MTCS: A Method of Analyzing the Trac Capacity of Urban Bus Lane Based on Vissim Simulation

As an effective method of improving the attractiveness of urban public transport and alleviating urban trac congestion, bus lanes play an important role in the urban public transport system. The research on the capacity of bus lanes is conducive to improve the operation eciency of urban bus roads and improve the service level of urban public transport. To obtain the maximum capacity of the bus lane, on one hand, the empirical formula can be used for theoretical calculation, and on the other hand, the simulation model can be established for analysis and verication. Based on the idea of simulation, a method using Vissim is proposed, called MTCS (Minimum Trac Capacity Substitution Method). The method divides the bus lane into different sections by intersections and stops, establishes simulation model of the bus lane to calculate the trac capacity of each section such as vehicle speed and ow and select the minimum trac capacity of the sections as the trac capacity of the bus lane, which is veried by using the road saturation. The simulation process uses the actual travel speed and trac ow of the bus lane as evaluation indicators, with the aim of maximizing the road trac ow while the actual speed of vehicles on the road is close to the desired speed, thus achieving the desired road trac state. To verify and improve the effectiveness of the method, its analysis results are compared with the empirical formula, and various methods of enhancing trac capacity are quantitatively simulated. The parameters of the simulation model are set by the actual bus lane example, and the experimental results show that by the methods of modifying the stop-station mode and the signal-lamp cycle, 10% and 14% improvements can be achieved, respectively. This has a good reference value for the construction of bus lanes and the adjustment of road facilities.


Introduction
With the rapid development of China's economy, the size of the city is expanding and the tra c demand is developing. With all kinds of motor vehicles, non-motor vehicles and buses competing for right of road use, bus delays and tra c jams are very common, and these phenomena are restricted by various factors, such as setting of road grade, expected road speed and composition of vehicle road etc. In order to alleviate urban tra c congestion, the construction of dedicated urban bus lanes has become one of the common solutions. In the study of bus lanes, the capacity of bus lanes is the starting point. According to which various measures and methods to optimize the current tra c situation are proposed to improve the e ciency of urban bus road operations and enhance the level of urban public services.
Domestic and foreign work on the calculation and simulation of bus lane capacity is more, and its capacity refers to the maximum number of bus vehicles carrying a certain number of passengers that can pass in one direction in a certain section over a period of time. In terms of capacity formula calculation: mainly based on the U.S. Highway Capacity Manual and Transit Capacity and Quality of Service Manual 2nd Edition, the existing methods are basically inherited from these two basic methods. Thus, Hua and Guangning Liu [1][2] calculated according to the in uencing factors of each type of capacity, and the statistical order of each type of in uencing factors was ranked. Ling Ding [3] studied dedicated bus lanes (DBL), intermittent bus lanes (IBL) and commonly used bus lane strategies to determine the best managed bus lanes (MBL) for different tra c conditions, using delay and time occupancy being as evaluation metrics. The results showed that tra c conditions have a signi cant impact on tra c performance, and volume having a higher impact on bus lane performance. Yongju Hu [4] et al. calculated the intersection capacity using the parking line method and following the Urban Road Design Code, and pointed out that the planar intersection is the key to in uence the tra c capacity. Dingxin Wu [5] studied the operational characteristics of urban road tra c and tra c ow, and obtained the lane distribution and speed distribution of different vehicle types; based on the survey data, he studied the bus entry and exit times and stopping times, and tted the relationship between the number of passengers getting on and off and the time of getting on and off; he also studied the interaction mechanism between urban bus and road tra c ow, including the relationship between bus ow and road capacity, and the impact of bus stopping on tra c ow; and he studied the setting conditions and impact of bus lanes. In terms of tra c simulation, tra c simulation can be divided into macro-simulation, meso-simulation and micro-simulation according to the different levels of detail of the  [10] analyzed the variability of bus arrival moments based on the dissipation process of vehicle queues at intersections, and combined the HCM2010 vehicle delay formula and road resistance function to model the average vehicle and per capita travel time for unset, conventional and dynamic bus lanes to compare and analyze their operational bene ts. Yajie Yang [11] calculated the road capacity by lane on the basis of HCM2010 and studied the impact of linear bus stops on road capacity in detail, and nally used Vissim to simulate and analyze the road capacity under the in uence of different stopping times and different bus arrival rates. Changxi Ma [12] proposed a control strategy for bus rapid transit (BRT) lanes in terms of time and space. In space, by using corresponding sensing methods and operation rules, BRT lanes are divided into a certain number of xed areas, to allow other vehicles to intermittently enter the bus lanes; in terms of time, a single-intersection bus priority strategy with intermittent bus lanes was proposed, and the results of simulation analysis showed that the intermittent BRT lane control scheme combining spatial and temporal optimized green wave coordination control outperformed other control schemes, using the BRT in Lanzhou, China, as an example.
In many studies on bus lane capacity, the changes in tra c ow and average vehicle speed of bus lanes are usually the main focus of consideration. Therefore, in this study, the tra c ow and travel speed are used as evaluation indicators for the bus lane capacity, and the road intersections and bus stops are used to divide the whole road into different sections, and the minimum value of the capacity of each section is taken as the upper limit of the capacity of the whole road; at the same time, the parameters affecting the bus lane capacity, such as the departure interval, tra c ow and travel speed, are studied quantitatively, and a variety of methods to improve the capacity of bus lane are veri ed by simulation.

