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Procedia - Social and Behavioral Sciences 96 (2013) 2248 - 2259

13th COTA International Conference of Transportation Professionals (CICTP 2013)

Study on Temporal Distribution Characteristics of Urban Freight

Corridors

Gaohua Guoa, Xiaofa Shia, Weifeng Lia*

aKey Laboratory of Road and Traffic Engineering, Ministry of Education, Tongji University, 200092, China

Abstract

The article has studied about the temporal distribution characteristics of freight transportation in common condition. The research applied SQL database to streamline and screen GPS data in programming language. The research used Matlab to check the validation and smoothness of the data, and it used Excel to analyze the time characteristics of the freight traffic in Shenzhen City and then utilized traffic wave theory model to have quantitative calculation to get its impact. It portrayed the traffic delay generated by the superposition of passenger traffic and freight traffic in the passenger commuter rush-hour stage. With the analogy on the analysis of existing data, the study extracted the running characteristics from the freight traffic phenomenon based on the macroscopic traffic demand of freight transportation, temporal and spatial characteristics of the freight transportation in Shenzhen City. Besides, by the methods of the appropriate allocation of resources, the research results have a positive and important role in social production and traffic conditions. It may promote the development of the modern city and enhance the overall effectiveness of transportation as well. The study results want to achieve an enhancing positive and important impact on the core competitiveness of Shenzhen City in the context of globalization.

© 2013TheAuthors. Publishedby Elsevier Ltd.

Selectionandpeer-review underresponsibility ofChinese Overseas TransportationAssociation (COTA).

Keywords: Freight transportation ; Traffic Wave Theory ; temporal characteristics ; GPS data

1. Introduction

The operation of traffic in an urban city is always determined by the land use of the city and the temporal and spatial distribution characteristics of citizens' trips, so the determination of rush-hours is important to the normal operation of the city. Nowadays, the concept of the rush-hour has become clear, due to the tidal characteristics of

* Xiaofa Shi. Tel.: +86- 13816331510 E-mail address: xfshi999@163.com

1877-0428 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of Chinese Overseas Transportation Association (COTA). doi:10.1016/j.sbspro.2013.08.254

commuter traffic, the common definition of it is that a rush-hour is a part of the day during which traffic volume is obviously higher than the rest of the day because of commuter traffic and so on. Generally, it can be divided into morning peak hour and evening peak hour. However, the idea that passengers are more important than freight limits this definition within the passenger traffic system, which cannot fully describe the macroscopic traffic situation of a city.

In the city transportation, freight traffic and passenger traffic are the two main parts, between which there is an essential difference — big vehicles rate, starting delay and so on. The waving of these two kinds of traffic will result in many adverse effects to city traffic. So we need to understand the macroscopic time distribution characteristics of freight traffic.

Many researches about time distribution of traffic have been studied before, but they all concentrated into the solution of traffic congestion and the analysis of crashes, seldom considered the time distribution characteristics of freight traffic itself. This paper will based on the statistic and analysis of data and traffic wave theory, make the quantitative analysis of temporal and spatial distribution if city freight traffic.

2. Research Background

Robert Haining[1] has described a spatial data analysis of wide range of areas. Firstly, an overview of the importance of spatial data analysis of the position (location, background and space) has been given in the scientific and policy-related research. And then, covering the fundamental problem of how geospatial attribute indicates the latest methods of exploratory spatial data analysis and spatial model.

F.A. Lopez and C. Chasco[2] analyzed spatial correlation the dynamic changes in trends. It has showed some of the commonly used exploratory spatial data analysis (ESDA) technology and proposed the new exploratory spatial data analysis (ESTDA), which has proved the dependence of the calculated results of the real-time space.

Weinan He[3] took Beijing as the example. Based on a huge amount of the floating car data,the author analyzed the floating car data characteristics. And based on three indicators, establish judgement and screening methods of often-congested roads, What's more, it has built a GIS application system of screening often-congested roads, and at the same time, it has screened the temporal and spatial distribution characteristics of often-congested roads in Beijing.

Wen Cao[4] verified the validity, practicality and versatility of the model by the applications of floating car temporal and spatial data and geographic space-time data from the point of view of the application-oriented temporal data model based on Markov chain on the basis of existing research. Systematic study of the basic principles of the existing temporal data model through comparative analysis of space semantics, time semantics and spatial and temporal semantics can tease out the advantages and disadvantages of various temporal data model provides a fundamental learn for the further study of the temporal data model.

