formulated to minimize the total exposure of evacuees to the threat. A hypothetical large-scale chlorine gas spill in a high populated urban area (downtown Tucson, Arizona) has been modeled for testing the evacuation models where the network has varying threat levels. In addition to the proposed decomposition method, an efficient network-flow solution algorithm is also proposed to find the optimal routing of traffic in networks with several threat zones, where the threat levels may be non-uniform across different zones. The proposed method can be categorized in the class of "negative cycle canceling" algorithms for solving minimum cost flow problems. The unique feature in the proposed algorithm is introducing a multi-source shortest path calculation which enables the efficient detection and cancellation of negative cycles. The proposed method is proven to find the optimal solution, and it is also applied to and verified for a mid-size test network scenario.