1: Time-space diagram of vehicle trajectories

1: Time-space diagram of vehicle trajectories

Context 1

... The lognormal pdf ( fig. 5.19) has a shape similar to the empirical head- way density function, especially at high flow rates. As the coefficient of variation decreases, the mode moves towards the mean ( fig. 5.20). A closer examination of the pdf ( fig. 5.21), however, shows that the decrease of the density after the peak is too ...

... The most frequently-used measure of stochastic outflows is the departure headway distribution models (Luttinen, 1992;Jin et al., 2009). Departure headway is defined as the elapsed time between two consecutive vehicles departing from the intersection, when the light turns green (Niittymäki and Pursula, 1996). ...

... It was observed that PTD was difficult to measure directly in the field; hence, the proportion of vehicles traveling at headways less than 5 s was recommended as surrogate measure for its field measurement [23]. Although PTD had been used for operational analysis of two-lane highways, other studies reported that the use of 5 s headway is not consistent with field data2526272829. Guell and Virkler [25] criticized the 5 s criterion for field estimation of PTD and suggested that revising the 5 s headway criterion to a range of 3.5 to 4 s would provide more useful LOS classes, reasonable and regular results. Similarly, a study conducted in Canada reported that PTD estimates in accordance with HCM 1985 procedures are higher than those observed in the field [27]. ...

... Similarly, a study conducted in Canada reported that PTD estimates in accordance with HCM 1985 procedures are higher than those observed in the field [27]. It was also demonstrated that fast vehicles were only impeded by headways not exceeding 3 s [28]. In another reaction, Johnson [26] reported that field observations on different segments of rural two-lane roads in Sierra county, California shown that the average headway of vehicles traveling in platoons at or above posted speed limit was approximately 2 s. ...

The Highway Capacity Manual (HCM) uses Percent Time Spent Following (PTSF) as key service measure for assessing the level of service of two-lane highways. However, the indicator is difficult to measure directly in the field. For this reason, its estimation to date has been based on analytical procedures using equations derived from simulations and field observations at representative location based on surrogate measure; as the percent of vehicles traveling with headway less than 3 seconds (3 s). Findings from empirical studies confirmed that the HCM analytical procedures used in estimating PTSF yield results that are inconsistent with the 3 s surrogate measure and mostly overestimate the indicator. This paper presents a review on the estimation of PTSF on two-lane highways and suggests probable approach to substantiate the application of the current practice. Further, the authors of this paper argued that the use of 3 s as surrogate for estimating PTSF based on field observation at a specific point may not represent the actual time spent following over a long segment of two-lane highway since PTSF is space related measure. Hence, the authors suggest the use of test vehicle approach over the highway segment to be evaluated to identify the variables that are required for the development of a representative PTSF measurement model. It is expected that this review and suggestion offered will contribute in advancing performance analysis of two-lane highways.

... Since inaccurate estimation of departure flow often leads to inappropriate signal timing plan, great efforts had been devoted in finding better models for effective departure flow rate (King and Wilkinson, 1977; Ruehr, 1989; Yin, 2008; Yao et al., 2009; Xuan et al., 2011). In some recent studies, stochastic feature of departure headways had been emphasized and various distribution models for departure headways were proposed (Lee and Chen 1986; Teply and Jones, 1991; Luttinen, 1992 ). For example, it was shown in Jin et al. (2009) and Yin et al. (2011) that departure headways approximat ely follow position-depen dent log-normal distributions. ...

... Therefore, the relationship between the mean and standard deviation of the headway could be highly regarded. Unlike previous studies, which showed a convex or concave relationship for uninterrupted facilities (Luttinen, 1992), the CV and flow was linearly correlated in this study. Notably, the slope (1.183) of the fitted line for the relationship between the mean and standard deviation was steeper than that for uninterrupted facilities (0.453-0.777) (Al-Ghamdi, 2001). ...

  • Jinhwan Jang Jinhwan Jang

Vehicular time headway is of fundamental importance in traffic engineering. For any traffic simulation to effectively address traffic problems, accurate vehicle generation is essential. Previous researches on this subject have focused solely on the stochastic modeling of uninterrupted facilities. Yet little research has been conducted on interrupted facilities such as suburban arterials. This paper proposes theoretical headway models for a suburban arterial. Using a traffic detector based on laser sensors, a large amount of accurate headway data were obtained in Korea. To analyze the data according to different states of traffic flow, the headways were categorized into five flow groups. Subsequent runs tests for each headway group rejected the randomness assumption for the lowest flow (5–9 veh/min). Therefore, theoretical modeling was performed only for the four remaining flows (10–14, 15–19, 20–24, and 25–29 veh/min). The Johnson SB model achieved the best fit for a flow of 10–14 veh/min, whereas the Johnson SU model provided the best fits for the three other flows. The Log-Logistic and Log-normal models were also accepted for high flows. In addition to analyses on statistics of the collected headway, the characteristics of the fitted model revealed that the headway has somewhat different features, compared to those of uninterrupted facilities. This paper provides a better understanding of headway for interrupted facilities and constitutes a starting point for developing a descriptively accurate simulation model for signalized arterials.

