Hindawi Publishing Corporation Advances in Mechanical Engineering Volume 2013, Article ID 656345, 8 pages http://dx.doi.org/10.1155/2013/656345
Research Article A Simplified Approach to Estimate the Urban Expressway Capacity after Traffic Accidents Using a Micro-Simulation Model Hong Chen,1 Yue-sheng You,1 Ji-biao Zhou,1 Lu Wang,1 and Zhen-hua Shang2 1 2
School of Highway, Chang’an University, Xi’an 710064, China Ji’nan Public Security Bureau and Traffic Police Detachment, Ji’nan 250000, China
Correspondence should be addressed to Yue-sheng You;
[email protected] Received 22 August 2013; Revised 1 November 2013; Accepted 8 November 2013 Academic Editor: Wuhong Wang Copyright © 2013 Hong Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Based on the decomposition of the evolution processes of the urban expressway capacity after traffic accidents and the influence factors analysis, an approach for estimating the capacity has been proposed. Firstly, the approach introduces the Decision Tree ID algorithm, solves the accident delay time of different accident types by the Information Gain Value, and determines congestion dissipation time by the Traffic Flow Wave Theory. Secondly, taking the accident delay time as the observation cycle, the maximum number of the vehicles through the accident road per unit time was considered as its capacity. Finally, the attenuation simulation of the capacity for different accident types was calculated by the VISSIM software. The simulation results suggest that capacity attenuation of vehicle anchor is minimal and the rate is 30.074%; the next is vehicles fire, rear-end, and roll-over, and the rate is 38.389%, 40.204%, and 43.130%, respectively; the capacity attenuation of vehicle collision is the largest, and the rate is 50.037%. Moreover, the further research shows that the accident delay time is proportional to congestion dissipation time, time difference, and the ratio between them, but it is an inverse relationship with the residual capacity of urban expressway.
1. Introduction With the acceleration of the urbanization process in China and the rapid growth of the motor vehicle ownership, the supply pressure of existing road network is increasing, and frequent traffic congestion of the local area and traffic safety issues also have become increasingly prominent. As an important part of the urban road infrastructure, the formation of the urban expressway, which meets city internal short-distance and external long-distance traffic demand, will strongly support and promote the reasonable adjustment of urban spatial structures and enhance urban transport accessibility features, fast function, and connectivity features on the whole. Moreover, its transport efficiency not only plays an important promoting role in improving the city’s economic development, but also becomes an important measure to alleviate urban traffic congestion. However, sudden traffic accidents on the expressway system will seriously affect the normal operation of urban traffic. The road capacity dropped significantly and the traffic flow was disordered after the occurrence of sudden traffic accident. The sudden traffic
accident may also cause traffic congestion of upstream road easily, even cause a number of casualties and property losses, and increase traffic delays and travel time. It will have a great impact on the regional road network. Therefore, the capacity researches of the urban expressway after traffic accident have important significance for providing decision support of timely response to the accident. In recent years, there have been numerous efforts from the domestic and foreign research institutions and scholars in the field of the urban expressway capacity from different angles. Abroad, the Highway Capacity Manual (2000) which is written by the U.S. Transportation Research Board (TRB) described the urban expressway capacity under normal conditions in detail. After careful modification and improvement for it, TRB published the Highway Capacity Manual (The 2010 version) in 2010. Swedish Capacity Manual published in 1977 also analyzed and studied the urban expressway capacity. In addition to this, abroad scholars researches for the capacity of the urban expressway mainly focused on the influences of the urban expressway capacity [1], weaving, merge capacity and their simulation [2–5], traffic flow characteristics and
2 models [6–8], level of service [9, 10], basic link capacity under bottleneck state [11, 12], travel time prediction model of urban expressway and its feasibility under bottleneck state [13, 14], and traffic control strategies which included on-ramp control [15, 16]. Domestically, the researches on road capacity started late. However, based on foreign advanced theory and the practical situation of the country’s roads, domestic scholars and experts carried out a detailed, extensive, and in-depth research for the urban expressway capacity, and had achieved obvious results. For instance, Chai et al. [17] put forward the bus stop capacity calculation method of the urban expressway under the condition of road congestion based on the influence factors of the bus stop capacity. Du et al. [18], Ming-yuan [19], Hai-jun et al. [20] simulated and analyzed the urban expressway capacity and traffic state. Du and Jian [21] estimated highway effective