A Two-Lane Cellular Automaton Model to Evaluate the Bus Lane with Intermittent Priority

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Introduction
e rate of motorization has outpaced the development of the carrying capacity of urban roads. Traffic congestion causes delays for buses operating in mixed traffic lanes and reduces the attractiveness of buses. Although dedicated bus lanes provide right-of-way to vehicles, they also cause a reduction in private vehicle capacity.
Viegas and Lu [1] firstly introduced a bus priority method named the intermittent bus lane (IBL). IBL utilizes real-time information on bus locations and variable message signs (VMSs) on the road to switch the bus lane status between closed and open based on predicted bus arrival times. e system receives the alert from an oncoming bus and issues a command to switch the lane from a regular lane to a temporary bus lane, while the indicator transmits the lane information to the regular vehicle. When the IBL indicator signals a temporary change in lane status, vehicles in the lane and the arriving bus have the right-of-way, and other vehicles are prohibited from entering. In the process, bus travel time would be reduced, resulting in increased delays in traffic.
To reduce the negative effects of the IBL, Eichler [2] developed a new strategy which is a bus lane with intermittent priority (BLIP). BLIP is reserved for buses, and private vehicles are admitted to enter the lane, although, requires that general vehicles leave the lane when buses are in demand. Flexibility in time and distance is a characteristic of BLIP, and infrastructure requirements include overhead signs, pavement lights, and bus detection. e original BLIP concept was based on road segments and used variable message signs (VMSs) to provide information on vehicle rights-of-way. e road network geometry and intersection locations determine the length of each road segment [3][4][5][6]. If a bus is detected to be moving in the lane, the road segment of BLIP will continue to change to a bus lane one by one. Once the bus passed, the segment will be available to general purpose traffic until the system issues a command again. It provides a compromise between dedicated bus lanes and buses operating in mixed traffic lanes. It provides a trade-off between bus priority and the delay suffered by general traffic.
is study investigates the implementation of BLIPs using connected vehicles. Vehicle-to-Vehicle (V2V) communications provide the necessary means for signaling the presence of an approaching bus to general traffic. Using a numerical simulation, the positive effects of operating BLIP under a connected vehicle environment can be quantified.

Literature Review
e implementation of BLIP has been studied in recent research. Eichler and Daganzo [2,7] study the feasibility, impacts, and benefits of BLIPs using kinematic wave theory. Although BLIP increases the average traffic density and traffic delay, it would not significantly reduce total road capacity. If the traffic volume does not exceed the road capacity of nonBLIP lanes, these delays are more than offset the advantages to public transport travelers. Xie and Leclercq [8] focus on the activation phase of the BLIP strategy also using the kinematic wave model. is research shows that BLIP's activation reduces the capacity and increases the travel time of buses. A simulation by the U.S. Dept. Of Transportation sets two segments in front of the bus as dedicated and off-limits to general purpose traffic. Simulation results indicate that BLIP reduces bus travel time by 14% and improves reliability by 28% [9].
For segment-based BLIP, private cars are restricted from using the lane in the whole segment. Since each roadway segment may not be equal in length, this may cause unequal benefits of BLIP depending on the segment. On one hand, there is a significant loss of road capacity for a long segment; on the other hand, the segment of insufficient length may weaken the effect of clearing general traffic out of the BLIP lane. ere would be better performance if general traffic that is following the bus could occupy the BLIP. In light of this, Wu et al. [10] proposed that a connected vehicles environment with frequent information interaction is conducive to BLIP. In connected vehicle environments, all vehicles are assumed to have V2V communication technologies to support car following and lane changing decisions. Vehicles that are both in front of and behind the target bus can better use the BLIP lane. Furthermore, a unified clear distance (dynamic moving segment) for general traffic could be set with minimum road capacity loss.
In a connected vehicle environment, existing studies have explored the implementation of forced lane change rules underlying the CV-based BLIP strategy. A microsimulation analysis shows CV-based BLIP could result in up to 32% benefit compared with a dedicated bus lane [3,10] in arterial. Recommended clear distance is between 300 and 500 meters. In addition, BLIP implementation is not recommended under a certain saturation degree. ree-lane cellular automaton (CA) models are proposed to evaluate the positive effects of BLIP operation [3,11]. Research results reveal strong connections among bus departure intervals, clear distance, and road capacity. Lane change behaviors, lane usage, and road capacity loss are investigated by these CA models. e recommended traffic density is between 30 and 90 pcu/km, the recommended clear distance is between 30 and 90 meters and the lower threshold of bus departure interval is 90 seconds.
Although the benefits and impacts of BLIP are investigated in recent research [2,3,[9][10][11][12][13][14] e preliminary conclusion of the case is that IBL will bring a 20% improvement in average bus speed, giving no signal priority at downstream intersections. Especially, during peak traffic congestion, the improvement effect is 50% [15]. erefore, the benefits of BLIP under two lanes should not be ignored. Furthermore, there is no research paper has studied the advantage of bus fuel saving and bus punctuality rate of BLIPs. In order to fill this gap, this paper develops a two-lane CA model to explore the benefits and impacts of BLIPs.

Model
CA models have been widely exploited to simulate various traffic flow scenarios and also have been equal to kinematic waves in traffic flow [7]. e CA model is a powerful tool for characterizing macroscopic and microscopic traffic flows. e CA model was originally adopted to simulate traffic in a single lane by Kai and Schreckenberg [16], and extended to a two-lane model with a stochastic lane change rule by Rickert et al. [17] and Chowdhury et al. [18]. Daoudia and Moussa (2003) developed an asymmetric lane change rule for the CA model. Nai et al. [19], Qian and Wang [20]; and Luo et al. [21] explored mixed private and public traffic flows using CA models. Research studies have also investigated bus priority strategies by constructing CA models [3,11,22,23]. ese studies indicate that the CA model can efficiently characterize some traffic flow phenomena occurring in multilane and mixed traffic flow scenarios for their fast performance. Based on the advantages of CA models, this paper proposes a twolane CA model underlying the asymmetric lane changing rule to investigate the impact of BLIP on urban traffic flow in connected environments.

Model Definition.
is model is under open boundary conditions, so a private car or bus can only be generated with a certain probability at the left head of the cells chain and can only be removed from the right end of the cells chain with another certain probability [24]. Hence, it is more similar to real urban traffic compared to the periodical boundary CA model and more convenient to set bus departure intervals. Bus stations are generally located near intersections, and buses can use the red-light time to stop. BLIP can be regarded as a significant component in traffic flow in urban areas. erefore, studies suggest that bus stations and intersections should be considered in the model [21,23]. e simulation is conducted on two one-dimensional cells chain with L cells, and one cell represents only one private cars or bus at a time ( Figure 1). e two cells chains represent two parallel one-way lanes of the hypothetical BLIP system, respectively. In previous CA models, the cell size is 7,5 meters. Evidence suggests that reducing the cell size can more accurately represent the physical features of vehicle movements [25,26]. In this paper, cells represent a series of 1.5 meters road divisions. e model simulates general purposed traffic and public traffic. For regular cars, the maximum speed is v c max � 15 cell/s (≈81 km/h) and is represented by five cells, which are v b max � 10 cell/s (≈54 km/ h) and ten cells for buses. e clear distance ahead of buses can be defined as 150 m, 300 m, 450 m, and 600 m. One timestep corresponds to one second in the real world. e significant variables and parameters are summarized in Table 1. Figure 2 describes vehicles' generate and eliminate rules in one time step. If it is empty at the first few cells of each lane and p ≤ p in , a new vehicle would be generated at the left boundary of the lane and runs forward at maximum speed. If p > p in or the leftmost cells are occupied by another vehicle, the vehicle would not be created. When the vehicle appears at the right end of the cells chain, the elimination mechanism will be triggered: if p ≤ p out , the vehicle should be removed; otherwise, the vehicle remains its location and it can not pass the right boundary. e parameters p in and p out are used to set traffic flow from the upstream intersection and congestion saturation at the downstream intersection especially, a generate and eliminate procedure in a time interval is as follows: the two ends of the BLIP are the upstream intersection A. And, the downstream intersection B, respectively, when bus i departs from upstream bus intersection A, the bus will be generated at the left of BLIP lane; when the bus i arrives at bus intersection B, it is removed from the system (if p ≤ p out ). Buses are only allowed to utilize the BLIP (right) lane, and lane changes of buses are prohibited.

