Statistical Analysis of VEHICLE TIME HEADWAYS

The properties of vehicle time headways are fundamental in many traffic engineering applications, such as capacity and level of service studies on highways, unsignalized intersections, and roundabouts. The operation of modern vehicle-actuated traffic signals is based on the measurement of time headways in the arriving traffic flow. In addition, the vehicle generation in traffic flow simulation is usually based on some theoretical vehicle time headway model. The statistical analysis of vehicle time headways has been inadequate in three important aspects: 1) There has been no standard procedure to collect headway data and to describe their statistical properties. 2) The goodness-of-fit tests have been either powerless or infeasible. 3) Test results from multi-sample data have not been combined properly. A four-stage identification process is suggested to describe the headway data and to compare it with theoretical distributions. The process includes the estimation of the probability density function, the hazard function, the coefficient of variation, and the squared skewness and the kurtosis. The four-stage identification process effectively describes those properties of the distribution that are most helpful in selecting a theoretical headway model. One of the major problems in the headway studies has been the method for goodness-of-fit tests. The two most commonly used tests are the chisquare test and the nonparametric Kolmogorov-Smirnov test. The chisquare test is not very powerful. The nonparametric Kolmogorov-Smirnov test should be applied only, when the parameters of the distribution are known. If the parameters are estimated from the data, as in typical headway studies, the nonparametric Kolmogorov-Smirnov test gives too conservative results. These problems are addressed by parametric goodness-of-fit tests based on Monte Carlo methods. Another great problem has been the lack of theoretical foundation in dealing with multi-sample data. The headway data usually consist of several samples, and the null hypothesis is tested against each of them. Two methods are presented to strengthen the evidence of multi-sample tests: 1) The combined probability method gives a single significance probability based on several independent tests. 2) The moving probability method is used to describe the variation of combined probabilities against traffic volume. These methods were applied to time headway data from Finnish twolane two-way roads. The independence of consecutive headways was tested using autocorrelation analysis, runs tests and goodness-of-fit tests for the geometric bunch size distribution. The results indicate that the renewal hypothesis should not be accepted in all traffic situations. This conclusion is partly supported by a further analysis of previous studies. Five theoretical distributions were tested for goodness of fit: the negative exponential distribution, the shifted exponential distribution, the gamma distribution, the lognormal distribution and the semi-Poisson distribution. None of these passed the tests. In the parameter estimation the maximum likelihood method was preferred. For distributions having a location (threshold) parameter, a modified maximum likelihood method was shown to give good estimates. The proposed procedures give a scientific foundation to identify and estimate statistical models for vehicle time headways, and to test the goodness of fit. It is shown that the statistical methods in the analysis of vehicle headways should be thoroughly revised following the guidelines presented here.