Benjamin G. Heydecker

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.

Representation of heteroskedasticity in discrete choice models

The Multinomial Logit, discrete choice model of transport demand, has several restrictions when compared with the more general Multinomial Probit model. The most famous of these are that unobservable components of utilities should be mutually independent and homoskedastic. Correlation can be accommodated to a certain extent by the Hierarchical Logit model, but the problem of heteroskedasticity has received less attention in the literature. We investigate the consequences of disregarding heteroskedasticity, and make some comparisons between models that can and those that cannot represent it. These comparisons, which use synthetic data with known characteristics, are made in terms of parameter recovery and estimates of response to policy changes. The Multinomial Logit, Hierarchical Logit, Single Element Nested Logit, Heteroskedastic Extreme Value Logit and Multinomial Probit models are tested using data that are consistent with various error structures; only the last three can represent heteroskedasticity explicitly. Two different kinds of heteroskedasticity are analysed: between options and between observations. The results show that in the first case, neither the Multinomial Logit nor the Single Element Nested Logit models can be used to estimate the response to policy changes accurately, but the Hierarchical Logit model performs surprisingly well. By contrast, in a certain case of discrete heteroskedasticity between observations, the simulation results show that in terms of response to policy variations the Multinomial Logit model performs as well as the theoretically correct Single Element Nested Logit and Multinomial Probit models. Furthermore, the Multinomial Logit Model recovered all parameters of the utility function accurately in this case. We conclude that the simpler members of the Logit family appear to be fairly robust with respect to some homoskedasticity violations, but that use of the more resource-intensive Multinomial Probit model is justified for handling the case of heteroskedasticity between options.

Analysis of Dynamic Traffic Equilibrium with Departure Time Choice

We present and analyse a model of the combined choice of departure time and route in a congested road network. Using the property of equilibrium solutions that for each origin-destination pair the total cost associated with travel is identical for all travellers, we establish a general result that relates assignments to various components of cost. The analysis is developed to include time-varying tolls and to establish a formula that will induce any specified inflow profile as an equilibrium. We introduce an iteration operator to calculate equilibrium inflow profiles, and present the results of example calculations for a range of test problems.

A decomposition approach for signal optimisation in road networks

The optimisation of signal timings plays an important role in the management of urban traffic, and in the full usage of existing and planned road networks. In recent years, considerable advances have been made in techniques for the optimisation of signal timings at isolated junctions operating under fixed-time control. This paper shows how these techniques can be applied in the optimisation of signal timings in coordinated networks by using a decomposition approach. The signal timings at a junction in a network can be specified fully by the sequence of stages, interstage structures, cycle time, stage durations and offset. Of these variables, the third, fourth and last are endogenous to network optimisation methods, the first and second being exogenous. Techniques have been developed recently to optimise all but the last variable (which is not there defined) at individual junctions, and these have been found to give considerable improvements in operational performance. The computational requirements of these methods is such that their direct extension to networks is not yet a practical proposition. This paper shows how the differences inherent between individual junction and network optimisation methods can be reconciled within a decomposition approach so that the latter can benefit from some of the advantages of the former. A simple example is used to illustrate the substantial benefits that can arise from this approach.

USE OF TRAVEL DEMAND SATISFACTION TO ASSESS ROAD NETWORK RELIABILITY

A new concept of network reliability is introduced to assess the performance of the road network. It is referred to as the travel demand satisfaction reliability (DSR). In order to understand this new concept, the attributes to recurrent travel demand are firstly investigated for the analysis of road network reliability. The latent travel demand (LTD) is then distinguished and estimated by elastic travel demand functions. The ratio of the equilibrium travel demand and LTD can be used to ascertain the extent of satisfying and revealing the latent travel demand (DSI), which is affected by both the uncertainty of the network degradation and of the recurrent travel demand. The DSR is defined as the probability that the road network can accommodate a given DSI. The DSR can be extended to include other reliability measures such as travel time reliability under certain conditions. In order to facilitate the presentation of the essential ideas, simple examples are employed for discussion together with mathematical formulation.

Uncertainty and variability in traffic signal calculations

The consequences of uncertainty and variability in data used for traffic signal calculations are investigated. A treatment of variable observations is devised and analysed. This shows that for small degrees of variability, use of mean values in conventional calculation methods will lead only to small losses in performance.

Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks

Creation of a new link or increase in capacity of an existing link can reduce the efficiency of a congested network as measured by the total travel cost. This phenomenon, of which an extreme example is given by Braess paradox, has been examined in conventional studies within the framework of static assignment. For dynamic traffic assignment, which makes account of the effect of congestion through explicit representation of queues, Akamatsu (2000) gave a simple example of the occurrence of this paradox. The present paper extends that result to a more general network. We first present a necessary and sufficient condition for the paradox to occur in a general network in which there is a queue on each link. We then give a graph-theoretic interpretation of the condition, which gives us a convenient method to test whether or not the paradox will occur by performing certain tests on information that describes the network structure. Finally, as an application of this theory, we examine several example networks and queueing patterns where occurrence of this paradox is inevitable.

Objectives, Stimulus and Feedback in Signal Control of Road Traffic

This article identifies the prospective role of a range of intelligent transport systems technologies for the signal control of road traffic. We discuss signal control within the context of traffic management and control in urban road networks and then present a control-theoretic formulation for it that distinguishes the various roles of detector data, objectives of optimization, and control feedback. By reference to this, we discuss the importance of different kinds of variability in traffic flows and review the state of knowledge in respect of control in the presence of different combinations of them. In light of this formulation and review, we identify a range of important possibilities for contributions to traffic management and control through traffic measurement and detection technology, and contemporary flexible optimization techniques that use various kinds of automated learning.

Adaptive Dynamic Control for Road Traffic Signals

Control of road traffic by signals requires timings for the stages during which signal indications remain constant. Approaches to calculation of these durations include traffic-responsive strategies as well as fixed-time ones. In all cases, these control methods require some parameters that will ultimately depend on traffic flows. The present paper introduces an adaptive method for responsive control that adjusts the stage durations according to traffic flows. The methodology used for this is approximate dynamic programming, which uses a state-dependent estimate of future optimised costs to assess decisions. Results are presented for example applications, showing favourable performance by comparison with other approaches.

CAPACITY AT A SIGNAL-CONTROLLED JUNCTION WHERE THERE IS PRIORITY FOR BUSES

A discussion of the benefits of bus priority schemes shows the importance of providing adequate capacity for all streams of traffic. The analysis of capacity at a signal-controlled road junction is extended to cases where stages may be truncated or omitted in some cycles. The problem of finding signal settings which, when implemented with priority, emulate some which are known to provide a given level of capacity when implemented without priority is considered. Two commonly used rules to give priority by selective vehicle detection are analysed in detail and a third is considered briefly to illustrate the flexibility of the methods used. The range of conditions under which these priority methods can be implemented without causing any loss of capacity is quantified. If an additional rule is implemented to prevent priority from being granted too frequently, then this range covers most practical operating conditions. In cases outside this range, consequent losses of capacity can be estimated. A numerical example based upon a real bus priority experiment is provided.