Available online at www.sciencedirect.com
ScienceDirect Transportation Research Procedia 20 (2017) 746 – 750
12th International Conference "Organization and Traffic Safety Management in large cities", SPbOTSIC-2016, 28-30 September 2016, St. Petersburg, Russia
Investigation of Dependencies Between Parameters of Twocomponent Models of the Kinetic Theory of Traffic Flow and Traffic Characteristics Vladimir Zyryanov, Victor Kocherga, Ivan Topilin a* Don State Technical University, Rostov-on-Don, 1 Gagarina sg.,, Rostov-on-Don, 344000, Russia
Abstract The paper reports the results of studies of changes in parameters of two-component model of the kinetic theory of transport flows. The paper states a ratio between cars stopping at the same time in the network, specific travel time and specific standing time under varying traffic conditions. The dependencies obtained allow forecasting changes in traffic conditions considering different levels of traffic organization. Also, the paper addresses the issue of application of information obtained from probing cars to assess traffic conditions on the road network and proposes an algorithm to simulate the required level of the road network saturation using probing cars. © Published by Elsevier B.V. This © 2017 2016The TheAuthors. Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 12th International Conference "Organization and Traffic Peer-review under responsibility of the organizing committee of the 12th International Conference “Organization and Traffic Safety Safety Management in large cities". Management in large cities” Keywords: traffic flow; simulation; probing cars.
1. Introduction Development of intelligent transport systems made it possible to enhance significantly the ability of traffic monitoring in order to perform in-process control of traffic and information support of traffic participants. One of the most important components of the modern monitoring systems is floating cars. In the foreign literature, the term "probing car" is more widespread in recent years. Probing cars gather a wide range of information, e.g. the data on
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2352-1465 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 12th International Conference “Organization and Traffic Safety Management in large cities” doi:10.1016/j.trpro.2017.01.120
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location of the car, its speed, travel time, incidents and traffic jams. However, before one could apply the data obtained using floating cars, it is necessary to validate conditions under which the information was gathered and compile a list of the data to be collected using floating cars. Solving these issues prompted an interest in two-component model of the traffic flow theory (two - fluid model) set on a different basis. Similar models were developed by Herman and Prigogine (1979); they introduced moving and static flows based on comparing traffic with two-component fluid flows (part of flow is moving, whereas the other part is immobile). Therefore, using this type of model we can obtain not only the parameters of traffic loads, but also an estimate for a number of cars traveling at a given time, standing at signal controlled intersections or stuck in traffic jams. Parameters of two-fluid models are also sensitive to changes in geometric characteristics of the network and to methods of traffic control. In the first paper, Herman and Prigogine (1979) proved the possibility of applying these models and showed how the model parameters can be used to assess traffic conditions. This was followed by Chang and Herman (1981) studies in the behavior of two-fluid models under various traffic conditions. They set limits for the main varying parameters in these models and demonstrated the potential to estimate fuel consumption. Also, Herman and Ardekani (1984, 1985, 1987) conducted comparative studies of the traffic conditions in different cities on the basis of two-fluid models and determined the potential range of changing the parameters in two-fluid models under different conditions. Currently, the parameters of two-fluid models are applied on the basis of the data collected using probing cars. However, there are numerous cases, when the accuracy of results obtained during the entire research workflow starting with obtaining input information to interpreting results was neglected. This paper addresses some aspects of improving the reliability of using two-component model parameters and probing cars approach. 2. Main text 2.1. Application of two-component models to assess traffic conditions The basic correlations of a two-component model of the kinetic theory of traffic flows deal with dependencies, relating specific parameters of traveling and parking, and specific travel time under unobstructed conditions. The assessment of traffic conditions depends on stability of meeting these conditions and on parameter combination. When the two-component models of traffic flows are developed all relations for moving cars and standstill cars should be determined. In addition to dividing the traffic density into a two-component model, the division of trip time should be also applied. In this situation having a common database for comparison and obtaining comparable results requires using a specific travel time expressed in minutes per kilometer. Let us recall that formulas to express these relations are as follows:
°ts ° °t ® ° ° °¯
1
n
t tmn 1t n 1 tm n 1 ; § § k ·n · ¨1 ¨ ¸ ¸ ¨ ¨ kj ¸ ¸ © © ¹ ¹
(1)
where ts is the specific standing time; tm is the specific time of travelling under unobstructed conditions; k is the density of a traffic flow; kj is the maximum density; n is the model variable. If variable n is increasing then specific standing time decreases under the same specific travel time. On the other hand, changing coefficient n we can reproduce the structure of driving modes under different travel times having the same specific standing time. In general, when parameter n = 0 and when the value of travel is constant, travel time would increase proportionally to increasing the standing time. If n> 0, then increasing standing time would lead to increase in trip time at a high rate since the travel time is also growing. Experimental records for different combinations of parameter n and travel time under unobstructed conditions tm are shown in Figure 1.