... This proves the effectiveness of his new model. 8 Simulations also reveal that the above model yield relatively larger spacing errors when the velocity is low (see the curves of empirical and simulated spacings from t = 30 s to t = 60 s in Fig. 8(b) for a example). This is mainly because the braking rule (9) is an oversimplification here. ...

In this paper, we link two research directions of road traffic-the mesoscopic headway distribution model and the microscopic vehicle interaction model-together to account for the empirical headway/spacing distributions. A unified car-following model is proposed to simulate different driving scenarios, including traffic on highways and at intersections. Unlike our previous approaches, the parameters of this model are directly estimated from the Next Generation Simulation (NGSIM) Trajectory Data. In this model, empirical headway/spacing distributions are viewed as the outcomes of stochastic car-following behaviors and the reflections of the unconscious and inaccurate perceptions of space and/or time intervals that people may have. This explanation can be viewed as a natural extension of the well-known psychological car-following model (the action point model). Furthermore, the fast simulation speed of this model will benefit transportation planning and surrogate testing of traffic signals.

... It contains useful information about the interaction between the cars, and it is mostly responsible for the fluctuations observed in traffic flow, even on a macroscopic scale. Consequently, the traffic engineering literature has a long record of different assumptions to describe the empirically observed headway distributions [1] [11] [28]. Usually, the underlying process is not stated explicitly, except in the case of free flow, where a Poissonian process is assumed. ...

  • Peter Wagner Peter Wagner

By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear stochastic process with multiplicative noise, $\dot T_i = \alpha (m_T - T_i) + D T_i\xi$. The resulting stationary distribution has a power-law tail, especially for densities where cars are interacting strongly. Analyzing additionally the headways for accelerating and decelerating cars, the slow-to-start effect proposed as a mechanism for traffic jam stability can be demonstrated explicitly. Finally, the standard deviation of the speed differences between following cars can be used to get a clear characterization of (at least) three different regimes of traffic flow that can be identified in the data. Using the empirical results to enhance a microscopic traffic flow model, it can be demonstrated that such a model describes the fluctuations of traffic flow quite satisfactorily.

... Many theoretical distributions were attempted ranging from simple to complex ones. A list of candidate distributions was initially developed from previous research (e.g., Gerlough and Huber 1975; Luttinen 1992). Sometimes, but not too frequently, several distributions were found to reasonably fit the observed data; however, the one that gave the minimum chi-square values was selected. ...

... ean. In distribution functions CV is the proportion of standard deviation to expectation. The negative exponential distribution has a CV equal to 1.Figure 8 depicts CV values for a freeway site and an arterial site. All CV points of the freeway site stay above those of the arterial site indicating higher variability of headways at the freeway site. Luttinen (1992) found that polynomial curves fit the same data for high-speed and low-speed roads. He observed that under heavy traffic, the proportion of freely moving vehicles is small. The variance of headways is accordingly small [ international research, the CV values fall in the range of 0.5 to less than 1.5 over a range of flow rates from less t ...

... This result might indicate that motorists on arterials drive closer together than those on freeways. This result again is not consistent with the similar analysis by Luttinen (1992), who found convex curves for both low and high speed; again, this may be attributed to differences in driving behavior. ...

  • Ali S. Al-Ghamdi

The headway between vehicles in a traffic stream is of fundamental importance in traffic engineering applications. Previous research in this subject has focused on modeling theoretical distributions for low and medium traffic flow conditions. Yet little research has studied congested traffic conditions, that is, the high traffic flow state. In the same context, there appears to be a lack of clear-cut boundaries for the three flow states (low, medium, and high). This study attempts to determine such boundaries on the basis of traffic conditions observed at the study sites. Although observed headways at arterial sites follow a gamma distribution, distributions that fit freeway headways differ according to the traffic flow state. The Erlang distribution provided a good fit to the observed headways at sites with high traffic flows.

... This suggests a concave shape for the curves. On the other hand, the coefficient of variation of vehicle headways is highest at medium flow rates and decreases below unity at high flow rates (Luttinen 1992). This suggests a convex shape. ...