Vehicle Movement Rules.
In the CA model, gap     In the premise of safety, the principle of the private car immediately drive away is described in the following:

Numerical Simulations
In this section, simulations of urban roads are performed based on the proposed CA model. e main road includes 1600 cells (2400 meters). We generate one vehicle at the left head of each cell chains as input to the CA model with probability p in (0 ≤ p in ≤ 1), and initialize the input variables as follows: t depart � 60 s, l c d � 300 m, p rand � 0.25, p in � 1, p out � 0.7 [3,11]. We performed two groups of numerical simulations for a normal urban double-lane road without the implementation of bus priority and BLIP (Group A), and an urban double-lane road with BLIP (Group B).  Journal of Advanced Transportation To analyze the functions of BLIP, six aspects are explored: time-space distributions, average travel time, average speed, fuel consumption, bus punctuality, and passenger capacity. Figure 3 Figure 3(b) illustrates that in Group A, the rear vehicle will choose to follow the bus or change lanes and overtake the bus. is may lead to congestion in downstream which reduces the bus speed. is problem is significantly solved by introducing the BLIP strategy. Private cars in the clear segment in front of the bus are dispersed away from the BILIP lane (Figure 3(d)). is leads to a vacuum in front of the bus and a significantly lower traffic density of the BILP. erefore, in Group B, the headway of the two buses is more consistent with their departure intervals after introducing the BLIP strategy. is results in more consistent high speeds, better fuel efficiency, and shorter delays for buses.

Time-Space Distributions.
However, the mandatory lane change leads to more complex merging behaviors in the right lane. It may also induce greater traffic density and more disturbance in the left lane (Figure 3(c)). e simulation results (Figure 4) additionally show that in Group B, the vehicle density in the left lane expands by at least 15%, with the most extreme increase being 25%, due to the forced lane change criterion. Comparatively, the vehicle density in the right lane diminishes by at least 16%, with the most extreme decrease being half.

Average Travel Time.
e BLIP strategy is developed to mainly ensure the stability of the bus ( Figure 5). Lane changing of general traffic flow disturb bus traffic, increasing the number of brakes and travel time. Here, the stability is measured by the average travel time given different traffic densities. As presented in Figure 5, when the density ρ < 0.3, the traffic flow can be considered as a free flow which is the same between the travel time of Group A and Group B. Given 0.3 ≤ ρ ≤ 1, in the Group B scenario, the bus performs better in terms of average travel time even during the peak period. BLIP strategy decreases bus travel time by providing buses with a dedicated bus lane temporarily. e average bus travel time is reduced by more than 25% given 0.5 ≤ ρ ≤ 0.8.
As presented in Figure 6, performs better than that of Group A due to reduced traffic density. Overall, private cars in Group B have an average 13% lower travel time on lane 2.

Average Speed Distributions.
is section discusses the impact of the average speed by the BLIP strategy, with the same input variables as in Section 4.1. Figure 7 shows that there is no significant difference in the range of average speed between lanes if BLIP is not implemented. Buses in groups A and B use only lane 2. Before introducing the BLIP strategy, normal vehicles will make lane changes to obtain higher speeds, which is the reason why the average speeds of the two lanes are similar. In Group B, the average speed of the BLIP lane increased by 50% compared to Group A. When a bus passes, the average speeds on the BLIP lane and the regular lane reach their peaks and troughs simultaneously, respectively. In addition, numerical simulations  indicate that the BLIP strategy enables buses to show outstanding speed performance even at high traffic flow density. BLIP gives higher priority to buses, therefore the average speed of buses on lane 2 is higher. At the same time, the BLIP strategy provides a clear segment for the bus in front, which results in a lower Lane2 flow density and achieves a higher average speed. Figure 7(b) shows that the average bus speed fluctuation is more severe in Group A than in Group B. e histogram shown in Figure 8 further demonstrates this phenomenon. e skewed and centralized distribution of average speed and high average speed provide passengers with a smooth experience, increases the fuel efficiency of the bus high, and improves the quality of bus service.

Fuel Consumption.
e strong correlation between fuel consumption and average speed has been demonstrated by the Clean Urban Transport in Europe (CUTE) project [27]. e discussion of the fuel consumption of buses in this section is based on setting the maximum speed as 7.72 cell/s and the minimum speed as 1.05 cell/s. Since BLIP can increase the average bus speed, which will certainly affect the bus fuel consumption. Here, we define y (average fuel consumption, liter diesel equivalents per 100 km) as a function of x (average bus speed, km per hour). Figure 9 shows the correlation between bus fuel consumption and average bus speed [27,28]. e maximum and minimum values of speed are fixed and therefore the maximum and minimum values of fuel consumption are fixed. e lower Journal of Advanced Transportation the average bus speed, the greater the fuel consumption [27][28][29][30][31][32][33][34]. We use the results of Li [35] on the relationship between fuel consumption and speed: y � 326.7x −0.765 − 8.876, In this study, function (1) is used in the CA model to evaluate fuel consumption in both cases. Figures 10 and 11 and Table 2 investigate the average bus instantaneous fuel consumption in Group A and Group B. As shown in Figure 10(a), due to frequent acceleration and deceleration of buses, bus instantaneous fuel consumption changes dramatically. e maximum average bus fuel consumption is more than 77 liters/100 km. According to the cumulative curve in Figure 11(a), about 80% of the average bus fuel consumption exceeds 10 L/100 km, and close to 40% of the average bus fuel consumption is more than 20 L/100 km. e mean of average bus fuel consumption for Group A is 24.3034 L/100 km. Numerical simulations support that BLIP creates an excellent energy saving effect. e relatively stable high speed well ensures the bus has a smooth ride and high fuel efficiency (Figure 10(b)). ere are more than 60% of the average bus fuel consumption maintains at 10 L/ 100 km (Figure 11(b)). Besides, there are more than 20% of the average bus fuel consumption is only slightly larger than 10 L/100 km. e mean of the average bus fuel consumption is 11.8046 L/100 km and is less than half of which in Group A.

