Vikash V Gayah

ABSTRACT Models are formulated to predict the added vehicle and person delays that can occur when a bus stop is located a short distance upstream or downstream of a signalized intersection. Included in the set of models are those that predict the expected delays that cars collectively incur when a bus blocks one of multiple lanes while loading and unloading passengers at the stop. Others in this set predict the expected added delays incurred by the bus due to car queues. Each model is consistent with the kinematic wave theory of highway traffic, as is confirmed through a battery of tests. And each accounts for the randomness in both, bus arrival times at a stop, and the durations that buses dwell there to serve passengers. Though the models are analytical in form, solutions come through iteration. Hence model applications are performed with the aid of a computer. The applications presented herein show that bus delays can often be shortened by placing the bus stop downstream of its neighboring signalized intersection, rather than upstream of it. In contrast, car delays are often shortened by placing the stop some distance upstream of the intersection, rather than downstream. We further show how exerting a measure of control on bus arrivals can further enhance these benefits to cars without further delaying the buses. The models are also used to assess the net person delays collectively incurred by car- and bus-travelers.

We consider an analytical signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill–Whitham–Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitly addresses traffic-derived emissions as constraints or objectives. We seek to tackle this problem using a mixed integer mathematical programming approach. Such class of problems, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to solve in many cases (Bertsimas et al., 2011b), the mere fact of having integer variables is not the most significant challenge to solving LWR-E problems; rather, it is the presence of the potentially nonlinear and nonconvex emission-related constraints/objectives that render the program computationally expensive.

To address this computational challenge, we proposed a novel reformulation of the LWR-E problem as a mixed integer linear program (MILP). This approach relies on the existence of a statistically valid macroscopic relationship between the aggregate emission rate and the vehicle occupancy on the same link. This relationship is approximated with certain functional forms and the associated uncertainties are handled explicitly using robust optimization (RO) techniques. The RO allows emissions-related constraints and/or objectives to be reformulated as linear forms under mild conditions. To further reduce the computational cost, we employ a link-based LWR model to describe traffic dynamics with the benefit of fewer (integer) variables and less potential traffic holding. The proposed MILP explicitly captures vehicle spillback, avoids traffic holding, and simultaneously minimizes travel delay and addresses emission-related concerns.

This paper extends the continuum signalized intersection model exhaustively studied in Han et al. (2014) to more accurately account for three realistic complications: signal offsets, queue spillbacks, and complex signal phasing schemes. The model extensions are derived theoretically based on signal cycle, green split, and offset, and are shown to approximate well traffic operations at signalized intersections treated using the traditional (and more realistic) on-and-off model. We propose a generalized continuum signal model, which explicitly handles complex vehicle spillback patterns on signalized networks with provable error estimates. Under mild conditions, the errors are small and bounded by fixed values that do not grow with time. Overall, this represents a significant improvement over the original continuum model, which had errors that grew quickly with time in the presence of any queue spillbacks and for which errors were not explicitly derived for different offset cases. Thus, the new model is able to more accurately approximate traffic dynamics in large networks with multiple signals under more realistic conditions. We also qualitatively describe how this new model can be applied to several realistic intersection configurations that might be encountered in typical urban networks. These include intersections with multiple entry and exit links, complex signal phasing, all-red times, and the presence of dedicated turning lanes. Numerical tests of the models show remarkable consistency with the on-and-off model, as expected from the theory, with the added benefit of significant computational savings and higher signal control resolution when using the continuum model.

ABSTRACT We consider an adaptive signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). Such problem explicitly considers traffic-derived emission as side constraints. We seek to tackle this problem using a mixed integer mathematical programming approach. Such a problem class, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to compute in many cases (Bertsimas et al., 2011), the mere fact of having integer variables is not the most significant challenge to computing solutions of MIPs; rather, it is the presence of the nonlinear and nonconvex emission-related constraints that render the program computationally expensive. To address this issue, we proposed an efficient and practical way of solving the LWR-E problem, by formulating it as a mixed integer linear program (MILP). This methodology relies on the existence of a strong correlation between the aggregate vehicle emissions rate and certain macroscopic traffic quantities, such as the number of vehicles on a link. This correlation is fitted by a function and deviations from this function are treated as parameter uncertainty. We then apply robust optimization techniques to reformulate the emissions-related constraints into convex and tractable forms. To further reduce the computational cost, we employ the link transmission model to represent traffic dynamics. The final proposed MILP explicitly captures vehicle spillback, avoids traffic holding and features time-varying signal cycle and splits, as well as the aforementioned emissions constraints.

