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Microscopic Analysis of Climbing Lane Performance at Freeway Uphill Section
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2016 International Symposium of Transport Simulation (ISTS’16 Conference), June 23~25, 2016 2016 International Symposium of Transport Simulation (ISTS’16 Conference), June 23~25, 2016
Microscopic Analysis of Climbing Lane Performance at Freeway Microscopic Analysis of Climbing Lane Performance at Freeway Uphill Section Uphill Section a a
Seongjin Choi a, Jonghae Suh a, Hwasoo Yeo a,* Seongjin Choi a, Jonghae Suh a, Hwasoo Yeo a,* Civil and Environmental Engineering Department, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea Civil and Environmental Engineering Department, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea
Abstract Abstract Freeways which are designed for high-speed vehicular traffic seems to have some problems with the sections with inclines due to the performance in accelerations of heavy trucks and seems high occupancy vehicles (HOVs). problem, Freeways which aredrop designed for high-speed vehicular traffic to have some problems withTo thecomplement sections withthis inclines due installing auxiliary lane separate low speed vehicles from high speed vehicles. This isTo called a climbing lane. There to the performance droptoinlaterally accelerations of heavy trucks and high occupancy vehicles (HOVs). complement this problem, are mainlyauxiliary two types 1) pocket typevehicles climbing lanehigh andspeed 2) overtaking In Korea, many installing laneoftoclimbing laterallylane: separate low speed from vehicles. type This climbing is called alane. climbing lane. There sections with inclines areclimbing located near area, leading to somelane attentions the performances of climbing at various are mainly two types of lane:urban 1) pocket type climbing and 2) on overtaking type climbing lane. Inlane Korea, many traffic input conditions. To do so,urban microscopic traffictosimulator based on is used for analysis. Some adjustments sections withflow inclines are located near area, leading some attentions onOFFA the performances of climbing lane at various are made on flow the OFFA to depict behaviortraffic without short gap mode to demonstrate performance of heavy traffic input conditions. To asymmetric do so, microscopic simulator based on and OFFA is used for analysis. Somedrop adjustments truck vehicles. delay is usedasymmetric to evaluate behavior operational efficiency to collision is used to evaluate safetydrop performance. are made on theTotal OFFA to depict without shortand gaptime mode and to demonstrate performance of heavy As a result of simulation study, the to overtaking type usuallyefficiency showed better performance inisboth and safety truck vehicles. Total delay is used evaluate operational and time to collision usedoperational to evaluateefficiency safety performance. performance. However, study, at some inputtype flow with showed high truck ratio conditions,in the of overtaking type As a result of simulation the traffic overtaking usually better performance bothperformances operational efficiency and safety climbing lane However, broke down, showing lowinput operational efficiency and safety performance. climbing lane operation performance. at some traffic flow with high truck ratio conditions, theTherefore, performances of overtaking type depending on the traffic demand should considered.efficiency and safety performance. Therefore, climbing lane operation climbing lane broke down, showing lowbeoperational depending on the traffic demand should be considered. © 2016 The Authors. Published by Elsevier B. V. Copyright © 2017 The Authors. Published by Elsevier B.V. Selection andAuthors. Peer-review under responsibility of Dept of Transportation Engineering University © 2016 The Published by ElsevierofB. V. Selection and Peer-review under responsibility Dept. of Transportation Engineering, University of Seoul. of Seoul. Selection and Peer-review under responsibility of Dept of Transportation Engineering University of Seoul. Keywords: Climbing lane; Car-Following; Microscopic Traffic Simulator; Moving Bottleneck Keywords: Climbing lane; Car-Following; Microscopic Traffic Simulator; Moving Bottleneck
1. Introduction 1. Introduction A freeway can be defined as a road infrastructure designed for high-speed vehicular traffic. For this characteristic there to be some problems sectionsvehicular with inclines. A freeway of canfreeways, be defined as aseems road infrastructure designedwith for the high-speed traffic. For this characteristic of freeways, there seems to be some problems with the sections with inclines. * Corresponding author. Tel.:+82-42-350-3634; fax: +82-42-350-3610. E-mail address:author. [email protected] * Corresponding Tel.:+82-42-350-3634; fax: +82-42-350-3610.
E-mail address: [email protected] 2214-241X © 2016 The Authors. Published by Elsevier B. V. Selection and under responsibility Dept of Engineering University of Seoul. 2214-241X © Peer-review 2016 The Authors. Published by of Elsevier B.Transportation V. Selection and Peer-review under responsibility of Dept of Transportation Engineering University of Seoul.
Copyright © 2017 The Authors. Published by Elsevier B.V. Selection and Peer-review under responsibility of Dept. of Transportation Engineering, University of Seoul. 10.1016/j.trpro.2017.03.081
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Fig. 1. Types of Climbing lane (a) pocket type; (b) overtaking type
Performance drops in acceleration occurs with heavy trucks and high occupancy vehicles (HOVs) (Lan et al. (2003)). This cause a traffic problem called as “moving bottleneck.” Moving bottleneck is caused by a vehicle travelling with a speed which is less than the prevailing traffic. This low speed vehicle forces following vehicles behind lower speed to its speed, forming a vehicle queue behind. (Newell (1998)) This causes system performance drop in terms of total travel time. Also some high speed driving vehicles often attempt to overtake these low speed vehicles that causes safety problems as well. Due to these problems, installing auxiliary lane to laterally separate low speed vehicles like heavy trucks and HOVs from high speed vehicles like passenger vehicles. In many nations, the auxiliary lane, also called as climbing lane, is suggested to be installed and operated at uphill section. In United States (California Department of Transportation (2012)), it suggests installation of additional lane where speed difference of heavy vehicles and passenger cars is above 15 kilometers per hour (herein after kph). In Germany (European Commission (2000)), the starting point of auxiliary lane is located where average speed of heavy vehicles is lower than 70kph. Japan has regulation of this lane to be installed where longitudinal slope is steeper than 5%. Specifically, in case of freeways where its desired speed is larger than 100kph, climbing lanes are installed where longitudinal slope is larger than 3%. (Japan Highway Public Corporation (1990)) In Korea regulation for installation of the auxiliary lane is same as the one in Japan. (Korean Ministry of Land, Transport and Maritime Affairs (2012)) There are mainly two types of climbing lane: 1) pocket type climbing lane and 2) overtaking type climbing lane. The former one, pocket type climbing lane (see Fig. 1. (a)), is that the auxiliary lane is located at the outer-most side of the lane. This is supposed to enforce slow vehicles to use this auxiliary lane not to disturb faster vehicles. However, from the data achieved from other field researches, the compliance rate, which is the rate of heavy vehicles to use the auxiliary lane, the lateral separation ratio of slow vehicles, is relatively low. With the low compliance rate, it is not enough to relieve moving bottleneck. The fact that heavy vehicles should change lane twice, both at the diverging and merging locations, makes drivers of heavy vehicles feel reluctant to use the climbing lane. Also, some fast vehicles abuse this climbing lane for overtaking slow vehicles. This implies some safety problems, too. A different type to complement this problems of pocket type climbing lane is overtaking type climbing lane. (see Fig. 1. (b)) In overtaking type climbing lane, an additional lane is installed at the inner-most lane for high speed vehicles. At the diverging location, the entrance to the climbing lane, heavy vehicles do not need to change lane and these vehicles naturally flow into the outer-most lane. This improves the lateral separation of slow vehicles and heavy vehicles, and eventually help relieve the moving bottleneck. However, some reports have reported that the number of accidents have increased since the passing type of climbing lane has been installed, implying there might be a safety problem in overtaking type climbing lane. As seventy percent of the land in Korea is covered with mountains, it is inevitable to install roadways in sections with inclines. As a result, in Korean freeways, there are 28 pocket type climbing lanes and 53 overtaking type climbing lanes. On the contrary to the countries where mountains are usually located in rural area, in Korea these climbing lanes are usually located near cities where daily traffic using climbing lane sections might be higher than that in other countries. Therefore, there have been increasing attentions to the studies on operational efficiency and safety of climbing lane at uphill sections. Lee et al. (2010) analyzed the effectiveness of the change of type of climbing lane
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from pocket type to overtaking type in terms of traffic efficiency and economic perspectives and concluded that the overtaking type of climbing lane shows improvements on traffic efficiency and it is also economical. However, Kim et al. (2014) analyzed traffic accident data in climbing lane sections where their types were changed from pocket type to overtaking type. They used Comparison-Group Method to evaluate the safety performance change since the climbing lane type change. In their research, the expected number of traffic accidents without the change was 40.81, however, there were 71 traffic accidents in climbing lane sections. Therefore, they concluded that the overtaking type climbing lane might be more dangerous in terms of traffic accidents. However, since the individual number of traffic accidents were small, around 5 to 15 cases for each section, there still remains a doubt on their statistical results. Although many researchers have tried to analyze the performances of climbing lane, it is somewhat difficult to assess the performance of climbing lane on various traffic conditions due to the lack of real data. In the cases like this, a simulation study is necessary to evaluate the operational and safety performances of climbing lane. Some studies which analyzed climbing lane in Korea usually used microscopic traffic simulator called VISSIM for their study. However, there are some limitations because it doesn’t properly depict driver merging behavior. Recently, a study including driver’s merging behavior in over-saturated flow at freeway, Oversaturated Freeway Flow Algorithm (OFFA), (Yeo et al. (2008)) has been presented. However, this model cannot demonstrate natural deceleration caused by the slope of the uphill sections. By supplementing natural deceleration caused by uphill slope, the performance of each type of climbing lane in various traffic demand conditions can be evaluated and eventually the optimal solution for the type of climbing lane can be provided. In this research, by using microscopic traffic simulator based on OFFA model, the traffic operational efficiency and traffic safety of installation of climbing lanes for each type case and non-operating case will be examined. Total travel time delay and average speed will be used for the examination of operational efficiency, and collision risk estimated by surrogate safety measures will be used for the examination of traffic safety. The structure of the paper is as follows. In Section 2, the simulation model used to assess climbing lane will be discussed with the improvements made in this paper. In Section 3, the simulation set up is presented. In Section 4, the results of simulation are presented. The paper is finished with a conclusion and reference in section 5 and 6, respectively. 2. Simulation Model 2.1. Modifications on Oversaturated Freeway Flow Algorithm The simulation model is based on the Oversaturated Freeway Flow Algorithm (OFFA) (Yeo et al. (2008)). OFFA is an integrated model describing lateral and longitudinal behavior of drivers based on the real trajectory data of vehicles. The longitudinal behavior (i.e. car-following behavior) is formulated to determine next position of a following vehicle. According to the model, the next position of the following vehicle is related with the current speed, desired speed, vehicle performance characteristics and driver characteristics. In the free flow condition, the vehicle accelerates until the moving speed becomes the desired speed of the driver. However, in the congested condition, the vehicle keeps certain spacing with the leader vehicle based on Newell’s linear car-following model (Newell (2002)). The lane changing is divided into two types: mandatory lane changes and discretionary lane changes. The former one represents how the drivers have to change lane to reach their destination in on- and off- ramp merging. On the other hand, the latter one represents the situation that the drivers change lane to gain benefits to their driving, such as faster speed or larger spacing. In addition, there is a traffic behavior called asymmetric behavior analyzed by Yeo and Skabardonis (2009). In OFFA model a small modification called short gap mode is used to demonstrate asymmetric characteristics and to be more consistent with the real trajectory data. As the car-following model of OFFA is based on Newell’s linear car-following model, one problem may arise. The linear car-following model uses the location of leader vehicle at time t t (here, is reaction time) and jam spacing of follower vehicle ( s jam ) to calculate the next position of the follower vehicle. (see Eq. (1)) However, to use it in microscopic traffic simulation, which usually uses simulation time step (ex. NGSIM uses 0.1s time interval) which is much smaller than the reaction time (around 1s~1.5s according to Green (2000)), lots of stacks to store trajectory is needed. As a result, the simulator has to store the position data of the leader for somewhat long period of
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time ( ). These data stacks require lots of use of memory in computation of simulation algorithm with protracted t computation time. For developing a microscopic traffic simulation for on-line simulation this heavy computation can be an obstacle. Therefore, directly applying original Newell’s linear car-following model is not appropriate to use in microscopic traffic simulator. (1) xfollower (t t) xleader (t t ) s jam Another problem is related with the short gap mode mentioned above. Short gap mode is used in the original OFFA to model asymmetric behavior. According to Yeo and Skabardonis (2009), this short gap mode is applied to the vehicles in deceleration phase, especially to the vehicles involved in the lane changing (Yeo et al. (2008)). Such vehicles include the lane changing vehicles, the lane-change receiving vehicles, and the lane-change cooperating vehicles. The short gap mode is modeled by multiplying a coefficient to the jam gap and wave travel time as shown in the Eq. (2). jam LC jam , LC (2) gn gn n n However, this adjustment of parameter cannot fully depict the phenomenon because the short gap mode parameter chosen is an arbitrary, artificial parameter and this makes discontinuity of parameters in simulations. Therefore, an integrated model that can be applicable at any state should be formulated without changes in parameters. To complement these problems, in this research, the relationship between the position of leader vehicle and the position (to be calculated) of follower vehicle is modified. With the assumption expressed in Eq. (3), the modified relationship is expressed as Eq. (4) (3) xleader (t t ) xleader (t t) vleader (t t) (4) xfollower (t t) xleader (t t) vleader (t t) s jam In free flow condition, where the speeds of vehicles, including the leader and the follower vehicles, don’t change a lot, the modified car-following model is same with the original Newell’s linear car-following model. In other words, the modified car-following model (Eq. (4)) is same with the original Newell’s linear car-following model (Eq. (5)) with following condition: (5) vleader (t) vleader (t t) for t (t,t ) However, in congested traffic, where acceleration and deceleration occur, the shockwave is generated and propagated to upstream, this modified model makes difference in position at next time step. Fig. 2 shows the comparison between trajectory based on the original Newell’s linear car-following model and the modified base carfollowing model. In the deceleration case, as shown in the Fig. 2. (a), the following vehicle shortens the gap with reaction time . This shows the behavior of deceleration phase in asymmetric theory without applying short gap mode. Furthermore, as shown in the Fig. 2. (b), when the leader vehicle is accelerating, the follower vehicle extends the gap with the reaction time , which coincides with the acceleration phase behavior in asymmetric theory (Yeo et al.
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Fig. 2. Comparison between trajectory based on original Newell’s linear car-following model and the modified base car-following model. (a) Deceleration case and (b) Acceleration case
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(2008)). By modifying base car-following model, the data stacks are not necessary because the time input of the model is synchronized to t t as expressed in Eq.(4). Also, without adjusting driver characteristic parameters (i.e. reaction time and jam spacing), that is to say without using short gap mode, asymmetric driving behavior can be illustrated based on the modification. 2.2. Uphill Section Effect Modelling To demonstrate vehicle-performance drop of heavy trucks and HOVs (herein after truck class vehicles) in the simulation, the incline effects on the acceleration should be modeled. For the simplicity of the model, the acceleration is recalculated with the effect of the uphill section as shown in the Eq. (6). Acc Acc sin g( 9.8m / s2 ) Acc _ freeflow sin g( 9.8m / s2 )
(6)
Dec Dec sin g( 9.8m / s ) 2
As well as the acceleration drop due to the incline of the roadway, the free flow speed of truck class vehicles is limited to demonstrate the low speed. The formulation is expressed in the Eq. (7)with the free flow drop ratio ( ) of truck class vehicles. value is with the speed regulation of freeway in Korea. Usually, if the speed limit of normal class vehicles is 110 kph, that of truck class vehicles is 90 kph and if the speed limit of normal class vehicles is 100 kph, that of truck class vehicles is 80 kph. Therefore, is usually around 0.8~0.85. v ff trucks (1 )vff passenger (7)
3. Simulation 3.1. Climbing Lane Section for Simulation In Korea, there are 87 uphill sections where the climbing lane is installed. Each section has different geometric characteristics with different length, slope, and curvature of the section. However, it is not possible to evaluate these different geometric characteristics and it is not necessary. As the purposes of the study are to evaluate traffic operational efficiency and traffic safety performance of each type of climbing lane, these performances should be analyzed in same road conditions. Therefore, for the simulation, same road characteristics are used. The length of the climbing lane for simulation is 2 km and the slope of the climbing lane is 4% with two main lanes as shown in the Table 1. Specific configuration of the climbing lane section model is depicted in Fig. 3 Table 1. Road characteristics Road Characteristic Length (km)
2
Slope (%)
4
Number of main lanes
2
Fig. 3. Climbing Lane Section Model forSimulation
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3.2. Simulation Parameters The simulation parameters include driver characteristics and vehicle performances as well as the climbing lane compliance rate. The driver characteristic parameters used for the simulation are reaction time and jam gap. The vehicle performance parameter includes vehicle acceleration and deceleration rate, and free flow speed of the vehicles depending on the type (normal or truck class vehicles). A field video test has been conducted to achieve these parameters from real data, however, it is not possible to achieve data like reaction time, jam gap, and acceleration and deceleration rate. The data achieved is free flow speed and the climbing lane compliance rate. For other parameters that is not able to be achieved from the field video analysis, the calibrated values from vehicle trajectory data of NGSIM data set are used to randomly generate (Yeo et al. (2008)). The parameters and its distribution parameters are specified in Table 2. Table 2. Simulation input parameters Parameters
Normal Vehicle
Truck class vehicle
Free Flow Speed (kph)
110
90
Reaction Time (s)
μ = 0.58 σ = 0.39 lognormal
μ = 0.58 σ = 0.39 lognormal
Jam gap (m)
μ = 3.75 σ = 0.98 normal
μ = 4.21 σ = 3.80 normal
Vehicle Length (m)
μ=5 σ = 0.5 normal
μ = 10 σ=1 normal
Max Acceleration (m/s^2)
μ = 4.48 σ = 0.98 normal
μ = 4.68 σ = 0.93 normal
Max Deceleration (m/s^2)
μ = 4.36 σ = 0.82 normal
μ = 4.52 σ = 0.88 normal
Climbing Lane Compliance Rate
Overtaking Type: 60%, Pocket Type: 20%
3.3. Simulation Scenarios In the field video test mentioned in Section 3.2, it was hard to make quantitative evaluation, because the traffic inflows were not diverse and only free flow states are observed. However, to evaluate the traffic operational efficiency and traffic safety performance of each climbing lane types, various traffic inflows should be used. Therefore, in the simulation, various traffic demands as well as various truck ratios will be used to compare traffic operational efficiency and traffic safety performance of pocket type, overtaking type, and non-operating case (herein after, closed type). Each traffic demand with various input flows and truck ratios is simulated 10 times. 4. Simulation Result 4.1. Operational Efficiency In this paper, to assess the operational efficiency of each climbing lane, total delay, which is a widely used index for operational efficiency, is used. The total delay can be estimated with the N-curve, also known as the cumulative vehicle count curve. The total delay can be calculated by computing the area between the virtual arrival curve and departure curve. It is assumed that there exist two virtual detectors in the simulation. One is located between section
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1 and section 2 for arrival counts and another is located between section 6 and section 7 for departure counts as shown in Fig. 3 The average total delay results of each climbing lane type are shown in Table 3 and the boxplot of the results are shown in Fig. 4. The result shows that both overtaking and pocket type shows lower total delay than that of closed type. In other words, both overtaking and pocket type improves operational efficiency in terms of total delay. According to the simulation result, overtaking type performs 20~30% better than the closed type and pocket type performs 0~10 % better than the closed type. However, with high traffic flow, the operational efficiency of both types break down and show bigger total delays especially when the truck ratio is relatively high. This is due to the delay caused by many merging vehicles with low speed. To supplement the problem that the operational efficiency drops in high traffic input flow situation, using overtaking type mixed with closed type depending on the traffic input flow should be considered for better operation. Table 3. Average total delay results of each climbing lane type in traffic various traffic inflows (unit : s) Total Delay (s) Input Flow
Truck Ratio 20 %
30 %
40 %
600 veh/hr
Closed : 2552 Overtaking : 2116
Closed : 3247 Overtaking : 2535
Closed : 3607 Overtaking : 3356
Pocket
Pocket
Pocket
700 veh/hr
800 veh/hr
900 veh/hr
1000 veh/hr
: 2230
1200 veh/hr
1300 veh/hr
1400 veh/hr
: 3623
Closed : 3397 Overtaking : 2468
Closed : 3811 Overtaking : 3204
Closed : 4928 Overtaking : 3615
Pocket
: 3468
Pocket
: 3942
Pocket
: 4628
Closed
: 4107
Closed
: 5530
Closed
: 6058
Overtaking : 3263
Overtaking : 4387
Overtaking : 4423
Pocket
: 4610
Pocket
: 5273
Pocket
: 5631
Closed
: 5669
Closed
: 6724
Closed
: 7178
Overtaking : 4255
Overtaking : 5123
Overtaking : 5092
Pocket
: 5411
Pocket
: 6944
Pocket
: 7093
Closed
: 7356
Closed
: 7497
Closed
: 8454
Overtaking : 5357 1100 veh/hr
: 3015
Overtaking : 5949
Overtaking : 6277
Pocket
: 6993
Pocket
: 8427
Pocket
: 8138
Closed
: 8485
Closed
: 9118
Closed
: 10574
Overtaking : 6430
Overtaking : 7424
Overtaking : 8690
Pocket
: 8125
Pocket
: 9132
Pocket
: 10192
Closed
: 10113
Closed
: 12072
Closed
: 11936
Overtaking : 6098
Overtaking : 8586
Overtaking : 10715
Pocket
Pocket
Pocket
: 9621
: 9798
: 12421
Closed : 10933 Overtaking : 10965
Closed : 11690 Overtaking : 12523
Closed : 11656 Overtaking : 14893
Pocket
: 10862
Pocket
: 12792
Pocket
: 13124
Closed
: 13095
Closed
: 14004
Closed
: 14153
Overtaking : 14502
Overtaking : 11826
Overtaking : 13383
Pocket
Pocket
Pocket
: 15600
: 13629
: 13984
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(a)
(b)
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(c)
Fig. 4. Total delay of each climbing lane type. (a) 20% (b) 30% and (c) 40% truck ratio
4.2. Safety Performance As many widely used microscopic traffic simulators are collision-less simulators (simulators without traffic accidents), it is not able to simulate traffic accident through these microscopic traffic simulators. Therefore, safety performance of each climbing lane type cannot be directly estimated by using microscopic traffic simulator since the simulator cannot depict the accident cases. Instead of directly estimating safety performance, surrogate measures of traffic safety are usually used to assess traffic safety performance. A numerous number of so-called surrogate safety measures are developed to estimate the collision risk in vehicular conflicts. A widely used surrogate safety measures is called TTC (Time To Collision, (Hayward (1972)). In the simulation, TTC is recorded when a vehicle changed lane. Among the TTC collected, some of cases which TTC is relatively small, in other words not safe, are sampled to evaluate average safety performance of the climbing lane type. The average TTC results of each climbing lane type are shown in Table 4, and the boxplot of the results are shown in Fig. 5. As shown in the Fig. 5 and Table 4, in the closed type, the safety performance is the worst among 3 cases. The closed type showed 2~8% lower average TTC than that of the overtaking type, and showed around 5~12% lower average TTC than that of the pocket type. With the lateral separation of slow truck vehicles, the safety performance of inclined sections is increased in terms of TTC in lane-change situations. This means that the drivers in overtaking and pocket type climbing lane tends not to conduct dangerous lane-changes comparing with the drivers in closed type. However, as the traffic input flow increases, average TTCs decrease in both overtaking type and pocket type. This is because the drivers change lane to avoid bottlenecks near merging section. In conclusion, the safety performances of both climbing lane types are better than that of the closed type. Between pocket type and overtaking type, pocket type seems to have better safety performance, showing bigger average TTCs at low traffic input flow, although the gap vanishes as the traffic input flow increases.
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Table 4. Average TTC results of each climbing lane type in traffic various traffic inflows (unit : s) TTC(s) Input Flow
Truck Ratio 20 %
30 %
40 %
600 veh/hr
Closed : 2.46 Overtaking : 2.46
Closed : 2.451 Overtaking : 2.497
Closed : 2.505 Overtaking : 2.514
Pocket
: 2.419
Pocket
: 2.489
Pocket
: 2.497
Closed
: 2.367
Closed
: 2.397
Closed
: 2.347
700 veh/hr
800 veh/hr
900 veh/hr
Overtaking : 2.417
Overtaking : 2.372
Overtaking : 2.404
Pocket
: 2.368
Pocket
: 2.392
Pocket
: 2.383
Closed
: 2.032
Closed
: 2.169
Closed
: 2.006
Overtaking : 2.16
Overtaking : 2.078
Overtaking : 2.121
Pocket
: 2.281
Pocket
: 2.288
Pocket
: 2.365
Closed
: 2.198
Closed
: 2.215
Closed
: 2.141
Overtaking : 2.231
Overtaking : 2.238
Overtaking : 2.244
Pocket
Pocket
Pocket
: 2.184
: 2.214
: 2.311
1000 veh/hr
Closed : 2.097 Overtaking : 2.143 Pocket
: 2.15
Pocket
: 2.173
Pocket
: 2.181
1100 veh/hr
Closed
: 2.03
Closed
: 2.024
Closed
: 1.969
1200 veh/hr
1300 veh/hr
1400 veh/hr
Closed : 2.142 Overtaking : 2.166
Closed : 2.119 Overtaking : 2.178
Overtaking : 2.187
Overtaking : 2.109
Overtaking : 2.072
Pocket
: 2.118
Pocket
: 2.126
Pocket
: 2.12
Closed
: 1.992
Closed
: 1.922
Closed
: 1.988
Overtaking : 2.063
Overtaking : 2.112
Overtaking : 2.1
Pocket
: 1.994
Pocket
: 2.066
Pocket
: 2.059
Closed
: 2.002
Closed
: 2.042
Closed
: 2.004
Overtaking : 2.008
Overtaking : 2.065
Overtaking : 2.037
Pocket
: 2.009
Pocket
: 2.022
Pocket
: 2.078
Closed
: 1.966
Closed
: 1.957
Closed
: 1.896
Overtaking : 1.943
Overtaking : 2.035
Overtaking : 2.009
Pocket
Pocket
Pocket
(a)
: 1.98
: 1.969
(b) Fig. 5. TTC of each climbing lane type. (a) 20% (b) 30% and (c) 40% truck ratio
: 2.005
(c)
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5. Conclusion In this paper, operational efficiencies and safety performances of climbing lane types are analyzed with the use of microscopic traffic simulator based on OFFA. To do so, some adjustments are made on the OFFA to depict asymmetric behavior without short gap mode and to demonstrate performance drop of heavy truck vehicles. Total delay is used to estimate operational efficiency and time to collision (TTC) is used to estimate safety performance. From the simulation result, lateral separation of slow truck vehicles helps increase operational efficiency in terms of minimizing total delay. Both overtaking type and pocket type showed less total delay than that of closed type. Between these two types, overtaking type has better operational efficiency. However, as the traffic input flow increases, the likelihood that overtaking type can be less efficient than other types increases, especially with high truck ratio. In addition to the result of operational efficiency, lateral separation of slow truck vehicles improves safety performance of inclined section, as well. In the simulation results, closed type is concluded to be the most dangerous climbing lane type because it usually has small average TTCs of lane changing situations. Pocket type seems to be safer than overtaking type because it has bigger average TTCs, however, the difference disappears as the traffic input flow increases. As a result, the optimal type of climbing lane can be concluded as the “overtaking type.” Usually, overtaking type showed better performance in terms of operational efficiency with considerably small deficiency in safety performance. Although overtaking type showed better performances in some aspects, it also showed some performance drops such as operational efficiency drop in high traffic input flow with high truck ratio. To supplement this problem, mix-using overtaking type and closed type should be considered depending on the traffic input flow of the inclined section. For further research, calibration of parameters should be included. Due to the lack of real trajectory data in Korea, calibrated values from vehicle trajectory data of NGSIM data set are used. To make the simulation result more reliable, real trajectory data in Korea, especially in climbing lane sections should be collected and calibrated for the simulation. In addition, in this research, simple equation is assumed to model performance drop of truck vehicles in inclined section. However, using the models from Lan (2003) and Arkatkar and Arasan (2010), the simulation can be more realistic although the calibration for these models with real traffic data is needed. Also, in this research, TTC is used to estimate safety performance. However, using TTC is like looking at the just one snapshot of a certain situation because the speed is assumed to remain steady until the collision. There are several other surrogate safety measures such as Stopping Headway Distance (SHD) from Kweon (2008) and Deceleration based Surrogate Safety Measures (DSSM) from Tak et al. (2015). Using these more elaborate surrogate safety measures, the safety performance of climbing lane section can be estimated more properly. Acknowledgements This research was supported by Railroad Specialized Graduate School of the Ministry of Land, Infrastructure and Transport (MOLIT) in Republic of Korea. 6. Reference Arkatkar, S. S., and Arasan V. T., 2010. Effect of Gradient and Its Length on Performance of Vehicles under Heterogeneous Traffic Conditions. Journal of Transportation Engineering 136.12, 1120-1136 California Department of Transportation, 2012. Highway Design Manual 6th Ed, 200-219 European Commission, 2000. Thematic Study of Transport: Country Report – Germany Green, M., 2000. “How Long Does It Take to Stop?” Methodological Analysis of Driver Perception-Brake Times. Transportation Human Factors 2.3, 195-216 Hayward, J., 1972. Near-miss determination through use of a scale of danger. Highway Research Record 384, 22-34 Japan Highway Public Corporation, 1990. “Road Design Manual, Chapter 1” (日本道路公団, 1990. “設計要領 第 1 集”) Kim. B. S., Kim, S. G., Yun, I. S., Oh, Y. T., Hong, D. P., Lee, K. H., 2014. A Study on the Safety of Passing-type Climbing Lanes in Expressways using C-G Method. Journal of Korean Society of Road Engineers 16 (1), 99-109 Korean Ministry of Land, Transport and Maritime Affairs, 2012. “Road Design Manual” 210.8 (국토해양부, 2012. “도로설계편람” 210.8) Kweon, Y., 2008. Development of Crash Prediction Models Using Real Time Safety Surrogate Measures. Univ. Virginia, Charlottesville, VA, USA, Res. Rep. No. UVACTS-15-0-104
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Lan, C. J., Menendez, M., 2003. Truck Speed Profile Models for Critical Length of Grade. Journal of Transportation Engineering 129.4, 408-419 Lee, E. J., Park, K. J., Han, K. H., Beak, K. M., 2010. Effectiveness Analysis of Improved Pasing Method Considering Traffic Pattern on Climbing Lane. Journal of Korean Society of Road Engineers 12(2), 91-97 Newell, G. F., 1998. A Moving Bottleneck. Transportation Research Part B: Methodological 32.8, 531-537 Newell.G. F., 2002. A Simplified Car-Following Theory: A Lower Order Model. Transportation Research Part B: Methodological 36.3, 195-205 Tak, S., Kim, S., Yeo, H., 2015. Development of a Deceleration-Based Surrogate Safety Measure for Rear-End Collision Risk. Intelligent Transportation Systems, IEEE Transactions on Transportation System 16.5, 2435-2445 Yeo, H., Skabardonis, A., Halkia, J., Colyar, J., Alxiadis, V., 2008. Oversaturated Freeway Flow Algorithm for Use in Next Generation Simulation. Transportation Research Record: Journal of the Transportation Research Board. 2008, 68-79
ScienceDirect ScienceDirect ScienceDirect Transportation Research Procedia 00 (2016) 000–000 Transportation Research Procedia (2017) 98–109 Transportation Research Procedia 0021 (2016) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
2016 International Symposium of Transport Simulation (ISTS’16 Conference), June 23~25, 2016 2016 International Symposium of Transport Simulation (ISTS’16 Conference), June 23~25, 2016
Microscopic Analysis of Climbing Lane Performance at Freeway Microscopic Analysis of Climbing Lane Performance at Freeway Uphill Section Uphill Section a a
Seongjin Choi a, Jonghae Suh a, Hwasoo Yeo a,* Seongjin Choi a, Jonghae Suh a, Hwasoo Yeo a,* Civil and Environmental Engineering Department, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea Civil and Environmental Engineering Department, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea
Abstract Abstract Freeways which are designed for high-speed vehicular traffic seems to have some problems with the sections with inclines due to the performance in accelerations of heavy trucks and seems high occupancy vehicles (HOVs). problem, Freeways which aredrop designed for high-speed vehicular traffic to have some problems withTo thecomplement sections withthis inclines due installing auxiliary lane separate low speed vehicles from high speed vehicles. This isTo called a climbing lane. There to the performance droptoinlaterally accelerations of heavy trucks and high occupancy vehicles (HOVs). complement this problem, are mainlyauxiliary two types 1) pocket typevehicles climbing lanehigh andspeed 2) overtaking In Korea, many installing laneoftoclimbing laterallylane: separate low speed from vehicles. type This climbing is called alane. climbing lane. There sections with inclines areclimbing located near area, leading to somelane attentions the performances of climbing at various are mainly two types of lane:urban 1) pocket type climbing and 2) on overtaking type climbing lane. Inlane Korea, many traffic input conditions. To do so,urban microscopic traffictosimulator based on is used for analysis. Some adjustments sections withflow inclines are located near area, leading some attentions onOFFA the performances of climbing lane at various are made on flow the OFFA to depict behaviortraffic without short gap mode to demonstrate performance of heavy traffic input conditions. To asymmetric do so, microscopic simulator based on and OFFA is used for analysis. Somedrop adjustments truck vehicles. delay is usedasymmetric to evaluate behavior operational efficiency to collision is used to evaluate safetydrop performance. are made on theTotal OFFA to depict without shortand gaptime mode and to demonstrate performance of heavy As a result of simulation study, the to overtaking type usuallyefficiency showed better performance inisboth and safety truck vehicles. Total delay is used evaluate operational and time to collision usedoperational to evaluateefficiency safety performance. performance. However, study, at some inputtype flow with showed high truck ratio conditions,in the of overtaking type As a result of simulation the traffic overtaking usually better performance bothperformances operational efficiency and safety climbing lane However, broke down, showing lowinput operational efficiency and safety performance. climbing lane operation performance. at some traffic flow with high truck ratio conditions, theTherefore, performances of overtaking type depending on the traffic demand should considered.efficiency and safety performance. Therefore, climbing lane operation climbing lane broke down, showing lowbeoperational depending on the traffic demand should be considered. © 2016 The Authors. Published by Elsevier B. V. Copyright © 2017 The Authors. Published by Elsevier B.V. Selection andAuthors. Peer-review under responsibility of Dept of Transportation Engineering University © 2016 The Published by ElsevierofB. V. Selection and Peer-review under responsibility Dept. of Transportation Engineering, University of Seoul. of Seoul. Selection and Peer-review under responsibility of Dept of Transportation Engineering University of Seoul. Keywords: Climbing lane; Car-Following; Microscopic Traffic Simulator; Moving Bottleneck Keywords: Climbing lane; Car-Following; Microscopic Traffic Simulator; Moving Bottleneck
1. Introduction 1. Introduction A freeway can be defined as a road infrastructure designed for high-speed vehicular traffic. For this characteristic there to be some problems sectionsvehicular with inclines. A freeway of canfreeways, be defined as aseems road infrastructure designedwith for the high-speed traffic. For this characteristic of freeways, there seems to be some problems with the sections with inclines. * Corresponding author. Tel.:+82-42-350-3634; fax: +82-42-350-3610. E-mail address:author. [email protected] * Corresponding Tel.:+82-42-350-3634; fax: +82-42-350-3610.
E-mail address: [email protected] 2214-241X © 2016 The Authors. Published by Elsevier B. V. Selection and under responsibility Dept of Engineering University of Seoul. 2214-241X © Peer-review 2016 The Authors. Published by of Elsevier B.Transportation V. Selection and Peer-review under responsibility of Dept of Transportation Engineering University of Seoul.
Copyright © 2017 The Authors. Published by Elsevier B.V. Selection and Peer-review under responsibility of Dept. of Transportation Engineering, University of Seoul. 10.1016/j.trpro.2017.03.081
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Fig. 1. Types of Climbing lane (a) pocket type; (b) overtaking type
Performance drops in acceleration occurs with heavy trucks and high occupancy vehicles (HOVs) (Lan et al. (2003)). This cause a traffic problem called as “moving bottleneck.” Moving bottleneck is caused by a vehicle travelling with a speed which is less than the prevailing traffic. This low speed vehicle forces following vehicles behind lower speed to its speed, forming a vehicle queue behind. (Newell (1998)) This causes system performance drop in terms of total travel time. Also some high speed driving vehicles often attempt to overtake these low speed vehicles that causes safety problems as well. Due to these problems, installing auxiliary lane to laterally separate low speed vehicles like heavy trucks and HOVs from high speed vehicles like passenger vehicles. In many nations, the auxiliary lane, also called as climbing lane, is suggested to be installed and operated at uphill section. In United States (California Department of Transportation (2012)), it suggests installation of additional lane where speed difference of heavy vehicles and passenger cars is above 15 kilometers per hour (herein after kph). In Germany (European Commission (2000)), the starting point of auxiliary lane is located where average speed of heavy vehicles is lower than 70kph. Japan has regulation of this lane to be installed where longitudinal slope is steeper than 5%. Specifically, in case of freeways where its desired speed is larger than 100kph, climbing lanes are installed where longitudinal slope is larger than 3%. (Japan Highway Public Corporation (1990)) In Korea regulation for installation of the auxiliary lane is same as the one in Japan. (Korean Ministry of Land, Transport and Maritime Affairs (2012)) There are mainly two types of climbing lane: 1) pocket type climbing lane and 2) overtaking type climbing lane. The former one, pocket type climbing lane (see Fig. 1. (a)), is that the auxiliary lane is located at the outer-most side of the lane. This is supposed to enforce slow vehicles to use this auxiliary lane not to disturb faster vehicles. However, from the data achieved from other field researches, the compliance rate, which is the rate of heavy vehicles to use the auxiliary lane, the lateral separation ratio of slow vehicles, is relatively low. With the low compliance rate, it is not enough to relieve moving bottleneck. The fact that heavy vehicles should change lane twice, both at the diverging and merging locations, makes drivers of heavy vehicles feel reluctant to use the climbing lane. Also, some fast vehicles abuse this climbing lane for overtaking slow vehicles. This implies some safety problems, too. A different type to complement this problems of pocket type climbing lane is overtaking type climbing lane. (see Fig. 1. (b)) In overtaking type climbing lane, an additional lane is installed at the inner-most lane for high speed vehicles. At the diverging location, the entrance to the climbing lane, heavy vehicles do not need to change lane and these vehicles naturally flow into the outer-most lane. This improves the lateral separation of slow vehicles and heavy vehicles, and eventually help relieve the moving bottleneck. However, some reports have reported that the number of accidents have increased since the passing type of climbing lane has been installed, implying there might be a safety problem in overtaking type climbing lane. As seventy percent of the land in Korea is covered with mountains, it is inevitable to install roadways in sections with inclines. As a result, in Korean freeways, there are 28 pocket type climbing lanes and 53 overtaking type climbing lanes. On the contrary to the countries where mountains are usually located in rural area, in Korea these climbing lanes are usually located near cities where daily traffic using climbing lane sections might be higher than that in other countries. Therefore, there have been increasing attentions to the studies on operational efficiency and safety of climbing lane at uphill sections. Lee et al. (2010) analyzed the effectiveness of the change of type of climbing lane
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from pocket type to overtaking type in terms of traffic efficiency and economic perspectives and concluded that the overtaking type of climbing lane shows improvements on traffic efficiency and it is also economical. However, Kim et al. (2014) analyzed traffic accident data in climbing lane sections where their types were changed from pocket type to overtaking type. They used Comparison-Group Method to evaluate the safety performance change since the climbing lane type change. In their research, the expected number of traffic accidents without the change was 40.81, however, there were 71 traffic accidents in climbing lane sections. Therefore, they concluded that the overtaking type climbing lane might be more dangerous in terms of traffic accidents. However, since the individual number of traffic accidents were small, around 5 to 15 cases for each section, there still remains a doubt on their statistical results. Although many researchers have tried to analyze the performances of climbing lane, it is somewhat difficult to assess the performance of climbing lane on various traffic conditions due to the lack of real data. In the cases like this, a simulation study is necessary to evaluate the operational and safety performances of climbing lane. Some studies which analyzed climbing lane in Korea usually used microscopic traffic simulator called VISSIM for their study. However, there are some limitations because it doesn’t properly depict driver merging behavior. Recently, a study including driver’s merging behavior in over-saturated flow at freeway, Oversaturated Freeway Flow Algorithm (OFFA), (Yeo et al. (2008)) has been presented. However, this model cannot demonstrate natural deceleration caused by the slope of the uphill sections. By supplementing natural deceleration caused by uphill slope, the performance of each type of climbing lane in various traffic demand conditions can be evaluated and eventually the optimal solution for the type of climbing lane can be provided. In this research, by using microscopic traffic simulator based on OFFA model, the traffic operational efficiency and traffic safety of installation of climbing lanes for each type case and non-operating case will be examined. Total travel time delay and average speed will be used for the examination of operational efficiency, and collision risk estimated by surrogate safety measures will be used for the examination of traffic safety. The structure of the paper is as follows. In Section 2, the simulation model used to assess climbing lane will be discussed with the improvements made in this paper. In Section 3, the simulation set up is presented. In Section 4, the results of simulation are presented. The paper is finished with a conclusion and reference in section 5 and 6, respectively. 2. Simulation Model 2.1. Modifications on Oversaturated Freeway Flow Algorithm The simulation model is based on the Oversaturated Freeway Flow Algorithm (OFFA) (Yeo et al. (2008)). OFFA is an integrated model describing lateral and longitudinal behavior of drivers based on the real trajectory data of vehicles. The longitudinal behavior (i.e. car-following behavior) is formulated to determine next position of a following vehicle. According to the model, the next position of the following vehicle is related with the current speed, desired speed, vehicle performance characteristics and driver characteristics. In the free flow condition, the vehicle accelerates until the moving speed becomes the desired speed of the driver. However, in the congested condition, the vehicle keeps certain spacing with the leader vehicle based on Newell’s linear car-following model (Newell (2002)). The lane changing is divided into two types: mandatory lane changes and discretionary lane changes. The former one represents how the drivers have to change lane to reach their destination in on- and off- ramp merging. On the other hand, the latter one represents the situation that the drivers change lane to gain benefits to their driving, such as faster speed or larger spacing. In addition, there is a traffic behavior called asymmetric behavior analyzed by Yeo and Skabardonis (2009). In OFFA model a small modification called short gap mode is used to demonstrate asymmetric characteristics and to be more consistent with the real trajectory data. As the car-following model of OFFA is based on Newell’s linear car-following model, one problem may arise. The linear car-following model uses the location of leader vehicle at time t t (here, is reaction time) and jam spacing of follower vehicle ( s jam ) to calculate the next position of the follower vehicle. (see Eq. (1)) However, to use it in microscopic traffic simulation, which usually uses simulation time step (ex. NGSIM uses 0.1s time interval) which is much smaller than the reaction time (around 1s~1.5s according to Green (2000)), lots of stacks to store trajectory is needed. As a result, the simulator has to store the position data of the leader for somewhat long period of
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time ( ). These data stacks require lots of use of memory in computation of simulation algorithm with protracted t computation time. For developing a microscopic traffic simulation for on-line simulation this heavy computation can be an obstacle. Therefore, directly applying original Newell’s linear car-following model is not appropriate to use in microscopic traffic simulator. (1) xfollower (t t) xleader (t t ) s jam Another problem is related with the short gap mode mentioned above. Short gap mode is used in the original OFFA to model asymmetric behavior. According to Yeo and Skabardonis (2009), this short gap mode is applied to the vehicles in deceleration phase, especially to the vehicles involved in the lane changing (Yeo et al. (2008)). Such vehicles include the lane changing vehicles, the lane-change receiving vehicles, and the lane-change cooperating vehicles. The short gap mode is modeled by multiplying a coefficient to the jam gap and wave travel time as shown in the Eq. (2). jam LC jam , LC (2) gn gn n n However, this adjustment of parameter cannot fully depict the phenomenon because the short gap mode parameter chosen is an arbitrary, artificial parameter and this makes discontinuity of parameters in simulations. Therefore, an integrated model that can be applicable at any state should be formulated without changes in parameters. To complement these problems, in this research, the relationship between the position of leader vehicle and the position (to be calculated) of follower vehicle is modified. With the assumption expressed in Eq. (3), the modified relationship is expressed as Eq. (4) (3) xleader (t t ) xleader (t t) vleader (t t) (4) xfollower (t t) xleader (t t) vleader (t t) s jam In free flow condition, where the speeds of vehicles, including the leader and the follower vehicles, don’t change a lot, the modified car-following model is same with the original Newell’s linear car-following model. In other words, the modified car-following model (Eq. (4)) is same with the original Newell’s linear car-following model (Eq. (5)) with following condition: (5) vleader (t) vleader (t t) for t (t,t ) However, in congested traffic, where acceleration and deceleration occur, the shockwave is generated and propagated to upstream, this modified model makes difference in position at next time step. Fig. 2 shows the comparison between trajectory based on the original Newell’s linear car-following model and the modified base carfollowing model. In the deceleration case, as shown in the Fig. 2. (a), the following vehicle shortens the gap with reaction time . This shows the behavior of deceleration phase in asymmetric theory without applying short gap mode. Furthermore, as shown in the Fig. 2. (b), when the leader vehicle is accelerating, the follower vehicle extends the gap with the reaction time , which coincides with the acceleration phase behavior in asymmetric theory (Yeo et al.
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Fig. 2. Comparison between trajectory based on original Newell’s linear car-following model and the modified base car-following model. (a) Deceleration case and (b) Acceleration case
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(2008)). By modifying base car-following model, the data stacks are not necessary because the time input of the model is synchronized to t t as expressed in Eq.(4). Also, without adjusting driver characteristic parameters (i.e. reaction time and jam spacing), that is to say without using short gap mode, asymmetric driving behavior can be illustrated based on the modification. 2.2. Uphill Section Effect Modelling To demonstrate vehicle-performance drop of heavy trucks and HOVs (herein after truck class vehicles) in the simulation, the incline effects on the acceleration should be modeled. For the simplicity of the model, the acceleration is recalculated with the effect of the uphill section as shown in the Eq. (6). Acc Acc sin g( 9.8m / s2 ) Acc _ freeflow sin g( 9.8m / s2 )
(6)
Dec Dec sin g( 9.8m / s ) 2
As well as the acceleration drop due to the incline of the roadway, the free flow speed of truck class vehicles is limited to demonstrate the low speed. The formulation is expressed in the Eq. (7)with the free flow drop ratio ( ) of truck class vehicles. value is with the speed regulation of freeway in Korea. Usually, if the speed limit of normal class vehicles is 110 kph, that of truck class vehicles is 90 kph and if the speed limit of normal class vehicles is 100 kph, that of truck class vehicles is 80 kph. Therefore, is usually around 0.8~0.85. v ff trucks (1 )vff passenger (7)
3. Simulation 3.1. Climbing Lane Section for Simulation In Korea, there are 87 uphill sections where the climbing lane is installed. Each section has different geometric characteristics with different length, slope, and curvature of the section. However, it is not possible to evaluate these different geometric characteristics and it is not necessary. As the purposes of the study are to evaluate traffic operational efficiency and traffic safety performance of each type of climbing lane, these performances should be analyzed in same road conditions. Therefore, for the simulation, same road characteristics are used. The length of the climbing lane for simulation is 2 km and the slope of the climbing lane is 4% with two main lanes as shown in the Table 1. Specific configuration of the climbing lane section model is depicted in Fig. 3 Table 1. Road characteristics Road Characteristic Length (km)
2
Slope (%)
4
Number of main lanes
2
Fig. 3. Climbing Lane Section Model forSimulation
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3.2. Simulation Parameters The simulation parameters include driver characteristics and vehicle performances as well as the climbing lane compliance rate. The driver characteristic parameters used for the simulation are reaction time and jam gap. The vehicle performance parameter includes vehicle acceleration and deceleration rate, and free flow speed of the vehicles depending on the type (normal or truck class vehicles). A field video test has been conducted to achieve these parameters from real data, however, it is not possible to achieve data like reaction time, jam gap, and acceleration and deceleration rate. The data achieved is free flow speed and the climbing lane compliance rate. For other parameters that is not able to be achieved from the field video analysis, the calibrated values from vehicle trajectory data of NGSIM data set are used to randomly generate (Yeo et al. (2008)). The parameters and its distribution parameters are specified in Table 2. Table 2. Simulation input parameters Parameters
Normal Vehicle
Truck class vehicle
Free Flow Speed (kph)
110
90
Reaction Time (s)
μ = 0.58 σ = 0.39 lognormal
μ = 0.58 σ = 0.39 lognormal
Jam gap (m)
μ = 3.75 σ = 0.98 normal
μ = 4.21 σ = 3.80 normal
Vehicle Length (m)
μ=5 σ = 0.5 normal
μ = 10 σ=1 normal
Max Acceleration (m/s^2)
μ = 4.48 σ = 0.98 normal
μ = 4.68 σ = 0.93 normal
Max Deceleration (m/s^2)
μ = 4.36 σ = 0.82 normal
μ = 4.52 σ = 0.88 normal
Climbing Lane Compliance Rate
Overtaking Type: 60%, Pocket Type: 20%
3.3. Simulation Scenarios In the field video test mentioned in Section 3.2, it was hard to make quantitative evaluation, because the traffic inflows were not diverse and only free flow states are observed. However, to evaluate the traffic operational efficiency and traffic safety performance of each climbing lane types, various traffic inflows should be used. Therefore, in the simulation, various traffic demands as well as various truck ratios will be used to compare traffic operational efficiency and traffic safety performance of pocket type, overtaking type, and non-operating case (herein after, closed type). Each traffic demand with various input flows and truck ratios is simulated 10 times. 4. Simulation Result 4.1. Operational Efficiency In this paper, to assess the operational efficiency of each climbing lane, total delay, which is a widely used index for operational efficiency, is used. The total delay can be estimated with the N-curve, also known as the cumulative vehicle count curve. The total delay can be calculated by computing the area between the virtual arrival curve and departure curve. It is assumed that there exist two virtual detectors in the simulation. One is located between section
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1 and section 2 for arrival counts and another is located between section 6 and section 7 for departure counts as shown in Fig. 3 The average total delay results of each climbing lane type are shown in Table 3 and the boxplot of the results are shown in Fig. 4. The result shows that both overtaking and pocket type shows lower total delay than that of closed type. In other words, both overtaking and pocket type improves operational efficiency in terms of total delay. According to the simulation result, overtaking type performs 20~30% better than the closed type and pocket type performs 0~10 % better than the closed type. However, with high traffic flow, the operational efficiency of both types break down and show bigger total delays especially when the truck ratio is relatively high. This is due to the delay caused by many merging vehicles with low speed. To supplement the problem that the operational efficiency drops in high traffic input flow situation, using overtaking type mixed with closed type depending on the traffic input flow should be considered for better operation. Table 3. Average total delay results of each climbing lane type in traffic various traffic inflows (unit : s) Total Delay (s) Input Flow
Truck Ratio 20 %
30 %
40 %
600 veh/hr
Closed : 2552 Overtaking : 2116
Closed : 3247 Overtaking : 2535
Closed : 3607 Overtaking : 3356
700 veh/hr
800 veh/hr
900 veh/hr
1000 veh/hr
: 2230
1200 veh/hr
1300 veh/hr
1400 veh/hr
: 3623
Closed : 3397 Overtaking : 2468
Closed : 3811 Overtaking : 3204
Closed : 4928 Overtaking : 3615
: 3468
: 3942
: 4628
Closed
: 4107
Closed
: 5530
Closed
: 6058
Overtaking : 3263
Overtaking : 4387
Overtaking : 4423
: 4610
: 5273
: 5631
Closed
: 5669
Closed
: 6724
Closed
: 7178
Overtaking : 4255
Overtaking : 5123
Overtaking : 5092
: 5411
: 6944
: 7093
Closed
: 7356
Closed
: 7497
Closed
: 8454
Overtaking : 5357 1100 veh/hr
: 3015
Overtaking : 5949
Overtaking : 6277
: 6993
: 8427
: 8138
Closed
: 8485
Closed
: 9118
Closed
: 10574
Overtaking : 6430
Overtaking : 7424
Overtaking : 8690
: 8125
: 9132
: 10192
Closed
: 10113
Closed
: 12072
Closed
: 11936
Overtaking : 6098
Overtaking : 8586
Overtaking : 10715
: 9621
: 9798
: 12421
Closed : 10933 Overtaking : 10965
Closed : 11690 Overtaking : 12523
Closed : 11656 Overtaking : 14893
: 10862
: 12792
: 13124
Closed
: 13095
Closed
: 14004
Closed
: 14153
Overtaking : 14502
Overtaking : 11826
Overtaking : 13383
: 15600
: 13629
: 13984
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(a)
(b)
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(c)
Fig. 4. Total delay of each climbing lane type. (a) 20% (b) 30% and (c) 40% truck ratio
4.2. Safety Performance As many widely used microscopic traffic simulators are collision-less simulators (simulators without traffic accidents), it is not able to simulate traffic accident through these microscopic traffic simulators. Therefore, safety performance of each climbing lane type cannot be directly estimated by using microscopic traffic simulator since the simulator cannot depict the accident cases. Instead of directly estimating safety performance, surrogate measures of traffic safety are usually used to assess traffic safety performance. A numerous number of so-called surrogate safety measures are developed to estimate the collision risk in vehicular conflicts. A widely used surrogate safety measures is called TTC (Time To Collision, (Hayward (1972)). In the simulation, TTC is recorded when a vehicle changed lane. Among the TTC collected, some of cases which TTC is relatively small, in other words not safe, are sampled to evaluate average safety performance of the climbing lane type. The average TTC results of each climbing lane type are shown in Table 4, and the boxplot of the results are shown in Fig. 5. As shown in the Fig. 5 and Table 4, in the closed type, the safety performance is the worst among 3 cases. The closed type showed 2~8% lower average TTC than that of the overtaking type, and showed around 5~12% lower average TTC than that of the pocket type. With the lateral separation of slow truck vehicles, the safety performance of inclined sections is increased in terms of TTC in lane-change situations. This means that the drivers in overtaking and pocket type climbing lane tends not to conduct dangerous lane-changes comparing with the drivers in closed type. However, as the traffic input flow increases, average TTCs decrease in both overtaking type and pocket type. This is because the drivers change lane to avoid bottlenecks near merging section. In conclusion, the safety performances of both climbing lane types are better than that of the closed type. Between pocket type and overtaking type, pocket type seems to have better safety performance, showing bigger average TTCs at low traffic input flow, although the gap vanishes as the traffic input flow increases.