Empirical formula for public transport lane capacity
The section composition of the bus lane can be divided into road intersections, bus stops and basic travel surfaces, and the capacity of each part can be calculated separately based on the following empirical formula [13][14][15].
Where: C x indicates the road intersection capacity (number of vehicles/hour), C s indicates the bus stop capacity (number of vehicles/hour), C Ln indicates the basic travel road capacity after n stops (number of vehicles/hour), and the meanings of other related parameters are shown in Table 1. Table 1 Parameter declaration of empirical formulas  (4), the bus lane full road capacity C is generated from the Equation (1) - (3), which is the minimum value of capacity in the road intersections, bus stops and basic travel surface. The parameter γ indicates the road saturation, which is one of the important indicators re ecting the level of road service, calculated by the ratio of the current tra c volume and the maximum capacity of the road section, the larger the value represents the lower the level of road service.

Bus lane capacity simulation model
The simulation model is constructed based on Vissim simulation software, using actual Google Maps data to set the base map, and the parameters needed are the same as those used in the empirical formula. Some of the parameters use default values based on experience, while others need to be set according to actual conditions, mainly including bus routes, stop distribution and stopping methods, driving behaviour, etc. The driving behaviour parameters include the desired speed of the vehicle, the safety distance between the front and rear of the vehicle, the number of vehicles visible within the sight distance of the rear driver, and the distribution of bus stopping times.
As shown in Figure 1, the simulation process starts with the construction of the road network model, which requires the use of actual bus route data, stopping station data, and driving behaviour parameters like expected vehicle speed, safety distance, acceleration, deceleration reaction time, stopping time as inputs, and is completed by setting different road conditions on the actual tra c base map. The simulation process uses the actual travel speed and tra c ow of the bus lane as evaluation indicators, with the aim of maximizing the road tra c ow while the actual speed of vehicles on the road is close to the desired speed, thus achieving the desired road tra c state. Similar to the empirical formula calculation, the simulation model also divides the road into intersections, stops and the basic travel surface and other parts, taking the minimum value of the capacity of which as the capacity value of the whole road, and then nally using the road saturation for veri cation.

Simulation model setting Take the bus lane (from west to east) of Hubin East Road-Lotus Intersection in Siming District, Xiamen
City, Fujian Province, for example, the road has two bus stops starting from the intersection at the west end, dividing the road into three basic travel sections, as shown in Figure 2.
For this road, the values of the relevant parameters in Table1 were obtained through the actual survey, as shown in Table2.  Figure 2 as the tra c base map of the simulation model, the relevant roadway information to be set is mainly as follows.
-Intersection signal ratios; East Hubin Road -Lotus intersection is a cross-shaped intersection, southeast and northwest four lanes are equipped with a signal, and tra c capacity is limited by the intersection signal green signal ratio. Green letter ratio refers to the proportion of time available for vehicle tra c in a signal cycle. Here, the signal proportioning using two-phase setting method, green letter ratio of 53/170.

-Bus routes;
For a total of 25 bus lines in three directions, the line trajectory and the corresponding stopping method are set according to the actual situation. The desired speed of each route is set to 25km/h, and the tra c ow of the road section is changed by adjusting the departure interval. The stopping methods all adopt the linear station stopping.

-Vehicle stopping time;
Since the study is concerned with the tra c ow rather than the number of passengers, the vehicle stopping time is set using a uniform method for the whole road. The vehicle stopping time is also used in the subsequent quantitative simulation of the method to enhance the capacity of the bus lane.

1) Average travel speed;
The running speed of the vehicle is affected by the road tra c ow, and the tra c ow is related to the departure interval, therefore, different departure intervals are selected in the simulation experiment to measure the corresponding average travel speed, and the results are shown in Figure 3.
From the speed curve in the gure, it can be found that the average speed of the vehicle has a large increase, higher than 15km/h, starting from the departure interval of 240s; after the departure interval of 600s, the average speed increase trend becomes slower. This indicates that, with the increase of the departure interval, the in uence of the reduced tra c ow on the vehicle speed improvement becomes smaller and smaller. Therefore, the departure interval should not be set too large from the perspective of roadway use e ciency.