capacity after an unexpected traffic accident. Hong-ping et al. [22] and Yang et al. [23] analyzed influence factors of the urban expressway capacity from the free-flow speed and the number of lanes, respectively. Long et al. [24], Long and Xiao-Guang [25], Ma et al. [26] analyzed and studied the urban expressway off-ramp and on-ramp capacity. Li et al. [27] studied the capacity of the urban expressway shunt, merge area. Zhong et al. [28, 29] and Chen et al. [30] give the recommended values of the ideal capacity, and simulate the capacity of the urban expressway weaving area. Zhang and Yong-Feng [31] improved a better traffic flow model on the basis of the analysis of traffic flow characteristics on the expressway weaving area. In summary, most work focused on the research of the urban expressway capacity under normal conditions. These researches promote the development of the urban expressway capacity and provide a theoretical reference for urban expressway planning, design, and service level analysis. But due to accident statistic difficulties and other reasons which cause research depth of the urban expressway capacity lowly after traffic accidents, the efficiency of traffic accident rescue and emergency response measures will be directly affected. In view of this, the paper disassembles the evolution processes of the urban expressway capacity after traffic accidents and analyzes influence factors at first. Then, it introduces the Decision Tree ID algorithm and the Traffic Flow Wave Theory and takes the accident delay time as the observation cycle. Finally, it simulates the capacity by the VISSIM simulation software, which quantitatively describes the attenuation characteristics of the urban expressway capacity after traffic accidents. That will provide new ideas for traffic control measures, travel information service, traffic organization, and emergency rescue, which effectively protect safe, effective, and orderly operation of urban roads.
2. The Evolution Processes of the Urban Expressway Capacity after Traffic Accidents After the occurrence of the accident, the road capacity of the accident point will reduce. When the capacity is less than the upstream traffic low, the upstream vehicles will line up in the event point and continue to extend to the upstream, even
Advances in Mechanical Engineering B
A tMC
C
D
E
tP
tR
tS
tA tA + tS
Figure 1: Continued congestion time. Notes: 𝑡𝑀𝐶 —the accident monitoring and confirmation time; 𝑡𝑅 —the accident response time; 𝑡𝑃 —on-site processing time; 𝑡𝑆 —therecovery time; 𝑡𝐴 —the accident delay time; 𝑡𝐴 + 𝑡𝑆 —continued congestion time. C C0 C3 C2 C1 C2
0
Step I
Step II
tMC + tR t1 t2 tA
tP
Step III
tS t3
tS
t4
t
Figure 2: The evolution processes of the urban expressway capacity after traffic accident. Notes: 𝑡1 —accident starts, 𝑡2 —the duration of the accident, 𝑡3 —accident ends, and 𝑡4 —congestion ends.
extending to the upstream intersection. When the accident is cleared, the road capacity gradually restored and congested traffic flow began to dissipate. Continued congestion time is composed of the accident delay time and congestion dissipation time, as shown in Figure 1. 𝐴 represents the start of the accident state; 𝐵 represents the confirmation of the accident state; 𝐶 represents the arrival of the police; 𝐷 represents the end of the accident state; 𝐸 represents the end of the crowded state. The evolution processes of the urban expressway capacity after an unexpected traffic accident are divided into three stages that are corresponding to continued congestion time, as shown in Figure 2. 𝐶0 represents link capacity (veh/h) of the urban expressway before the accident or after traffic recovery; 𝐶1 represents link capacity (veh/h) of the urban expressway before the police arrives; 𝐶2 representslink capacity (veh/h) of the urban expresswayunder the condition of accident processing; 𝐶3 represents link capacity (veh/h) of the urban expressway under the conditions of traffic recovery. Step I. When an unexpected traffic accident causes the temporary closure of the local lanes, the accident lane capacity plunged to zero, but it will recover until traffic accident is cleared. Meanwhile, the vehicles on the accident lane change original lane to the adjacent lane, and the traffic flow in a certain range is in a turbulent state. The interaction of the vehicles is relatively large, and passable lane capacity is smaller than its normal capacity. Step II. After the arrival of the police, when the space occupied by rescue vehicles, traffic signs, and other facilities is larger
Advances in Mechanical Engineering than that of the accident, the capacity is smaller than that before the arrival of the police; that is 𝐶2 is slightly less than 𝐶1 ; on the contrary, the capacity is larger than that before the arrival of the police, that 𝐶2 is slightly larger than 𝐶1 . In order to simplify the capacity analysis of Step I and Step II and solve the urban expressway capacity after traffic accidents, 𝐶2 is equivalent to 𝐶1 here. Step III. After the end of the accident, because crowded traffic flow caused by traffic accident is not completely dissipated, the urban expressway capacity, which is influenced by traffic composition, speed, and front spacing of crowded traffic flow, is smaller than its normal capacity; that is, 𝐶3 is slightly less than 𝐶0 .