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Standing time, min/km
Standing time, min/km
tf = 1.31 min/km tf = 1.08 min/km
Travel time, min/km
Travel time, min/km
Fig. 1. Experimental travel time expressed as a function of standing time.
The set of parameters in the two-component model allows using them to assess the operational quality of the road network [Zyryanov (2012), Zyryanov and Kocherga (2006)]. To examine this issue in detail, it is required to differentiate between dependencies of parameters of the two-component model as the inclination angle of dt/dts and dt/fs depends on the travel time under unobstructed conditions and on parameters n and p:
dt dts
1 ª n tm n1 º )( ) » «1 ( n 1 t »¼ «¬
dt dfs
(n 1)tm (1 ( k k ) p )n 2
dts dfs
1
j
1 n 2 n (n 1)tm1t n1
(2)
(3)
nt (4)
where fs is the share of simultaneously immobile cars in the flow. Analyzing formulas 2−4 reveals that dependencies of ts and t have a steeper inclination angle for larger values of coefficient n and the travel time under unobstructed conditions. Changing standing time causes large changes in travel times for dependencies having steeper inclination angle. If travel time under unobstructed conditions increases, then the influence of coefficient n on the change in dependency between time travel and standing time increases. The influence of parameter p on dynamics of parameters in a two-component model is shown in Figure 2 using the dependency between p and dt/dfs as an example.
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parameter p Fig. 2. Influence of parameter p on changing travel time under changing the share of simultaneously immobile cars.
Figure 2 reveals that increasing parameter p leads to a greater increase in travel time under the same increase in the share of simultaneously immobile cars. For example, for value p = 0.5 the change in travel time would total 0.63 min/km for 0.01 change in the share of simultaneously immobile cars, while at p = 0.7 this change would total 0.27. Thus, in order to improve the traffic control management it is necessary to seek the way to lower values of tm and n in the road network increasing the value of p. Complying with these trends makes the road network more flexible in terms of maintaining traffic conditions under increased traffic loads. 2.2. Specificity of using the data application to assess traffic conditions The method selected for data gathering can have a significant impact on the values of parameters in the twocomponent model. It is important to know how data averaging time influences the values of travel time and standing time, as well as the form of correlation of these parameters. The following key factors that affect the value of the input data of travel time and standing time can be marked out at the stage of determining parameters in the twocomponent model: x x x x x
time and space intervals over which the data is averaged; specific grouping applied to the data gathered; duration of observation periods; the range of variation of driving conditions and traffic loads during observation periods; number of probing cars to make data sampling.
There are rather simple methods to determine the number of probing cars for a road segment, but the situation becomes more complicated when it is required to populate with probing cars the whole road network. It should be noted, that the actual distribution of the travel time can differ from the target time especially under difficult traffic conditions and disturbing effect of highway entering and street light signals. Consequently, the maximum permissible error in estimating the travel time can vary both in time and in space for different traffic conditions and for different segments of the network. Both the type of distribution and the values of statistical parameters vary, as well as the standard deviation of travel time varies, which is particularly important for operating the algorithm. As a rule, deteriorating traffic conditions result in increasing variations in speed and travel time. That is why the calculation results obtained for separate road segments cannot be automatically projected over the whole road network. One of the main aspects in solving this issue deals with uneven spatial and time distribution of probing cars over all segments in the road network. Here, we should take into account the influence of such aspects as changes in
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the length of trip, the structure of the road network, distribution of traffic loads in the network and the time to average the data obtained using probing cars [Zhankaziev (2016)]. Therefore, when the data provided by probing cars travelling urban road networks is used it is necessary to assess the trip time for specific routes when the time of delays during turning at intersections is taken into account. Since distribution of trip length in the network depends on location of various facilities in the road network, it is imperative to create the correspondence matrices and traffic routes [Zyryanov (2014)]. However, it is practically impossible to imagine a situation when measurements at all network segments and at any time are made using probing cars. Therefore, it is necessary to determine the acceptable level of probability to cover all segments of the network by probing cars. For this purpose, the following simulation algorithm can be used to determine the required number level of probing cars in the road network: x solving the issue of distribution of traffic flows in the network on the basis of generated correspondence matrices; x determining the number of probing car sampling s in the road network as compared to the total trips in the network; x solving the issue of trip distribution of probing cars travelling in the road network; x determining the share of participants for which the number of probing cars corresponds the originally calculated value and for which a reliable estimate of traffic conditions can be made using probing cars; x if the obtained result of probable distribution of all participants of the road network is less than specified, then the simulation steps are repeated until the desired result is reached. This algorithm can be applied to predict reliability in assessing traffic conditions on the road network using the data provided using probing cars. Obviously, the key aspect in implementing this algorithm deals with developing a correspondence matrix and challenging the issue of dynamic allocation of traffic flows both in whole network and for the probing cars. 3. Conclusion The combination of two-component models of traffic flows and information provided by probing cars allows evaluating and predicting traffic conditions both on the local and the network level. The data obtained reveals the properties of two-component models and shows the dependence of model parameters on traffic conditions. The recommendations formulated on gathering the baseline data using probing cars for further use in two-component models allow obtaining reliable information on efficiency of traffic management. References Ardekani S. A., Herman R. (1984). Characterizing traffic conditions in urban areas. Transportation Science, 18(3): 101–139. Ardekani S. A., Herman R. A. (1985). Comparison of the quality of traffic service in downtown networks of various cities around the worlds. Traffic Engineering and Control, (26): 574–581. Ardekani S. A., Herman R. (1987). Urban network-wide variables and their relations. Transportation Science, (21) 1. Chang M. F., Herman R. (1981). Trip time versus stop time and fuel consumption characteristics in cities. Transportation Science, 15(3): 183– 209. Herman R., Prigogine I. (1979). A two–fluid approach to town traffic. Washington: Science, vol. 204, pp. 148–151. Naumova N. A., Zyryanov V. V. (2015). Methodology of dynamic calculation of correspondence matrix [Metod dinamicheskogo rascheta matricy korrespondencij]. Scientific Journal “Fundamental Research”, (2-21): 4622–4624 (in Russian). Zhankaziev S. V. (2016). Intelligent transport systems [Intellektual'nye transportnye sistemy]. Moscow: Moscow Automobile and Road Construction State Technical University, 120 p. (in Russian). Zyryanov V. V. (2012). Traffic management and transportation [Upravlenie dorozhnym dvizheniem i perevozki]. Rostov-on-Don: Rostov State University of Civil Engineering, 148 p. (in Russian). Zyryanov V. V. (2014). Methods of calculation of minimal density of probing cars on road networks [Metody opredelenija minimal'no neobhodimogo urovnja nasyshhenija ulichno-dorozhnoj seti probnymi avtomobiljami]. Journal “Science Review”, (11-3): 949–952 (in Russian). Zyryanov, V., Kocherga, V. (2006). Simulation for development of urban traffic: The Rostov-on-don approach of traffic management. In proceedings of 13th World Congress on Intelligent Transport Systems and Services, ID1050, pp. 1–8.