Bus Punctuality.
Buses are operated on the basis of the scheduled timetable. Punctuality is the key criterion for timetable-based bus services, where passengers arrive at bus stops according to the scheduled time of bus departure. e improvement of punctuality can reduce bus delays and reduce average passenger waiting time. Figure 12 presents the travel time of each bus in Group A and Group B. It shows that the data of travel time in Group A are more discrete than which is in Group B. e fixed bus headway is disrupted by downstream traffic flow. And, this leads to the unequal travel time of each bus. It takes some buses more than 150 s to pass the road section. Meanwhile, it only takes some other buses slightly more than 80 s to pass the same road section. Table 3 further supports this view. e mean and median of bus  travel time in Group B is a bit less than which is in Group A. But the variance and mean square error of bus travel time in Group A are much greater than are in Group B. To explore the bus punctuality in both cases, the difference between bus arrival time and timetable is shown in Figure 13. Approximately 34.5% of the difference is less than 10 seconds and 75.9% of the difference is less than 29 seconds in Group A. In contrast, there are 67.85% of the difference is less than 12 seconds and 93.2% of the difference is less than 23 seconds in Group B. It is clear that the BLIP could reduce the difference between bus arrival time and timetable and improve the reliability of bus operation.

Passenger Capacity.
Buses Simulation above reveals that the BLIP has several benefits in travel time saving and fuel consumption saving. However, the challenge to this result arises from the fact that some studies have concluded that BLIP has a negative contribution to road capacity. Most of the existing studies believe that the BLIP reduces the road capacity for private cars while improving the stability and efficiency of bus operation [3,8,9,11]. Hence, passenger capacity as another evaluation metric is used in this study. Passenger capacity means the number of passengers passing through a road section. To measure this indicator, average car occupancy is set to 1.3 passengers [36,37], and average   bus occupancy is set to 28 passengers [38,39]. Initializing inputs for the variables as follows: t depart � 120 s, l cd � 300 m, p rand � 0.25, p in � 1, p out � 0.7. Figure 14   reduced. But buses run on duty, and the total passenger capacity does not decrease significantly. In the long-term operation, the total passenger has risen slightly. It illustrates that the BLIP contributes to the improvement of passenger capacity in the long run.

Conclusion
is study concentrates on developing an evaluation framework for a double-lane V2V based BLIP system. e main contribution of this article is to evaluate the performance of BLIP under two-lane arterials and connected vehicle environments. A special asymmetric lane change rule for general traffic is set in the CA model to offer a temporary dedicated bus lane. e numerical simulation results show that both average bus speed and bus punctuality are significantly improved by BLIP. Average bus travel time saving is more than 25% at a certain traffic density range and fuel consumption saving is more than 50%. Although BLIP might slightly reduce the road capacity, it shows almost no negative impact on passenger capacity. e proposed two-lane CA model can accurately and efficiently simulate the implementation of the BLIP strategy and the macroscopic and microscopic characteristics of traffic flow. is model can be further used to evaluate the effectiveness of more complex traffic control strategies. In an automated networked vehicle environment, the model represents specific traffic control strategies in terms of cellular update rules. Since the simulation of more complex control measures can be achieved by adjusting the update rules, the model can be used for more forward-looking studies related to traffic flow control.
Since self-driving and Cooperative Adaptive Cruise Control (CACC) vehicles are fast approaching the practical, the benefits of the BLIP strategy would be more remarkable. And, CACC based BLIP implementation would be easier. More extensive simulation numerical experiments will be conducted to assess the effectiveness of the proposed strategy considering CACC vehicles.

Data Availability
e electronic data used to support the findings of this study are currently under embargo while the research findings are commercialized. Requests for data, 12 months after publication of this article, will be considered by the corresponding author.