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Table 4. Average TTC results of each climbing lane type in traffic various traffic inflows (unit : s) TTC(s) Input Flow
Truck Ratio 20 %
30 %
40 %
600 veh/hr
Closed : 2.46 Overtaking : 2.46
Closed : 2.451 Overtaking : 2.497
Closed : 2.505 Overtaking : 2.514
: 2.419
: 2.489
: 2.497
Closed
: 2.367
Closed
: 2.397
Closed
: 2.347
700 veh/hr
800 veh/hr
900 veh/hr
Overtaking : 2.417
Overtaking : 2.372
Overtaking : 2.404
: 2.368
: 2.392
: 2.383
Closed
: 2.032
Closed
: 2.169
Closed
: 2.006
Overtaking : 2.16
Overtaking : 2.078
Overtaking : 2.121
: 2.281
: 2.288
: 2.365
Closed
: 2.198
Closed
: 2.215
Closed
: 2.141
Overtaking : 2.231
Overtaking : 2.238
Overtaking : 2.244
: 2.184
: 2.214
: 2.311
1000 veh/hr
Closed : 2.097 Overtaking : 2.143 Pocket
: 2.15
: 2.173
: 2.181
1100 veh/hr
Closed
: 2.03
Closed
: 2.024
Closed
: 1.969
1200 veh/hr
1300 veh/hr
1400 veh/hr
Closed : 2.142 Overtaking : 2.166
Closed : 2.119 Overtaking : 2.178
Overtaking : 2.187
Overtaking : 2.109
Overtaking : 2.072
: 2.118
: 2.126
: 2.12
Closed
: 1.992
Closed
: 1.922
Closed
: 1.988
Overtaking : 2.063
Overtaking : 2.112
Overtaking : 2.1
: 1.994
: 2.066
: 2.059
Closed
: 2.002
Closed
: 2.042
Closed
: 2.004
Overtaking : 2.008
Overtaking : 2.065
Overtaking : 2.037
: 2.009
: 2.022
: 2.078
Closed
: 1.966
Closed
: 1.957
Closed
: 1.896
Overtaking : 1.943
Overtaking : 2.035
Overtaking : 2.009
(a)
: 1.98
: 1.969
(b) Fig. 5. TTC of each climbing lane type. (a) 20% (b) 30% and (c) 40% truck ratio
: 2.005
(c)
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5. Conclusion In this paper, operational efficiencies and safety performances of climbing lane types are analyzed with the use of microscopic traffic simulator based on OFFA. To do so, some adjustments are made on the OFFA to depict asymmetric behavior without short gap mode and to demonstrate performance drop of heavy truck vehicles. Total delay is used to estimate operational efficiency and time to collision (TTC) is used to estimate safety performance. From the simulation result, lateral separation of slow truck vehicles helps increase operational efficiency in terms of minimizing total delay. Both overtaking type and pocket type showed less total delay than that of closed type. Between these two types, overtaking type has better operational efficiency. However, as the traffic input flow increases, the likelihood that overtaking type can be less efficient than other types increases, especially with high truck ratio. In addition to the result of operational efficiency, lateral separation of slow truck vehicles improves safety performance of inclined section, as well. In the simulation results, closed type is concluded to be the most dangerous climbing lane type because it usually has small average TTCs of lane changing situations. Pocket type seems to be safer than overtaking type because it has bigger average TTCs, however, the difference disappears as the traffic input flow increases. As a result, the optimal type of climbing lane can be concluded as the “overtaking type.” Usually, overtaking type showed better performance in terms of operational efficiency with considerably small deficiency in safety performance. Although overtaking type showed better performances in some aspects, it also showed some performance drops such as operational efficiency drop in high traffic input flow with high truck ratio. To supplement this problem, mix-using overtaking type and closed type should be considered depending on the traffic input flow of the inclined section. For further research, calibration of parameters should be included. Due to the lack of real trajectory data in Korea, calibrated values from vehicle trajectory data of NGSIM data set are used. To make the simulation result more reliable, real trajectory data in Korea, especially in climbing lane sections should be collected and calibrated for the simulation. In addition, in this research, simple equation is assumed to model performance drop of truck vehicles in inclined section. However, using the models from Lan (2003) and Arkatkar and Arasan (2010), the simulation can be more realistic although the calibration for these models with real traffic data is needed. Also, in this research, TTC is used to estimate safety performance. However, using TTC is like looking at the just one snapshot of a certain situation because the speed is assumed to remain steady until the collision. There are several other surrogate safety measures such as Stopping Headway Distance (SHD) from Kweon (2008) and Deceleration based Surrogate Safety Measures (DSSM) from Tak et al. (2015). Using these more elaborate surrogate safety measures, the safety performance of climbing lane section can be estimated more properly. Acknowledgements This research was supported by Railroad Specialized Graduate School of the Ministry of Land, Infrastructure and Transport (MOLIT) in Republic of Korea. 6. Reference Arkatkar, S. S., and Arasan V. T., 2010. Effect of Gradient and Its Length on Performance of Vehicles under Heterogeneous Traffic Conditions. Journal of Transportation Engineering 136.12, 1120-1136 California Department of Transportation, 2012. Highway Design Manual 6th Ed, 200-219 European Commission, 2000. Thematic Study of Transport: Country Report – Germany Green, M., 2000. “How Long Does It Take to Stop?” Methodological Analysis of Driver Perception-Brake Times. Transportation Human Factors 2.3, 195-216 Hayward, J., 1972. Near-miss determination through use of a scale of danger. Highway Research Record 384, 22-34 Japan Highway Public Corporation, 1990. “Road Design Manual, Chapter 1” (日本道路公団, 1990. “設計要領 第 1 集”) Kim. B. S., Kim, S. G., Yun, I. S., Oh, Y. T., Hong, D. P., Lee, K. H., 2014. A Study on the Safety of Passing-type Climbing Lanes in Expressways using C-G Method. Journal of Korean Society of Road Engineers 16 (1), 99-109 Korean Ministry of Land, Transport and Maritime Affairs, 2012. “Road Design Manual” 210.8 (국토해양부, 2012. “도로설계편람” 210.8) Kweon, Y., 2008. Development of Crash Prediction Models Using Real Time Safety Surrogate Measures. Univ. Virginia, Charlottesville, VA, USA, Res. Rep. No. UVACTS-15-0-104
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