ABSTRACT The day-to-day reliability of transportation facilities significantly affects travel behavior. To better understand how travelers use these facilities, it is critical to understand and characterize this reliability for different facilities. Early work in this area assumed that the variance of day-to-day travel times (a measure of the inverse of reliability) increases proportionally with the mean travel time; i.e., as the mean travel time increases, travel time reliability decreases. However, recent empirical data for a single bottleneck facility and a small urban network suggest a more complex relationship that exhibits hysteresis. When this phenomenon is present, the variance in travel time is larger as the mean travel time decreases (congestion recovery) than as the mean travel time increases (congestion onset). This paper presents an elegant theoretical model to describe the variance of travel times across many days in an urban network. This formulation shows that the hysteresis behavior observed in empirical floating car data on urban networks should not be unexpected, and that it is linked to the hysteresis loops that often exist in the Macroscopic Fundamental Diagram of urban traffic. To verify the validity of this formulation, data from a micro-simulation of the City of Orlando, Florida, are used to derive an observed relationship with which to compare to theory. The simulated data are shown to match the theoretical predictions very well, and confirm the existence of hysteresis in the relationship between the mean and variance of travel times that is suggested by theory. These results can be used as a first step to more accurately represent travel time reliability in future models of traveler decision-making.

ABSTRACT Recent advances in urban traffic network modeling have led to the proposal of several large-scale control strategies aimed at improving network efficiency, including metering vehicle entry, pricing network use, and allocating limited street space between multiple modes. However, these strategies typically require accurate real-time predictions of networkwide traffic conditions to be implemented, and it is often taken for granted that this information is available. In practice, this is not a trivial issue, because measuring traffic conditions across a large urban network in real time is not straightforward. For that purpose, this paper presents a method of indirectly estimating average vehicle densities across a network in real time by combining travel speed information from a few circulating probe vehicles with the macroscopic fundamental diagram (MFD) of urban traffic. The proposed method is advantageous because it requires relatively little data and involves few calculations. Tests of this methodology on a simulated network showed that the results were not accurate when the network was uncongested, but reliable density estimates could be obtained when the network was congested or approaching congestion, even if only a small fraction of vehicles served as probes. This result is promising because congested states are the most critical. Therefore, this methodology seems useful as a traffic-monitoring scheme to complement networkwide control strategies, provided that the network exhibits a well-defined and reproducible MFD.

In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the on-and-off nature of signal operation. While accurate, the use of binary variables can cause problems when studying large networks with many intersections. Instead, the signal control can be approximated through a continuum approach where the on-and-off control variable is replaced by a continuous priority parameter. Advantages of such approximation include elimination of the need for binary variables, lower time resolution requirements, and more flexibility and robustness in a decision environment. It also resolves the issue of discontinuous travel time functions arising from the context of dynamic traffic assignment.
Despite these advantages in application, it is not clear from a theoretical point of view how accurate is such continuum approach; i.e., to what extent is this a valid approximation for the on-and-off case. The goal of this paper is to answer these basic research questions and provide further guidance for the application of such continuum signal model. In particular, by employing the Lighthill–Whitham–Richards model (Lighthill and Whitham, 1955; Richards, 1956) on a traffic network, we investigate the convergence of the on-and-off signal model to the continuum model in regimes of diminishing signal cycles. We also provide numerical analyses on the continuum approximation error when the signal cycles are not infinitesimal. As we explain, such convergence results and error estimates depend on the type of fundamental diagram assumed and whether or not vehicle spillback occurs to the signalized intersection in question. Finally, a traffic signal optimization problem is presented and solved which illustrates the unique advantages of applying the continuum signal model instead of the on-and-off model.

This article provides a comprehensive overview of the novel idea of real-time traffic safety improvement on freeways. Crash prone conditions on the freeway mainline and ramps were identified using loop detector data, then intelligent transportation systems (ITS) strategies to reduce the crash risk in real-time are proposed. Separate logistic regression models for assessing the risk of crashes occurring under two speed regimes were estimated. The results show that the variables in the two models are consistent with probable mechanisms of crashes under the respective regimes (high-to-moderate and low speed). This study also discusses the analysis of parameters and conditions that affect crash occurrence on freeway ramps by type (on-/off-ramp) and configurations (diamond, loop, etc.) using five-minute traffic flow data obtained from the loop detectors upstream and downstream of ramps to reflect actual traffic conditions prior to the time of crashes. Finally, several traffic management strategies are evaluated for the resulting traffic safety improvement in real-time using PARAMICS microscopic traffic simulation and the measures of crash potential determined through the logistic regression models. The results show that, while variable speed limit strategies reduced the crash potential under moderate-to-high speed conditions, ramp metering strategies were effective in reducing the crash potential during the low-speed conditions.

We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data-driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic.