交通時(shí)間序列的時(shí)間依靠Hurst指數(shù)

1、交通時(shí)間序列的時(shí)間依靠Hurst指數(shù)    Time-Dependent Hurst Exponent in Traffic Time Series Abstract In this paper, we propose a new measure of variability, called the time-dependent Hurst exponent H(t), which fullycaptures the degree of variability of traffic flow at each time t. In order to ass

2、ess the accuracy of the technique, wecalculate the exponent H(t) for artificial series with assigned Hurst exponents H. We next calculate the exponentH(t) for the traffic time series observed on the Beijing Yuquanying highway. We find a much more pronouncedtime-variability in the local scaling expon

3、ent of traffic series compared to the artificial ones. In addition, the resultsshow that the traffic variability can exhibit a non-monotonic multi-fractal behavior. Keywords: Traffic flow, Nonlinear dynamics and nonlinear dynamical systems, Fractal, Time seriesanalysis 1. Introduction Many empirical

4、 studies have shown that traffic flow exhibits high variability. It changesabruptly when entering or leaving a congestion hour. Therefore, Transportation systems are complexentities. Their current state and future evolution depend greatly on myriad properties of interacting,often highly variable phy

5、sical and human elements. High variability in traffic has been shown to have asignificant impact on traffic performance 3, 5. The results from 3-6 show that knowledge of thetraffic variability characteristics helps to improve the efficiency of traffic control mechanisms. Importantly, modeling and fo

6、recasting traffic flow and congestion is a main task of traffic research,which requires the understanding of traffic characteristics, such as variability. Commonly used measures of traffic variability, such as the peak-to-mean ratio, the coefficient ofvariation of traffic speed time series, the indi

7、ces of dispersion for traffic flow, and the Hurst parameter,do not capture the fluctuation of time-variability. It is claimed in that the Hurst parameter is agood measure of variability and the higher the value of H, the burstier the traffic flow. However, webelieve that the Hurst parameter does not

8、 accurately capture the variability of traffic flow at all time. Moreover, it is known that different long-range dependent (LRD) processes with the same value of theHurst parameter can generate vastly different volatility behavior. Clearly, the single value Hurstparameter does not capture the fluctu

9、ation of the degree of traffic burstiness across all time, regardlessif the traffic process exhibits the long-range dependence or the short-range dependence (SRD). Usually many of these processes have piecewise fractal behavior with varying Hurst parameter. Such processes are usually referred to as

10、multi-fractal processes. Multi-fractal analysisbased on the Legendre spectrum is often used to study the multiscaling behavior of traffic flow. The process of estimating the Legendre spectrum involves higher order sample moments and negativevalues of moments. It is known that higher order sample mom

11、ents are not well-behaved andnegative values of moments tend to be erratic. In addition, the Legendre spectrum is difficult tointerpret. Hence, there is a need for an intuitively appealing, conceptually simple, and mathematically rigorousmeasure which can capture the various scaling phenomena that a

12、re observed in traffic data at each time. In this paper, we propose a new measure of variability, called the time-dependent Hurst exponentH(t), that fully and accurately captures the degree of variability of traffic flow at each time. Thetechnique is applied to artificially generated mono-fractal se

13、ries and to the traffic time series observedon the Beijing Yuquanying highway. We find a much more pronounced time-variability in the localscaling exponent of traffic series compared to the artificial ones. In addition, the results show that the traffic variability can exhibit a non-monotonic multi-

14、fractal behavior. The outline of this paper is as follows. In Section 2, we define the time-dependent Hurst exponentH(t). In Section 3, we calculate the time-dependent exponents H(t) for artificial series with assignedHurst exponents H and for the traffic time series observed on the Beijing Yuquanyi

15、ng highway,respectively. The conclusions of this paper are presented in Section 4.    2. The time-dependent Hurst exponent Let V (t) denote the number of events of a point process in the interval (0,t , t T . For eachfixed time interval > 0 , an event count sequence X =X ( ),

16、> 0,n =1,2,3,L n can beconstructed from each point process, where denotes the number of events that have occurred during the nth time interval of duration . Clearly,n X is defined for all > 0 . In this study, n X represents the number of vehicles observed from anarbitrary point in the traffic

17、flow during the nth time interval of duration . We refer as the timescale of the traffic flow, and it represents the length (i.e., 5 min., 2 min., 1 min. etc) of one sampleof X .    3. Application to artificial time series and traffic time series In order to assess the accuracy o

18、f the technique, we first calculate the exponent H(t) for artificialtime series with assigned different Hurst exponents H=0.5, 0.8. Using the modified Fourier filteringmethod, we generate different type of correlation signals Xn , where i = 1,2,L, N and N=213,with a zero mean and unit standard devia

19、tion. By introducing a designed power-law behavior in theFourier spectrum, the method can efficiently generate signals with power-law correlationscharacterized by an a-priori known correlation exponent H. Fig.1 shows the plot of the local scalingexponents H(t) for artificial series n X with assigned

20、 different Hurst exponents H=0.5,0.8. Next, we apply the above algorithm to the traffic time series. The data observed on the BeijingYuquanying highway over a period of about 12 days, from 5:30 AM on 3/21/2006 to 11:30 PM on4/1/2004 (24 hours for each day). The data were downloaded from the Highway

21、PerformanceMeasurement Project (FPMP) run by Beijing STONG Intelligent Transportation System CO. LTD,Beijing. The data for volume are collected 2 min for each lane of the instrumented highway locations. Here, we analyze traffic volume data, i.e. the series of the number of vehicles observed from ana

22、rbitrary point in the traffic flow during the nth time interval of duration 2 min. Fig.2 shows the plot ofthe local scaling exponents H(t) for the traffic flow series. It is apparent on comparingthat the artificial series are characterized by a localvariability of the correlation exponent weaker tha

23、n that of the traffic flow series. The small fluctuationsexhibited by the H(t) of the artificial series should be considered as the limits of accuracy of thetechnique. The results provide evidence that a more complex evolution dynamics characterizes thetraffic flow compared to artificial series havi

24、ng the same average value of the Hurst exponent.    4. Conclusions Commonly used measures of traffic variability, such as the Hurst parameter, do not capture thefluctuation of time-variability. Therefore, we developed a new and mathematically rigorous measure ofvariability, called the time-dependent Hurst exponent H(t), which fully