A probabilistic model for the behaviour of traffic at a roundabout

A discrete-time, Markov chain model is proposed to describe the behaviour of traffic travelling on a single-lane roundabout and queueing on approach roads to enter the roundabout. A general origin-destination matrix is allowed for trip ends, there is an arbitrary number of approach roads and there is room for a general number of vehicles on each weaving section. Attention is given to the equilibrium régime at an approach subject to heavy traffic conditions. It is shown that for such an approach the moments of the distribution of the length of the queue of waiting vehicles may be found by a heavy traffic approximation.     

A multi-path progression model for synchronization of arterial traffic signals

To contend with congestion and spillback on commuting arterials, serving as connectors between freeway and surface-street flows, this paper presents three multi-path progression models to offer progression bands for multiple critical path-flows contributing to the high volume in each arterial link. The first proposed model is a direct extension of MAXBAND under a predetermined phasing plan, but using the path-flow data to yield the progression bands. The second model further takes the phase sequence at each intersection as a decision variable, and concurrently optimizes the signal plans with offsets for the entire arterial. Due to the competing nature of multi-path progression flows over the same green duration, the third model is proposed with a function to automatically select the optimal number of paths in their bandwidths maximization process. The results of extensive simulation studies have shown that the proposed models outperform conventional design methods, such as MAXBAND or TRANSYT, especially for those arterials with multiple heavy path-flows. The research results from this study have also reflected the need to collect more traffic pattern data such as major path-flow volumes, in addition to the typical intersection volume counts.     

Optimising the control performance of traffic signals at a single junction

The optimal control performance of a single signal-controlled junction is investigated. Two existing methods for analysing this control problem are discussed. One of these, a combinatorial method, generates all possible control structures in terms of groupings of streams of traffic to have green together and the order in which right of way is granted. The other method allows an existing control structure to be optimised by convex programming techniques. Incompatibilities between these two approaches are illustrated and it is shown that they cannot be combined in a satisfactory manner. A new procedure is framed that allows a control structure generated by the combinatorial method to be optimised directly. This procedure is applied to an example junction to illustrate its use.     

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

The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is also shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios.     

Vehicle actuated signal performance under general traffic at an isolated intersection

We study green extension of a two-phased vehicle actuated signal at an isolated intersection between two one-way streets. The green phase is extended by a preset time interval, referred to as critical gap, from the time of a vehicle actuation at an advance detector. The green phase switches if there is no arrival during the critical gap. We develop an exact model to study the intersection performance with traffic following Poisson processes. We further extend the model to approximate the case of general traffic. Our model in the general case works well compared with Monte Carlo simulation. A few major observations include: (1) The optimal critical gap decreases with the traffic; (2) The optimal critical gap can be much larger (up to 5 s) than the common presumption of 2–3 s; (3) Queue clearance policy is not nearly optimal in general even in the case of heavy traffic.     

A multiple transfer function model for air traffic control systems

This paper considers the problem of modeling dynamic fluctuations in aircraft concentration within a group of air traffic control sectors. Using simultaneous time series recorded for each of the sectors, a multiple transfer function noise model is constructed. The modeling procedure demonstrates a data-dependent approach to ATC systems analysis which does not rely on describing the movement of individual aircraft.     

A two-stage fuzzy logic controller for traffic signals

This paper presents the design and evaluation of a fuzzy logic traffic signal controller for an isolated intersection. The controller is designed to be responsive to real-time traffic demands. The fuzzy controller uses vehicle loop detectors, placed upstream of the intersection on each approach, to measure approach flows and estimate queues. These data are used to decide, at regular time intervals, whether to extend or terminate the current signal phase. These decisions are made using a two-stage fuzzy logic procedure. In the first stage, observed approach traffic flows are used to estimate relative traffic intensities in the competing approaches. These traffic intensities are then used in the second stage to determine whether the current signal phase should be extended or terminated. The performance of this controller is compared to that of a traffic-actuated controller for different traffic conditions on a simulated four-approach intersection.     

On the probabilistic origin of dial's multipath traffic assignment model

Dial's multipath traffic assignment model is interpreted as a probabilistic choice model. Anomalies in path assignments generated by Dial's algorithm are related to the independence-of-irrelevant alternatives axiom.     

The design of tram priority at traffic signals

This paper outlines the guidelines being used to introduce tram priority at traffic signals in Melbourne. Where techniques being used to meet the guidelines are of interest they are briefly outlined. Similarly, where it has been found that it is not possible to meet the full requirements of the guidelines, the deficiencies of current techniques are outlined and areas for further investigation put forward.     

Distributed model predictive control for railway traffic management

Every day small delays occur in almost all railway networks. Such small delays are often called “disturbances” in literature. In order to deal with disturbances dispatchers reschedule and reroute trains, or break connections. We call this the railway management problem. In this paper we describe how the railway management problem can be solved using centralized model predictive control (MPC) and we propose several distributed model predictive control (DMPC) methods to solve the railway management problem for entire (national) railway networks. Furthermore, we propose an optimization method to determine a good partitioning of the network in an arbitrary number of sub-networks that is used for the DMPC methods. The DMPC methods are extensively tested in a case study using a model of the Dutch railway network and the trains of the Nederlandse Spoorwegen. From the case study it is clear that the DMPC methods can solve the railway traffic management problem, with the same reduction in delays, much faster than the centralized MPC method.     