Leilei Dai[5] built the model of real-time which estimates often-congested and occasional crowded situation on the basis of the analysis of regular pattern of the heavy traffic diffusion. The author used measured and simulated data to verify the validity of the model. And considering the diffusion time and space characteristics of traffic congestion, the estimation model of crowded duration, queue length, delays indicators have been established. The author used measured and simulated data to validate the model, and gave a comparative analysis and description of the traffic congestion.

Due to that researches about the temporal and spatial distribution characteristics mainly concentrate on passenger traffic, congestion control and traffic safety, but seldom consider the freight traffic. So the research by means of mathematical statistics and traffic wave theory in this paper has a strong practical significance.

3. Theory

In the research about microscopic traffic flow theory, traffic wave theory is always applied due to its efficiency of analyzing bottleneck traffic and congestion traffic. In this paper, although it aims to analyze the macroscopic traffic, but it can be assimilated as passenger traffic dissipated and freight vehicles gathered.

Fig3.1 temporal distribution diagram of freight and passenger traffic

The study pulled out of the flow of freight traffic and passenger traffic to analyze the distribution of traffic superposition imbalances during peak hours. It can be clearly learnt from Figure 3.1 that the bimodal effect of passenger traffic flows during peak hours. According to preliminary processing of the data in this article, it can be drawn that freight traffic flow presents the peak time of the single peak distribution. Under ideal conditions, freight peak time should be staggered with the passenger peak time, and after the superimposition waveform equalizer is well performed, which can never appear the extreme case of a maximum value. The paper has focused on the peak hours of overlapped flow, which used the freight flow and passenger flow to simulate arrival traffic and left traffic, and made a traffic wave theory analysis for actual freight corridors bottleneck points.

Generally, the arrival and departure of vehicles happen simultaneously on city roads. If the arrival vehicles can depart in time, there will be no queue and delay. When it comes to the bottleneck of the roads, situation that the amount of arrival vehicles is larger than the departure vehicles always occurs, causing queue and delay in the bottleneck.

Queuing vehicles slow the speed of the vehicle at the entrance to the bottleneck sections line up one after another while the build-up into the high-density queue and such the traffic wave is called aggregation wave. Queuing vehicles were launched through the bottleneck sections, and then evacuated to an appropriate density fleet. We call the traffic wave evacuation wave. The phenomenon that two different traffic flow-density part of the interface go through as a car fleet rear transmission is known as the fluctuations of the traffic flow. The aggregation wave and evacuation wave collectively referred to as the collecting and distributing wave, and wave velocity W is calculated as follows:

W= fl-Q2 _VKi-F2k2 K — K2 Ki — K 2

Where:

W: wave velocity;

Q1, Q2: the flow rate of two kinds of traffic state;

K1, K2: the flow density of two kinds of traffic state;

V1, V2: the flow velocity of two kinds of traffic state;

If the state of flow and density of front and rear traveling traffic are very close, the above formula can be evolved as:

w=^=dQ

This formula is the wave velocity formula of the weak wave, which is the formula of the spreading small turbulence traffic speed.

On the flow-density relationship curve, the slope of the secant is the collecting and distributing wave velocity and the slope of tangent is the wave velocity of weak wave. As shown in Figure 3.2, when the traffic flow of state A which is low-density and low-flow is transformed into state B which is high-density and high-flow, W> 0, which the direction of wave and the movement of the traffic flow is identical. When the traffic flow of state C which is high-density and low-flow is transformed into state B which is high-density and high-flow, W < 0, which the direction of wave and the movement of the traffic flow, is contrary. Both aggregation wave from A to B and evacuation wave from B to A are progressive wave; both aggregation wave from B to C and evacuation wave from C to B are backward wave. [6]

Similarly at this situation, because the passenger cars enters the end of the peak hour, the flow of freight vehicles begins to increase and extends towards upstream, the stopping time of freight vehicles is earlier than the time that passengers cars depart from bottleneck. Thus, the actual flow of the road is larger than its capacity. However, by means of traffic wave theory, the problem can be solved, so as to get a more accurate policy about road control and road management.

4. Data Overview

The data used in this paper is obtained from GPS trajectory data of all vehicles in Oct. 2011, it covers the network of arterial roads in Shenzhen. The spatial distribution is showed in Fig. 4.1. As to the amount of data statistics, the volume of data is about hundreds of millions. In order to guarantee not to lose data characteristics and also improve the efficiency of data processing, the paper selects the data from weekdays of a week that has typical characteristics to be the object of research. The paper also uses the Google Earth electronic map data of Shenzhen in the same period.