  • Tapio Luttinen Tapio Luttinen

The purpose of the research was to develop a capacity and level-of-service analysis method for Finnish two-lane highways. The methodology of the new U.S. Highway Capacity Manual (HCM 2000) was used as a framework for the analysis. The HCM method was, however, adjusted for Finnish conditions. Following the HCM2000 the percent time spent following (PTSF) and the average travel speed (ATS) were used as service measures. Traffic flow data were collected from 20 automatic traffic recorders on Finnish two-lane highways. A doubly synchronous counting process was used, in which each counting period both begins and ends at the time of vehicle arrival. Flow rate of counting period was estimated as the reciprocal of the average time headway in the same counting period. This method enabled the study of a subset, such as passenger cars, of a sample. The models and methods were developed for directional analysis of traffic flow. The opposing traffic flow was used as a parameter in the models. The direct effect of heavy vehicles was eliminated by analyzing only refined passengercar flow rates; i.e., passenger cars not in platoons following heavy vehicles. All heavy vehicles were excluded, as well as all vehicles following heavy vehicles in a platoon, until a headway larger than eight seconds was found. The impact of heavy vehicles was estimated as decrease in ATS and increase in PTSF. The models do not make any distinction between different types of heavy vehicles. Passenger-car equivalencies were not used, because they did not lead to any simplifications in the methods. The ATS of passenger cars has been suggested as a service measure, whereas HCM2000 uses the ATS of the mixed traffic flow of both passenger cars and heavy vehicles. The concave speed-flowmodel gave a slightly better fit to the data than the linear model. Especially at low volumes the shape of the speed flow curve appeared to be concave. The linear model, however, yielded simpler models without any significant compromise in accuracy. The analysis methods suggested are based on the linear model. The slope of the speed-flow curve was not as steep as in the HCM2000 model. The slope was steeper on highways with high free-flow speeds. Capacity was reached at lower densities than estimated in HCM2000 so that the HCM capacity estimates of 1,700 veh/h in one direction and 3,200 veh/h in both directions appear plausible. Under congested conditions the maximum flow rate is approximately 1,300 veh/h. The PTSF on Finnish highways was lower than suggested by HCM2000. On highways with 100 km/h speed limit the PTSF is slightly higher than on 80 km/h highways. The effect of directional split is higher and the effect of percent no-passing zones lower than indicated in HCM2000. The passing-lane analysis methodology inHCM2000 has been extended to the analysis of Finnish three-lane highways. The method was modified to consider the design of consecutive passing lanes in alternating directions and passing permitted on passing lanes only.

... On Finnish two-lane roads C(T ) approaches unity under low-volume conditions. As the volume increases, C(T ) increases, but it decreases again below unity at high volumes (13). ...

... Respectively, the kurtosis increases from 9 (φ = 1) to infinity (φ = 0). The squared skewness and the kurtosis of empirical vehicle headway distributions on Finnish two-lane roads have a very strong correlation (13). The KS 2 chart in Figure 1(d) indicates that M3 follows the regression curve for Finnish two-lane roads (10) much more closely than gamma and lognormal distributions. ...

  • R. Tapio Luttinen R. Tapio Luttinen

Cowan's M3 distribution has been used in several studies on unsignalized intersections, especially roundabouts. It allows separate analysis of follower and nonfollower headways, and it is simple enough for models of considerable complexity. Although M3 gives a simplistic model for short headways, it has many desirable properties as a headway distribution. It is possible to estimate its parameters with simple methods and with reasonable accuracy, and the estimated models give good results in the capacity analysis of unsignalized intersections. Described in this paper are the basic statistical properties of M3, and the accuracy of the method of moments and least-squares parameter estimators is evaluated. The validity of M3 in unsignalized intersection capacity analysis is evaluated by a Monte Carlo simulation with samples from M3 and semi-Poisson distributions.

... The influences of prevailing lane traffic composition, level of service, and roadway type were considered. Luttinen (1992) indicated that speed limit and road category both have a considerable effect on the statistical properties of vehicle headways. Wasielewski (1981) studied the effect vehicle size on vehicle-time headways in an uninterrupted environment. ...

  • M.M. Hamed M.M. Hamed
  • S.A. Jaber

In this paper a methodology is developed to describe the interaction between vehicle-time headways and a set of explanatory factors. This study departs from the classical vehicle-time headway approaches by considering the role of each driver in the traffic stream. More specifically, the problem is viewed as a disaggregate choice problem. The choice, in this case, is made by the driver, who has to make a decision in relation to the available time headway faced under certain conditions. Thebasic assumption is that the driver is likely to select the time headway that seems to provide the maximum utility. Estimation results indicate that traffic-related variables (prevailing lane speed, traffic volume, time headway in adjacent lane, lane traffic composition), number of passengers per vehicle, time of day, and the car following type structure have differential and, sometimes, significant impacts on the driver's choice of vehicle time headways. The results also show that there is interactionbetween time headways in one lane (median or shoulder lane) and the driver's selection of time headways in the other lane. Estimation results also show that drivers driving different passenger vehicles (private vehicle, taxi cab, service taxi, and mini-bus) considered different time headway alternatives, even under the same conditions. Therefore, grouping all passenger vehicles in one category is misleading and inappropriate. The results indicate that mini-bus drivers have a strong influence on other drivers' choice of time headways. More specifically, mini-bus drivers were more likely to consider very short (zero to 2.0 seconds) time headways and follow very closely lead vehicles (private vehicle, mini-bus, or service taxi). On the other hand, private vehicle, taxi cab, and service taxi drivers were more likely to keep longer time headways when following mini-buses. Other types of car following structures clearly showed the profound impact of the leading vehicle on the driver's choice of time headway. This approach provided better identification of and more insight into the underlying relationships between driver's choice of vehicle-time headways and other explanatory variables.