3. The Analysis of the Urban Expressway Capacity after Traffic Accidents 3.1. Influence Factors Analysis. According to the evolution processes of the urban expressway capacity after traffic accidents, analyze and study the evolution factors (what are the factors leading to the evolution of this capacity?). Different from the urban roads under normal circumstances (taking into account influencing factors of the capacity under normal conditions), the influencing factors of the urban expressway capacity after traffic accident have its particularity. In general, it is related to the inherent attributes of traffic accident, road space resource attributes of the accident point, traffic management measures of the accident point, and the accident delay time.
3 3.1.2. Road Space Resource Attributes of the Accident Point (I) The Number of Closed Lanes Near the Accident Point. After the accident, for security requirements and required space of on-site processing, sometimes it is necessary to close one or more lanes, which will greatly reduce the capacity of urban road and lead to traffic congestion and obstruction. (II) The Length and Width of the Carriageway. The longer the length of the closed lane, the lower travel speed in the lane and lane changing, and that also reduces the capacity of the accident sections. The narrower the width of the carriageway, the smaller the space and travel speed through the accident point, which will also have a certain impact on the capacity of the accident road. 3.1.3. Traffic Management Measures of the Accident Point (I) The Speed Limitation of the Accident Road. The speed is limited in the unclosed lane. Limited speed can improve its safety and balance traffic low speed and reduce secondary accidents, but its capacity will be reduced. (II) The Flow Limitation of the Accident Road. After the accident, in order to timely evacuate upstream vehicles and reduce delays, the vehicles of the corresponding import lane at the intersection near the accident point should be prohibited to transfer into the expressway. That can control traffic demand of the accident point and ease traffic pressure, which will increase the urban expressway capacity in a certain extent.
3.1.1. The Inherent Attributes of Traffic Accident (I) The Accident Types and the Severities. Common accident types in urban road are vehicle anchor, roll-over, fire, rearend and collision, and so forth. The accident severities include whether there are the casualties, road infrastructures of the accident point are damaged or not, the number and types of involved vehicles, and so forth. The accident delay time and traffic recovery time will vary with different accident types and the severities, and further influence action time of the urban expressway capacity reduction. (II) The Time and Location of the Accident. The time and location of the accident have a great influence on the urban expressway capacity. If the time is in the peak period, the traffic demand is big, and the mutual interference degree of the vehicles at the accident point will be great, which will further reduce the urban expressway capacity. If the spatial location of the accident is in the intersection, the space of straight vehicles and the vehicles transfer into expressway is very limited. Moreover, the driving directions of each import lane at the intersection are more and traffic flow interweaves with each other, which will also reduce the urban expressway capacity. Other situations can be analyzed through the actual situation.