Based on the concept of freight intensity, which is to take the routes with larger amount of number of vehicles distributed on the road as the paths of freight transportation. Capture the latitude and longitude of each section of paths. Statistically analyze the GPS points of the paths, the results are showed in Tab. 4.2.

Table 4.2 has checked the main freight channels of Shenzhen based on the frequency order of the record, and depicted the path diagram based on the GPS waypoints, making waypoints connected and corresponded. According to the statistic order, main freight paths are connected and then become the main freight channels.

Table4.2 the statistical comparison table of freight corridors in Shenzhen

North-south road Number of vehicles Record frequency East-west roads Number of vehicles Record frequency

Shenhui Road 1296 17497 Tourist Road 871 12907

Longda Expressway 969 12527 Zhongshan Avenue 456 9973

Fulong Road 958 11788 Shenhui Road 1182 8219

Dongshen Highway 551 8487 Nanping Expressway 1215 7407

Huanshi East Road 672 8475 Shenhai Expressway 885 5686

Link Expressway in the Pearl River Delta 407 6621 Kingswood Road 451 4107

Meiguan Expressway 398 6085 Shuiguan Expressway 674 3287

North Channel 338 4904 Binhe Avenue 149 2517

Shenzhen-Shantou Highway

225 2997 Meihua Road 138 1714

Long-Shenzhen Expressway 232 2891 Binhai Avenue 156 1445

White Pine Road 50 873 Yan Luo Highway 248 1073

Gem highway 44 662 Nigang West Road 22 523

Chau Yu Shi branch 7 112 Rosa Road 10 188

This paper picks data from Shenhui Road, Meiguan Highway and Haibin Avenue, which have large passenger and freight flow.

4.1. Ride Comfort Testing

Based on the purposes to simplify data quantity, remove repetitive data, correct and delete invalid data, expand the time interval and so on, the paper uses SQL database to search, screen and analyze the validity and numerical distribution of the data.

The comfort of the data has a great significance to overall analysis of database. Good comfort of the data can reflect the smooth and continuity of the flow indirectly. It can also reflect the validity and provide a solid foundation of effective for the data later.

After a series of screening and correction of data, the original data length has been compacted. Due to the worry that the comfort of vehicles smoothly running trajectory may be interrupted, This article used 3-D surface chart by means of matlab to verify the trajectory of randomly selected vehicles to.Figure4.2 shows the randomly selected license trajectory track data for surface fitting.

Fig4.2 3D fitting surface chart 1 of a randomly selected vehicle

Because the 3D coordinates of the 3D diagram are latitude and longitude and sequence respectively, and the data has been linear interpolated, the surface of the flitting chart is very gentle, and no great volatility appears. From the chart, one can see that the overall effect is very good. However, there is a mutation at the marked place, the reason of which is the loss of a period of data. Due to that the paper is to study the influence of freight channels and intensity of freight, whether packet loss or the exceed the monitoring area dose no big impact to this paper from the macroscopic phenomenon. So the validation and the comfort of vehicle data are good enough.

Fig4.3 3D fitting surface chart 2 of a randomly selected vehicle

Figure4.3 is a randomly selected vehicle trajectory data fitting surface chart, and it can be seen the abnormal volatility which is pointed out. According to the data analysis, it is found that the phenomenon derived from the offset of the GPS data, on the same path of the continuous latitude and longitude may float, resulting in a calibration error. However, the little degree of fluctuation, can import data batch manually, correct in ArcGIS and determine the path. So, the effectiveness of the vehicle data and the ride is good.

4.2. Mathematical Statistics of peak hour characteristics

In the traditional definition, the morning peak hours and evening peak hours of passenger traffic from Monday to Friday usually are 7:00 to 9:30, 16:30 to 19:00 respectively. The freight traffics are of great difference in different places. Thus, the paper selects vehicle frequency and number of vehicles as the basic variables to depict the peak hour, and takes half hour as the unit of time. The following are the statistics curves based on GPS data in different period of time. In order to find the differences, the paper overlaps the two linear curves, which results in that these two are almost superposition. It can summarize that the changes of number of vehicles and the vehicle frequency are the same.

Fig4.4 Probability charts of Number and Frequency of vehicles

After the summary of vehicle number and frequency, the paper depicts the cumulated frequency curve to prove the comfort of the data, checking if there is anything unexpected happened. The results show that the comfort of data is suitable for data analysis.

