This paper presents a lane-based optimization method for the integrated design of lane markings and signal settings for isolated junctions. Both traffic and pedestrian movements are considered in a unified framework. Capacity maximization and cycle length minimization problems are considered. The problems are formulated as Binary-Mix-Integer-Linear-Programs (BMILP), which are solvable by any standard branch-and-bound routine. The integer variables include the permitted movements on traffic lanes and successor functions to govern the order of signal displays, whereas the continuous variables include the assigned lane flows, common flow multiplier, cycle length, and starts and durations of green for traffic movements and lanes and pedestrian crossings. A set of constraints are set up to ensure feasibility and safety of the resulting optimal lane markings and signal settings. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Lane-based optimization of signal timings for isolated junctions

Traffic simulation models make assumptions about the safety-related behaviour of drivers. These assumptions may or may not replicate the real behaviour of those drivers who adopt seemingly unsafe behaviour, for example running red lights at signalised intersections or too closely following the vehicles in front. Such behaviour results in the performance of the system that we observe but will often result in conflicts and very occasionally in accidents. The question is whether these models should reflect safe behaviour or actual behaviour. Good design should seek to enhance safety, but is the safety of a design necessarily enhanced by making unrealistically optimistic assumptions about the safety of drivers’ behaviour? This paper explores the questions associated with the choice of values for safety-related parameters in simulation models. The paper identifies the key parameters of traffic simulation models and notes that several of them have been derived from theory or informed guesswork rather than observation of real behaviour and that, even where they are based on observations, these may have been conducted in circumstances quite different to those which now apply. Tests with the micro-simulation model DRACULA demonstrate the sensitivity of model predictions—and perhaps policy decisions—to the value of some of the key parameters. It is concluded that, in general, it is better to use values that are realistic-but-unsafe than values that are safe-but-unrealistic. Although the use of realistic-but-unsafe parameter values could result in the adoption of unsafe designs, this problem can be overcome by paying attention to the safety aspects of designs. The possibility of using traffic simulation models to produce estimates of accident potential and the difficulties involved in doing so are discussed.

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Modelling safety-related driving behaviour—impact of parameter values

Conventional design methods require the lane marking patterns, which are painted on ground showing road users the permissible turning directions on different approach lanes, as exogenous inputs to define the traffic stream grouping for analysis. This predefined grouping of traffic movements may restrict the design of signal timings in the optimisation procedures. More recently, a lane-based design method has been developed to relax the lane markings as binary-type control variables in a mathematical programming approach. The lane marking patterns and the signal timings can then be optimised simultaneously in a unified framework. This paper presents an extension work to further relax the numbers of approach lane in traffic arms as new integer variables which can then be optimised to give optimal lane arrangement in various arms of a junction to manage the given traffic demands more efficiently. All well-defined signal timings variables in the phase-based approach as well as the lane marking and lane flow variables in the lane-based approach together with their governing constraints are all preserved in the new formulation for the reserve capacity optimisation of isolated signal-controlled junctions.

Optimal allocation of turns to lanes at an isolated signal-controlled junction

The paper compares the results of extensive measurements of the capacity of nonpriority traffic streams at major/minor junctions and roundabouts with the predictions of models based on gap-acceptance theory. There are significant differences in the form of the relation between the capacity and the traffic flows in the priority streams. The simple gap-acceptance models are poor predictors of the capacity in the United Kingdom, for they seriously overpredict at low values of priority flow and underpredict at high values. At the lower values the gap-acceptance predictions can only be made to agree with the results of the empirical measurements by introducing a dependence of the “move-up” times on the value of the flows in the priority streams. The discrepancies at the higher values of priority flow are probably due to gap-forcing and priority reversal, both of which are commonly observed in the United Kingdom, but whose occurrence may vary from one country to another as a result of differences in driver beha...

Gap-acceptance and empiricism in capacity prediction

This paper presents a lane-based optimization method for minimizing delay at isolated signal-controlled junctions. The method integrates the design of lane markings and signal settings, and considers both traffic and pedestrian movements in a unified framework. While the capacity maximization and cycle length minimization problems are formulated as Binary-Mix-Integer-Linear-Programs (BMILPs) that are solvable by standard branch-and-bound routines, the problem of delay minimization is formulated as a Binary-Mix-Integer-Non-Linear Program (BMINLP). A cutting plane algorithm and a heuristic line search algorithm are proposed to solve this difficult BMINLP problem. The integer variables include the permitted movements on traffic lanes and successor functions to govern the order of signal displays, whereas the continuous variables include the assigned lane flows, common flow multiplier, cycle length, and starts and durations of green for traffic movements, lanes and pedestrian crossings. A set of constraints is set up to ensure the feasibility and safety of the resultant optimized lane markings and signal settings. A numerical example is given to demonstrate the effectiveness of the proposed methodology. The heuristic line search algorithm is more cost-effective in terms of both optimality of solution and computing time requirement.

A Lane-Based Optimization Method for Minimizing Delay at Isolated Signal-Controlled Junctions

DESCRIBES A COMPREHENSIVE PROGRAM OF MEASUREMENT OF SATURATION FLOW AT TRAFFIC SIGNALS AND THE DEVELOPMENT OF PREDICTION FORMULAS WHICH UPDATE THOSE IN: TRAFFIC SIGNALS BY F.V. WEBSTER AND B.M COBBE -- LONDON : HMSO, 1966

N B Hounsell

Papers

The prediction of saturation flows for road junctions controlled by traffic signals