3.1.4. The Accident Delay Time. The accident delay time is related to operating strength, accident types, severities, traffic conditions, and other factors. The stronger the operating strength, the shorter the accident delay time, and its capacity recoveries sooner. For influencing factors of the capacity of special accident roads, for example, tunnels and bridges, in addition to the above factors, there are other special influencing factors. The capacity of tunnels is related to lighting intensity, traffic signs of the tunnel entrance, and other factors; however, the bridge is related to slope and linear. 3.2. The Calculation of the Accident Delay Time and Congestion Dissipation Time. Taking into account influence factors of the urban expressway capacity after different accident types, the accident delay time will vary. Use the Information Gain Values based on ID algorithm of the Decision Tree to estimate the accident delay time of different accident types on the urban expressway, the formulas are as follows:
Gain (𝑆, 𝐴 1 ) = Entropy (𝑆) −
𝑆V , (1) Entropy (𝑆V ) |𝑆| V∈Value(𝐴) ∑
Advances in Mechanical Engineering
Table 1: The accident delay time of common accident types on the expressway. The accident delay time (average)/min
The accident types Anchor (the vehicles cannot move) Anchor (the vehicles can move) Roll-over (vehicle type are cars, no casualties) Roll-over (vehicle type are cars, injuries) Fire (vehicle type are cars, no casualties, no damage to the facility) Fire (vehicle type are cars, no casualties, damage to the facility) Rear-end (the number of related vehicles ≥3, vehicle type are cars, no casualties) Rear-end (the number of related vehicles ≥3, the vehicle type are cars, injuries) Collision (casualties but no deaths, vehicle type are cars) Collision (casualties but no deaths, vehicle type are bus)
15 7 33
Cumulative number of vehicles
4
Cumulative Maximum number of number of vehicles arriving queued vehicles The slope is recovery capacity of the state
18
The slope is the capacity of the accident roads t1 t2 t3 t4 Accident Accident Accident Congestion starts responds ends ends
36
Accident delay time Recovery time
48
t
Continued congestion time
23
Figure 3: The forming process of traffic congestion.
49 37
Set up road conditions and accident types
59 Set up traffic volume conditions
where
Input indicators
𝑚
Entropy (𝑆) = − ∑ 𝑝 (𝑢𝑖 ) log 𝑝 (𝑢𝑖 ) ,
(2)
Set up the simulation parameters
𝑖=1
Output indicators
𝑆 = sample collection; Entropy (𝑆) = information entropy; 𝑝(𝑢𝑖 ) = probability of Category 𝑖; 𝐴 = property; Value (𝐴) = the collection of the value of the property 𝐴; V = a value of the property 𝐴; 𝑆V = sample collection that the value of the property 𝐴 is V; |𝑆V | = 𝑆V contains sample number. Selecting an urban expressway accident as samples [32], according to above formulas, the accident delay time of common accident types on the expressway is calculated. The results are shown in Table 1. The dissipation time can be obtained from the Flow Wave Theory. The calculation formulas are as follows: 𝑄𝑤1 =
(V2 − V1 ) , (1/𝐾2 − 1/𝐾1 )
𝑄𝑤2 =
(V3 − V2 ) , (1/𝐾3 − 1/𝐾2 )
𝑡𝑆 =
(3)
𝑡𝐴 𝑄𝑊1 , (𝑄𝑊2 − 𝑄𝑊1 )
where 𝑄𝑊1 = the wave flow of Build-wave; 𝑄𝑊2 = the wave flow of evanescent wave; V3 , V2 , V1 = the speeds of the three kinds of traffic states; 𝐾3 , 𝐾2 , 𝐾1 = the density of the three kinds of traffic states. 3.3. Theory Analysis of the Capacity. The entire process of the urban expressway from traffic congestion to the dissipation is analyzed through the evolution processes of the urban expressway capacity after traffic accidents, as shown in Figure 3.
Estimate the capacity under traffic accident
Figure 4: The flow chart of simulation analysis of the urban expressway capacity after traffic accidents.
Figure 3 shows that the reciprocal of the ratio (slope) between the accident delay time and cumulative number of vehicles in the time period is the capacity of the accident road. The reciprocal of the ratio (slope) between congestion dissipation time and cumulative number of vehicles in the time period is the recovery capacity (it is slightly less than the actual capacity of the road). This paper discusses the former and assumes that traffic accidents take place on urban expressway sections.