2) Tra c ow;
Tra c ow is the most intuitive measure of road capacity, which is directly affected by the departure interval. Theoretically, the smaller the departure interval, the larger the tra c ow should be. Figure 4 gives the simulation results of the tra c ow on the road section 0 after the road intersection, the road section 1 after the rst stop and the road section 2 after the second stop at different departure intervals.
From the curve of Fig. 4, it is found that with the increase of the departure interval, the tra c ow presents a situation that rises rst and then decreases, and achieves the maximum value at the departure interval of about 310s, and the three cases are 276 pcu/h, 268 pcu/h and 258 pcu/h. The analysis of the reason why the tra c ow is not decreasing in the interval of 30-310s is mainly due to the stopping station setting on the road. The stopping station setting makes vehicles need to slow down and stop, thus causing congestion on the road section. The smaller the departure interval, the more serious the congestion is, which is also illustrated by the rising curve of the average travel speed in this interval in Figure 3.
Since the origin of the road in the example is the road intersection at the west end, the above tra c ow simulation results are actually limited by the tra c ow at the road intersection, which is different from the basic tra c road capacity calculation model of empirical equation (3). In order to better compare the simulation results of the basic road section with the results of the empirical formula, the design capacity of the road section set in Equation  is used as the origin tra c ow instead of the intersection tra c ow in the simulation model to calculate the capacity-related indexes after passing the rst stop; and then as the tra c ow after passing the rst stop, used in the simulation model to calculate the capacityrelated indexes after passing the second stop The results are shown in Table 3. Table 3 Comparison of tra c ability between simulation model and empirical formula In the calculation of the empirical formula, the road saturation γ is taken as 0.4, which is an empirical value in tra c science, indicating that the road tra c ow is 40% of the maximum tra c ow when the actual travel speed on the road is close to the desired speed. Using the designed simulation model, the different values of road saturation are veri ed and the results obtained are shown in Figure 5.
From Figure 5 can be seen, the saturation in 0.1 to 0.4 change, the average speed of the road basically unchanged, in a state of gentle change, at this time to increase the saturation to increase tra c ow, there is no impact on the speed of tra c; and when the saturation is greater than 0.4, the average speed of tra c began to decline signi cantly, and the downward trend as the saturation increases and accelerates, indicating that the road tra c ow is too large at this time, which signi cantly affects the road service level. Therefore, the road saturation set to 0.4 is feasible and reasonable.

2) Tra c capacity improvement method veri cation
Simulations were conducted to validate three methods of improving roadway capacity, including: (a) modifying the intersection signal cycle; (b) reducing the vehicle waiting time; and (c) adjusting the stopping station pattern. The obtained results are shown in Figure 6.
If the signal cycle is shortened when the road intersection green time remains unchanged, the intersection green signal ratio will be increased, which will be bene cial to improve the road tra c capacity. From Figure 6(a), it can be found that every 10s shortening of the signal cycle will increase the road communication capacity by nearly 10%. The reduction in vehicle stopping time will inevitably bring about an increase in roadway throughput, especially for the single-lane case. As can be seen in Figure 6(b), for every 1 second reduction in stopping time, the tra c ow will gain 1.2% improvement. Changing the stopping pattern of stops can improve roadway capacity to a greater extent, and the results in Figure 6(c) show that the use of harbor stops can bring about a 14% increase in capacity compared to straight-line stops.

Conclusions
For urban bus lane capacity, a method combining empirical equations and simulation models for comparative calculations was proposed. The target road is divided into several sections by road intersections and bus stops, and the minimum capacity value is used as the upper limit of the capacity of the whole road. At the same time, a variety of methods to improve the capacity of bus lanes are veri ed and analysed using simulation, which is a good reference for the construction of urban bus lanes and the adjustment and improvement of road facilities.
For the calculation of the actual bus lane capacity, the road intersection and bus stop tandem constraint method can also be used, using the last section of the vehicle direction of travel capacity as the full road capacity index. In this case, the vehicle loss function needs to be added to the travelled road surface after the intersection or stop, and the vehicle delay time can be added as the evaluation index of the capacity. These issues are analysed in depth in the next research work, so as to improve the simulation model involved. Figure 1 Flow of simulation Simulation results of vehicle ow Figure 5 Simulation results of saturation Simulation results of three methods to improve tra c capacity