Stochastic adaptive control model for traffic signal systems

An adaptive control model of a network of signalized intersections is proposed based on a discrete-time, stationary, Markov decision process. The model incorporates probabilistic forecasts of individual vehicle actuations at downstream inductance loop detectors that are derived from a macroscopic link transfer function. The model is tested both on a typical isolated traffic intersection and a simple network comprised of five four-legged signalized intersections, and compared to full-actuated control. Analyses of simulation results using this approach show significant improvement over traditional full-actuated control, especially for the case of high volume, but not saturated, traffic demand.     

Distributions of queue lengths at fixed time traffic signals

This paper presents a new model which studies probability distributions of queue lengths at fixed time traffic signals. It extends Haight's model for Poisson arrivals that the arrival distribution during the effective red period is general and the headway between two successive departures is not less than the minimum departure headway. Moreover, the probability generating function of the queue length, at the end of the effective red period, is derived. The probabilities of the queue lengths, at the ends of the effective green, actual red and amber periods, are also obtained. Comparison is made with Haight's model. Finally a case study for the proposed model is reported.     

Driving situations and driver decisions at road traffic signals

Driver performance in responding to the green-amber-red signal change was studied based on a sample of 2316 last crossing and first stopping vehicles collected by unobtrusive observations at 10 junction approaches in Singapore. Two schemes, a speed-distance diagram (S-D) and an acceleration-deceleration (A-D) diagram, were used to demarcate the driving situations; the driver actions, as revealed outcomes of driver decision-making, were mapped onto these diagrams. The speed-distance diagram can give some indication on what a driver would possibly do. The more complicated acceleration-deceleration diagram is useful for diagnosing the appropriateness of the driver actions. An application of the A-D diagram was demonstrated, and several situations prone to red-running were noted.     

A stochastic model for highway traffic

A nonlinear model for unidirectional flow of heavy traffic on a two-lane highway is considered. Features such as entrance, exit and lane transfer with time-dependent parameters are incorporated into the model, with the result that a number of previous models employed in the study of traffic flow become special cases of ours. Using the method of system-size expansion, an asymptotic analysis of the problem, including the time evolution of both deterministic and stochastic aspects of the traffic system, is carried out. In addition, a scheme for obtaining the moments of the probability distribution for systems of finite size is developed and a comparison is made with the exact results appropriate to a particular model. The agreement between the two sets of results turns out to be remarkably good.     

A probabilistic optimization model for allocating freeway sensors

This paper proposes a sensor location model to identify a sensor configuration that minimizes overall freeway performance monitoring errors while considering the consequences of probabilistic sensor failures. To date, existing sensor location models for freeway monitoring inherently assume that either deployed sensors never fail or the consequences of sensor failure are trivial matters. However, history has revealed that neither assumption is realistic, suggesting that ignoring failures in sensor allocation models may actually produce a significantly suboptimal configuration in the real world. Our work addresses this dilemma by developing a probabilistic optimization model that will minimize the error expectation by examining all possible failure scenarios, each with an occurrence probability. To ensure the scenario completeness and uniqueness, a sensor failure scenario is represented by using a binary string with 1 indicating an operational sensor at a given site and 0 for sensor failure or no sensor deployed. When applied to a case study network, it is shown that an optimal configuration that considers sensor failure is significantly different from an optimal configuration that ignores sensor failure, revealing that sensor failures pose non-trivial consequences on performance monitoring accuracy.     

A hierarchical control system for freeway traffic

A hierarchical control system consisting of three control layers is developed for the freeway traffic control problem. A simplified optimization problem for the overall freeway system is solved on-line in an optimization layer. Optimization results are used as reference values for an inferior decentralized direct control layer. Prediction of slowly varying variables like on-ramp demands and origin-destination rates as well as of particular model parameters are provided by a supremal adaption layer. The overall control structure is shown to be robust even in the case of strong unexpected disturbances like incidents.     

Application of advanced sampling for efficient probabilistic traffic modelling

In probabilistic traffic models, consideration of stochasticity in the dynamics of traffic gives a closer representation of a traffic system in comparison to that of a deterministic approach. Monte Carlo simulation is a broadly accepted method to consider variations in traffic within modelling. In this contribution, the possibility of increasing the efficiency of probabilistic traffic flow models using Monte Carlo simulation is analysed using variance reduction techniques and sequencing, for varied capacity and traffic demand values. The techniques of Importance Sampling, Latin Hypercube Sampling and Quasi-Random Sequencing are compared in a dynamic macroscopic traffic model to demonstrate the effectiveness of these techniques for reduction of the computational load when considering multiple input variations. Demonstration of their efficiency in traffic modelling is expected to lead to a wider application of the methods in practice.     

A hybrid model predictive control for traffic flow stabilization and pollution reduction of freeways

In this work a control system is developed and analyzed for the suppression of moving jamwaves and the reduction of pollutant concentrations near motorways. The system is based on the second-order macroscopic freeway traffic model METANET, joined by an emission dispersion model, introduced in a previous work of the authors. For the control tasks dedicated controllers are designed, both using the nonlinear model predictive control method. The control objectives require a distinction in the utilized control measures, thus different controllers are designed and used in predefined control modes. The first mode of the controller is responsible for keeping pollutant concentrations below prescribed limits under stable conditions. The second mode of the controller is working in case of a shockwave threat, aiming for traffic stabilization. Between the control modes switching is based on an appropriate rule set that satisfies the stability of the controlled system. The hybrid controller structure is realized by a finite automata. A complex case study is presented for the evaluation of the suggested controller.