4. The Simulation Model of the Urban Expressway Capacity after Traffic Accidents According to the theoretical analysis of the urban expressway capacity after traffic accidents, use Vissim simulation software to simulate and estimate the capacity. We obtain corresponding 20 groups output through the 20 groups simulations. Then, use the average value to analyze the results in order to reduce the error. The simulation analysis of the capacity is shown in Figure 4. 4.1. Road Conditions and Accident Types Settings. The road conditions are divided into road grade, travel direction,
Advances in Mechanical Engineering
Figure 5: The distribution function of the car maximum acceleration.
5
Figure 6: Expectation speed distribution of the car.
Table 2: The vehicle classification and conversion coefficient.
whether there is a separation zone, numbers of two-way lanes, lane width, and so forth. The accident types are divided into vehicle anchor, roll-over, fire, rear-end and collision. This paper takes the expressway of Xi’an city as the simulation background. The lane width is set as 3.750 m; unidirectional number of lanes is 3; simulation road length is 720.275 m. This paper takes a closer-left lane as an example to study. 4.2. Traffic Volume Conditions and Driving Behavior Parameters Settings. Traffic volume conditions include traffic composition, the proportion, traffic volume, speed, and so forth. Expectation speed curve of the road under the different road levels is set in accordance with the “urban road design specifications.” But after the accident, the speed will be less than the expectation speed. The distribution function of the car maximum acceleration and expectation speed distribution of the car after traffic accident are shown in Figures 5 and 6. On driving behavior parameters settings, forwardlooking minimum distance is 0.00 m, and the maximum distance is 250.00 m; back-sight minimum distance is 0.00 m, and the maximum distance is 150.00 m; last time of temporarily distracted is 0.00 seconds, continuous probability is 0.00%; the car following model uses the Wiedemann 74 model; car stop spacing is 2.00 m on average; the additional part of the safe distance is 2.00 m, and multiples part of the safe distance is 3.00 m. 4.3. The Simulation Parameters Settings. The related parameter settings are shown in Tables 2 and 3. Because there are no simulation modules of traffic accident in Vissim simulation software, this paper sets up red light on the accident lane to simulate traffic accidents. The signal begins to turn red when the accidents happened, and will turn green until the end of the accident. For the data in Table 3, for example, of the first line data, 2400 s is a signal cycle (green end time) and 1080 s = 180 s + 900 s is red end time. 900 s (15 min) is the accident delay time of
Vehicle type The proportion of vehicle components Reference conversion coefficient
Passenger car
The bus
Truck
84.00%
3.00%
13.00%
1.00
2.00
3.00
Note: the data come from traffic volume investigation and statistics of the Xi’an city expressway; passenger cars (including small trucks), bus (including medium-sized passenger), truck (including big bus, medium-sized trucks and large trucks).
the anchor (the vehicles cannot move); 180 s is the buffer time (that is time before the accident occurred), which can reduce the influence of the required time (simulation influence time) from vehicle appearance to the accident point for the simulation results at the beginning of the simulation. It should be larger than the simulation influence time but less than the accident delay time of corresponding accident types. Other situations are similar to this. In this paper, the output parameter is mainly the number of vehicles. 4.4. The Analysis of the Simulation Results. According to the accident delay time and the Flow Wave Theory (the free flow speed is 80 km/h, and blocking density is 106 vehicle/km), through above parameter settings to change the signal control parameters of traffic simulation, simulate the capacity of vehicle anchor, roll-over, fire, rear-end, and collision. The simulation data results are as shown in Table 4. Table 4 shows that the accident delay time and congestion dissipation time of vehicle anchor are the minimum, but the residual capacity of the accident road is the maximum, and the proportion is 69.926%; the accident delay time and congestion dissipation time of vehicle collision are the maximum, but the residual capacity of the accident road is the minimum, and the proportion is 49.963%; the proportion of the vehicle roll-over, fire, and rear-end is 56.87%, 61.611%, 59.796% respectively.
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Advances in Mechanical Engineering Table 3: Signal control parameter settings under different accident types.
Name Anchor Roll-over Fire Rear-end Collision
Red/Amber 0 0 0 0 0
Amber 0 0 0 0 0
Red End(s) 1080 2160 1260 1560 2400
Green End(s) 2400 3600 2400 3600 4620
Red End 2 — — — — —
Green End 2 — — — — —
Type Cycle Cycle Cycle Cycle Cycle
Cycle time(s) 2400 3600 2400 3600 4620
Table 4: The simulation data results. Type of accident Anchor (the vehicles cannot move) Roll-over (vehicle type are cars, no casualties) Fire (vehicle type are cars, no casualties, no damage to the facility) Rear-end (the number of related vehicles ≥3, vehicle type are cars, no casualties) Collision (casualties but no deaths, vehicle type are cars)
𝑡𝐴
𝑡𝑆
𝑡𝑆 /𝑡𝐴
𝑁1
𝑁2
𝐶𝑅
𝑛
𝐶𝑆
𝐶
𝛽
15
3.5
0.23
732
944
3776
3
1800
5400
69.926
33
46.2
1.4
1309
1689
3071
3
1800
5400
56.870
18
10
0.56
774
998
3327
3
1800
5400
61.611
23
18.4
0.8
960
1238
3229
3
1800
5400
59.796
37
51.7
1.40
1290
1664
2698
3
1800
5400
49.963
Notes: tA (min): the accident delay time, ts (min): crowded dissipation time, N1 (vehicle): cumulative number of vehicles, N2 (pcu): cumulative number of standard vehicles, CR (pcu/h): the residual capacity of the accident road, n: the number of lanes, CS (pcu/h): one Lane capacity, 𝛽 (%): the proportion of the residual capacity of the accident road, C: one-way road capacity.
According to the data of the simulation results, we further analyze and research the relationship between the accident delay time, congestion dissipation time, and the residual capacity of the urban expressway comprehensively, as shown in Figure 7. Note. The left axes in Figure 7 are the main axes (min), which represents congestion dissipation time, time difference of congestion dissipation time and the accident delay time; the right axes in Figure 7 are the secondary axes (%), which represents the ratio between congestion dissipation time and the accident delay time, the proportion of the residual capacity on the urban expressway. Abscissa represents the accident delay time (min). Figure 7 shows that the accident delay time is proportional to congestion dissipation time, time difference of congestion dissipation time, and accident delay time and their ratio, but it is an inverse relationship with the proportion of the residual capacity. With the increasing of the accident delay time, time difference of congestion dissipation time and the accident delay time is negative firstly and decrease constantly, it is positive and increase constantly later. When the accident delay time increased from 15 minutes to 37 minutes, the proportion of the residual capacity dropped by about 20%, but congestion dissipation time increased 48 minutes.
5. Conclusions The researches of the urban expressway capacity after traffic accident have a very important role in immediate emergency
55 50 45 40 35 30 25 20 15 10 5 0 −5 −10 −15
15
18
23
33
37
1.50 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
Congestion dissipation time Time difference of congestion dissipation time and the accident delay time The ratio between congestion dissipation time and the accident delay time The proportion of the residual capacity
Figure 7: Congestion dissipation time and the proportion of the residual capacity vary with the accident delay time.
and rescue measures were taken by urban traffic management departments, and the efficiency of emergency rescue reflects the level of city management and emergency response in a certain extent. So, its researches have important significance.
Advances in Mechanical Engineering Through the attenuation simulation of the urban expressway capacity after traffic accidents, the following conclusions can be drawn. (1) At first, this paper analyzes the evolution processes of the urban expressway capacity after traffic accidents. Then, it describes the influence factors of the capacity and calculates the accident delay time and congestion dissipation time on the basis of this. According to the forming process of traffic congestion, elaborates theoretical analysis and research of the capacity. Finally, it puts forward the calculation method of the capacity. The calculation method takes the Information Gain Value of the Decision Tree ID algorithm and the Traffic Flow Wave Theory as a theoretical basis, and simulates and studies the capacity by using VISSIM simulation software. The simulation results are almost consistent with the actual situation. It is shown that this method has a certain theoretical significance and practical value, and it can provide decision support for urban traffic management departments to take appropriate response measures. (2) Through the attenuation simulation of the urban expressway capacity after traffic accidents, the research results suggest that capacity attenuation of vehicle anchor is minimal, and the rate of attenuation is 30.074%; the next is vehicles fire, rear-end, and rollover, the rate of attenuation is 38.389%, 40.204%, and 43.130%, respectively; the capacity attenuation of vehicle collision is the largest, and the rate of attenuation is 50.037%. Through further analysis and research of the relationship between the accident delay time, congestion dissipation time, and the residual capacity of urban expressway, the results are shown in Figure 7, and the curve of congestion dissipation time, time difference of congestion dissipation time and the accident delay time and their ratio have the feature of slow change firstly, the mutation later, the gentle finally. (3) The accident delay time and the residual capacity of the urban expressway will be very different for different accident types. The ratio between congestion dissipation time and the accident delay time will be affected by the residual capacity: the bigger the residual capacity, the smaller the ratio conversely, the greater. But its quantitative analysis still needs to be studied further. Moreover, different locations and time of traffic accidents have a great influence on the urban expressway capacity, which still needs further research.