12000000 -f 10000000

8000000 6000000 4000000 2000000 0

Cumulative frequency

o o o o o o m o o o rn o o o № o o o ITi o o o № o o o m o o o m

o o 1—1 o rr-i o o vo o ir o Ol o o r) 1—1 CO 1—1 1—1 1—1 00 1—1 Cl 1—1 rN tN rN

Fig4.5 Cumulative frequency charts

Based on that, the paper uses the distribution figure of vehicle frequency and number to depict the peak hours of freight traffic. From the figure below, one can directly find the green part and purple part as the peak hour period, and the corresponded time period is 7:30-20:00, among which the peak hour period is 11:00-17:00. /-\

Number and Frequency Distribution

□ 0-100000 □ 100000-200000 [ 200000-300000 [ 300000-400000

Fig4.6 Number and Frequency Distribution Charts

4.3. Research on characteristics of Truck in rush hour with traffic wave theory

Due to lack of data of trucks, we make reasonable assumptions and analyze the data in hand with the data resource we can get.

Accumulated frequencies mentioned above are gathered in the curve below.

Fig4.7 Cumulative frequency fitting function graph

The curve fitting is achieved using fixed base prediction method. After comparison of various models, the cubic function y=ax is found the most appropriate one, with the functional equation:

y = —12.781x3 +1057.7x2 +98.526x+39117

Correlation coefficient R2=0 9992

The unit period traffic volumes are the difference of the cumulative frequency of the first derivative:

y =-38.343x2 +2115.4x + 98.526

Whereas, y with the meaning of the value of distribution of trucks all over the city per hour, is processed to accord with the international standard unit: pcu/h, which means:

Q =axbx y/c

Q1: Freight vehicle traffic flow ( pcu/h );

a: Unit time 30min converted to 1h, the conversion factor is 2.0;

b: Carts rate conversion, the freight vehicles carts rate is approximately 2.0;

c: Total number of trunk roads in Shenzhen, Estimate of about 80 to 100;

Consequently, the problem is transferred to the following question.

The trucks flow with the average speed of 50km/h and expression of (-38.343x2+2115.4x+98.526)/40 pcu/h is on the Binhai Avenue freight corridors in Shenzhen. Experientially, the speed would reduce to 12km/h if the flow encounters a bottleneck interwoven road section(Nanshan intersection eastern section of Guimiao Road and Binhai Avenue)with length of 2km. according to the ruled of traffic capacity in HCM2000, a reduction factor is multiplied and we get the traffic capacity of the bottleneck sections. At the end of the bottleneck sections, trucks are dispersed and form a continuous flow with speed of 30km/h and traffic flow of 1500pcu/h.

1) If the time t0 vehicles spend in the bottleneck sections is too long;

2) If the last time tj of heavy traffic is reasonable;

3) If the largest number of vehicles in line Nm if too large;

4) If the total number of vehicles in line N is too large;

5) If the largest length of the line Lq is too large;

6) If the total D is acceptable;

Assumptions are raised before handling the problem:

a) Freight traffic simulates aggregated traffic, and passenger traffic simulates dissipated traffic.

b) In order to simplify the model, freight traffic and passenger traffic is converted to standard car.

c) Passenger traffic at peak periods presented a quadratic function of the distribution of the parabola state.

d) The simulation of passenger traffic volume is quantitative modelling.

e) The basic situations of the above road section are normal circumstances, non-special circumstances.

f) Freight vehicle data selected for the operating conditions are during the normal working day in Shenzhen. Solution:

In order to make the traffic dissipated not to produce sustained crowded stranded queuing, the arrival rate is less than from the driving rate, the freight traffic volume:

Q =((-38.343x2+2115.4x+98.526) / 20(25))pcu / h<g2 =1200pcu/h

Use matlab solving:_

x=solve('-38.343x2+2115.4x+98.526=24000') x=solve('-38.343 x2+2115.4x+98.526=27000') x = x =

15.855566569487898959692746318194 19.881739526110787420639207135039

39.314868712049800229207444068578 35.288695755426911768260983251733

In theory, the peak hour is 7:30 to 19:00 or 9:30 to 17:00.

Therefore, the gradient segment time of both ends will become the core of the policy development. Because of existing duration segment that passenger commuter vehicle appears, the paper takes the factors into consideration in the most unfavourable period based on the linear parabolic relationship. The paper take the 8:00 to 8:30 as spread sheet conditions, and then x =17.