Acknowledgments The authors acknowledge that this paper has been supported by the National Natural Science Foundation of China (Grant no. 51208051) and the Fundamental Research Funds for the Central Universities (CHD2011ZD014).
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References [1] K. Watanabe, H. Akahane, H. Warita, and H. Okamura, “Identification of capacity balls and analysis of affectors of capacity on Tokyo Metropolitan expressway,” in Proceedings of the 5th International Symposium on Highway Capacity and Quality of Service, Yokohama, Japan, 2006. [2] M. Kuwahara, M. Koshi, and T. Suzuki, “Capacity and speed of weaving sections of the Tokyo Metropolitan expressway,” ITE Journal, vol. 61, no. 3, pp. 27–32, 1991. [3] M. Sarvi, M. Kuwahara, and I. Nishikawa, “Macroscopic study on merging capacity in Tokyo Metropolitan expressway,” in Proceedings of the 22nd Infrastructure Planning Conference, 1999. [4] M. Sarvi, M. Kuwahara, and I. Nishikawa, “A simulation model for evaluation of merging capacity on the Metropolitan expressway,” Production Research, vol. 52, no. 2, pp. 104–107, 2000. [5] C. Yang, C. Shao, and L. Liu, “Study on capacity of urban expressway weaving segments,” Procedia-Social and Behavioral Sciences, vol. 43, no. 1, pp. 48–56, 2012. [6] M. Iwasaki, “Empirical analysis of congested traffic flow characteristics and free speed affected by geometric factors on an intercity expressway,” Transportation Research Record, vol. 13, no. 20, pp. 242–250, 1991. [7] Y. Shiomi, T. Yoshii, and R. Kitamura, “Platoon-based traffic flow model for estimating breakdown probability at single-lane expressway bottlenecks,” Transportation Research B, vol. 45, no. 9, pp. 1314–1330, 2011. [8] J. Weng and Q. Meng, “Modeling speed-flow relationship and merging behavior in work zone merging areas,” Transportation Research C, vol. 19, no. 6, pp. 985–996, 2011. [9] T. E. Keeler and K. A. Small, “Optimal peak-load pricing, investment, and service levels on urban expressways,” The Journal of Political Economy, vol. 85, no. 1, pp. 1–25, 1977. [10] T. Sakai, K. Yamada-Kawai, H. Matsumoto, and T. Uchida, “New measure of the level of service for basic expressway segments incorporating customer satisfaction,” Procedia—Social and Behavioral Sciences, vol. 16, pp. 57–68, 2011. [11] H. Okamura, S. Watanabe, and T. Watanabe, “An empirical study on the capacity of bottlenecks on the basic suburban expressway sections in Japan,” in Proceedings of the 4th International Symposium on Highway Capacity, TRB Circular EC, 2000. [12] J. Xing, H. Takahashi, and K. Iida, “Analysis of bottleneck capacity and traffic safety in Japanese expressway work zones,” in Proceedings of the Annual Meeting of the Transportation Research Board, 2010. [13] T. O. Kurokawa, “A study on travel time prediction method on inter-city expressways using traffic capacity at the bottleneck,” in Proceedings of The 5th World Congress on Intelligent Transport Systems, Korea Paper No. 3060, Seoul, Republic of Korea, October 1998. [14] B. Mehran and H. Nakamura, “Considering travel time reliability and safety for evaluation of congestion relief schemes on expressway segments,” IATSS Research, vol. 33, no. 1, pp. 55–70, 2009. [15] Y. Iida, A Formulation of On-Ramp Traffic Control System with Route Guidance for Urban Expressway, IFAC, 1990. [16] T. Sasaki and T. Akiyama, “Fuzzy on-ramp control model on urban expressway and its extension,” Transportation and Traffic Theory, pp. 377–395, 1987. [17] Q. Chai, S. K. Chen, and B. H. Mao, “Capacity calculation on bus stop in expressway considering road congestion,” Journal of
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[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
Advances in Mechanical Engineering Jilin University (Engineering and Technology Edition), vol. 39, no. 2, pp. 58–62, 2009. P. F. Du, S. Q. Jin, and J. Li, “Simulation analysis of expressway capacity,” Journal of Hunan University (Natural Sciences), vol. 36, no. 6, pp. 7–12, 2009. Y. Ming-Yuan, “Calculated methods for the capacity of terminals along expressway,” Journal of Highway and Transportation Reseach and Development, vol. 12, no. 4, pp. 41–45, 1995. Z. Hai-Jun, Z. Jue, and Y. Xiao-Guang, “Analysis and simulation of traffic state on expressway during incident,” Journal of Traffic and Transportation Engineering, vol. 8, no. 2, pp. 116–121, 2008. X. Du and L. Jian, “The estimation of highway effective capacity after sudden traffic,” Journal of Highway and Transportation Research and Development, vol. 27, no. 11, pp. 154–158, 2010. L. Hong-Ping, P. Yu-Long, and Y. Zhong-Liang, “Factors influencing free flow speed on expressway,” Journal of Jilin University (Engineering and Technology Edition), vol. 37, no. 4, pp. 772–776, 2007. X. B. Yang, N. Zhang, and Y. Guan, “Behavior-based analysis of the relationship between expressway capacity and number of lanes,” China Civil Engineering Journal, vol. 42, no. 10, pp. 104– 109, 2009. K. Long, X. Yang, J. Yu et al., “Capacity of weaving section at off-ramp terminal of elevated expressway,” Shanghai Highways, no. 4, pp. 5–7, 2005. K. J. Long and Y. Xiao-Guang, “Capacity analysis on urban expressway on-ramp in alternate method,” Systems Engineering, vol. 22, no. 10, pp. 54–58, 2004. J. L. Ma, W. Wang, W. Q. Li et al., “Empirical capacity calculating method for expressway on-ramp mixed traffic flow,” Journal of Highway and Transportation Research and Development, vol. 22, no. 10, pp. 98–101, 2005. X. W. Li, R. Jian, L. Xiao-Ming, and Z. Zhi-Yong, “Traffic characteristics and capacity reasearch of urban expressway shunt, merge area,” Journal of Highway and Transportation Research and Development, vol. 23, no. 1, pp. 101–104, 2006. L. D. Zhong, J. Rong, X. D. Sun et al., “Capacity of weaving sections of urban expressway obtained with simulation method,” Journal of Highway and Transportation Research and Development, vol. 23, no. 4, pp. 88–93, 2006. L. D. Zhong, X. W. Li, J. Rong, F. T. Ren, and R. G. Zhou, “Confirmation of the capacity of urban expressway basic segment,” Journal of Beijing University of Technology, vol. 32, no. 7, pp. 605– 609, 2006. X. M. Chen, L. Yu, L. Zhu, J. Guo, and M. Sun, “Microscopic traffic simulation approach to the capacity impact analysis of weaving sections for the exclusive bus lanes on an urban expressway,” Journal of Transportation Engineering, vol. 136, no. 10, pp. 895–902, 2010. J. Zhang and J. Yong-Feng, “Research on traffic flow model of expressway weaving area,” China Journal of Highway and Transport, vol. 24, no. 5, pp. 89–93, 2011. B. B. Jiyang, X. N. Zhang, and L. J. Sun, “Traffic incident duration prediction grounded on Bayesian decision methodbased tree algorithm,” Journal of Tongji University, vol. 36, no. 3, pp. 319–324, 2008.