After finishing,

Q1 = 999.168pcu / h «1000pcu / h, Q2 = 1200pcu / h, Q3 = 1500pcu / h V1 = 50km / h, V2 = 12km / h, V1 = 30km / h

According to Q=K*V, it can be drawn:

Kx= 20pcu / km, K2= 100pcu / km, K3= 50pcu / km

Therefore,

Wave spreads along the road forward;

W = Q Ql =2.5(km/h)

K2 - Ki

W2= Q Q2 =-6(km/h)

K — K

Wave spreads along the road backward; y The time required for vehicles passing through the road:

V2x (K 2- Kj-{Q2- Qjx L

LxV2X (K 2- K.)

^ 2 — = Q.186(Ä)

y Congestion duration:

Q2- Ql Q3- Q2

K2~ Ki K3~ K 2

t.=tB=t0+ tA=t0+ L = 0.353(h )

The max number of vehicles in the crowded fleet:

Nm=(xA-xc)xK2= {V2- Wjx LxKVl = 158( pcu )

> Total number of Crowded vehicles:

N = tEE= - W )* j Q1 / V = 335( pcu)

> Max queue length:

L 3=^ = 1-58( to)

> Total delay time of queuing vehicle:

D = (tA-tT)xN = Lx{V1- V2)x -N- = 42.43(h)

K1 X V2

Since it is considered that the most unfavourable state of traffic flow conditions has been, the results can be well portrayed in the passenger commuter traffic peak, which delay is caused by superimposed passenger traffic and freight traffic. Here is the result calculated by the traffic flow wave theory quantitatively.

From the results, the time required by vehicle through the road section is about 12 minutes, converting to the average speed of vehicles through the sections 11km / h, and comparing to the rated speed of urban roads 50 to 60 km / h ,which is only 20% speed, is low traffic efficiency. The crowded duration is 22 minutes and too long waiting time may make the most of the driver feel irritable. What's more, the queue length becomes longer along with the congestion caused by an increase in the number of vehicles. Through calculation, the max queue length is 1.58km, already account for 80% of the road length in just 2km bottleneck road section, so the delays required by the formulation of policies and rules need to be improved.

5. Summary

In the traditional definition, the morning peak hours and evening peak hours of passenger traffic from Monday to Friday usually are 7:00 to 9:30, 16:30 to 19:00 respectively. But based on the calculation from traffic wave theory, the theoretical peak hour periods are 7:30-19:00 or 9:30-17:00, based on the mathematical statistical analysis, the peak hour period is 7:30-20:00.

Based on the results analysed from the Shenzhen GPS freight traffic data in this paper, several reasons can be found: Shenzhen west traffic channels for transit, foreign traffic show a long period of peak time, which should be last 8-9 hours from 9:30-17:00 to balance the insufficient of the road capacity. It can be learnt that high saturated traffic demand of continual Freeway traffic cannot be satisfied. According to other conference, it indicates that if the freight cars accounted for more than 50%, passenger traffic and cargo mixed mutual is interference, reducing security, leading to the overall decline in traffic capacity since the disparity of the model size.1-7-1 Because interchange impact of Binhai Avenue horn traffic bottleneck, the upstream vehicle is always in a clogged state downstream interrupted, resulting in inadequate intersection throughput.

The goal is under the condition that won't affect traditional peak hour period of passenger traffic, then to reduce freight traffic and the overlapped period of peak time between passenger and freight traffic, and to make the superimposed flow present a balanced status, by means of regulation to delay the peak hour time of freight traffic. Of course, in accordance with the Shenzhen existing network plan, transferring freight traffic or increasing freight channel construction may become the improvement measures.

The study of temporal distribution of urban freight corridors can be good for decision-makers in the mixed freight passenger road traffic control and provide auxiliary views in policies related to management.

References

[1] Robert Haining. Spatial data analysis: theory and practice [M]. Cambridge University Press, 2003.

[2] F.A. Lopez and C. Chasco. Space-Time Lags: Specification Strategy in Spatial Regression Models. 2004.

[3] Weinna He. Urban Congestion Spatial and Temporal Characteristics Based on the Floating Car Data [D]. Beijing Jiaotong University,

[4] Wen Cao. Spatial-temporal Data Model and Its Application [D]. PLA Information Engineering University, 2011.

[5] Leilei Dai. The Diffusion Law Model of Urban Trunk Road Traffic Congestion [D]. Jilin University,2006.

[6] Shangwu Zhou. Transportation Engineering [M]. Shanghai: Tongji University Press, 1987:P88~89.

[7]Wenfeng Hu. Bao'an District, Shenzhen, Anxi township Area town of domain Traffic Planning Study [D]. Harbin: Harbin Institute of Technology, 2004.