Cellular Automata Simulation of Urban Traffic Flow Considering Bus Lane

Based on the analysis of urban traffic flow affected by bus lane, a two-lane cellular automata model is established under the periodic boundary condition. The properties of traffic flow are investigated by analyzing the velocity-density and flow-density diagrams. The spatial-temporal diagrams with the two types of bus stop facilities are also discussed. Simulated results show that the bus lane can significantly improve the traffic flow , and the volume can increased by extending the bus stop length, and the bus stop with no overtaking facilities has less volume than the bus stop to permit overtaking.


INTRODUCTION
The urban traffic flow affected by public transit system has aroused the concern of many scholars in recent years. Scholars have studied theories and models of public transit system from different angels and many models have been proposed, such as car-following model, hydrodynamic model, and cellular automata model. In particular, cellular automata models with their ability to simulate both gross and subtle features of real traffic have gotten comprehensive research and application [1][2][3][4][5][6]. X.M. Zhao, Z.Y. Gao and B. Jia [7,8] studied the combined effects of the signalized intersection and its near-by bus stop using a two-lane CA model, and the effect of the bus stop between two neighboring intersection were investigated. Y.S. Qian, H.L. Wang and C.L. Wang [9] developed a CA model with different maximum speed vehicles mixed on single lane which considers the effect of harbor-shaped bus stop. B. Jia, X.G. Li and R. Jiang [10] investigated the influences of the non-harbor shaped bus stop and the harbor shaped bus stop on the traffic flow. A two-lane CA model is proposed by D.Q. Li , L.Y. Dong and S.Q. Dai [11] to simulate the traffic bottleneck induced by bus stopping. C.Chen, T.Wang and C.Y Li.et al [12] have studied the setting conditions of bus bay stop. A model of mixed vehicle with traffic parameters, such as bus-car volume, vehicle volume and ratio of bus-car and put forward running speed, is introduced by X.G. Yang, H. Xu and J. Wang [13]. Y.J. Liang and Y. Xue [14] studied the impact of the arrangement of bus stops without bus bay. A certain characteristics of the bus stop without stopping-lane were analyzed by S.J. Kang and Y. Xue [15]. However, as the important part of bus priority measures, little information has been published concerning the impacts of the bus lane, which is a bus track infrastructure where buses are separated from other traffic by road marking or studs, to the traffic flow.
Based on the NaSch model, a new two-lane cellular automata model considering the influence of the bus lane section on urban traffic flow under the periodic boundary condition is established. The model also considered the different driving rules and lane change rules between the car driver and the bus driver under the mutative traffic condition. For the section with bus lane and the section with off-line bus stops, the distribution of velocity-density and flow-density are provided. It is found that bus lane can significantly improve the traffic flow. By extending the length of the bus stop, the bus volume can be increased. And for the conditions studied, the provision of overtaking bays is likely to have a greater effect on speeds than does the provision of bus ordering.

BUS LANE
The two-lane CA model is built from the two-lane road under the periodic boundary condition. It is assumed here that vehicles move only in one direction. The road is illustrated in Fig. 1 with two lanes, the right and the left, which each lane of the road is divided into L cells. The road consists of two sections with same length. Section bus lane is the start of the road which the right lane is only use for buses. Section general traffic is the part between the middle of the road and the end of the road which the lane changing is permitted. The upstream part near the bus stop is section A and special lane-changing rules will be used in this section. There is one intersection between bus lane and general traffic section. For each section, there is one off-line bus stop with several bays (from the right to the left named Bay1, Bay2….) lies at the middle of the right lane (or the bus lane).

A. Forward motions
The NS model is used to control the vehicles moving forward in this paper. The variable (1) Acceleration: (1) (2)Deceleration: (3)Randomization with probability P : (4) Motion: In the formulas above, i n len is the length of vehicle i on the lane n , and ) (t gap i is the gap between vehicle i and its preceding vehicle 1 + i at time t which is calculates by (5).
In cases with the stop lane or the bus lane when the buses near the bus stop, the deceleration rule of the buses will follow the added rules (8), it means bus i will enter the bus stop with speed 1 as the first vehicle in the bus stop and move to the Bay 1 when the bus stop is empty.
If the Bay 1 is allocated, the bus will enter the stop with speed 1 and move to the Bay 2 as the second vehicle in the bus stop, and so on. And if all of the bays of bus stop are already been allocated, all the stopping buses will queue at the entry to the stop with speed 0.
When the stopping bus i staying Bay n at the bus stop, it can move forward with speed 1 if the bay 1 ! n is empty then its speed is updated as 0. If the bus staying in the Bay 1, it cannot move forward if its dwelling time is less than s T which speed is updated as 0. The bus becomes a non-stop bus when the dwelling time is equals s T and then waiting for exit the bus stop (for the general traffic section).

B. Lane-Changing Motions
Each of iteration consists of the two sequential steps. (2)The drivers of car are willing to change lane when its preceding vehicle is bus. If the following condition is satisfied, the car will change lane with probability car c P .
1 > i nBack gap (12) 0 ! i n gap (13) (3)All cars on the road and the stopping buses which do not lie in Section A will change lanes. The cars will change to the left lane and the bus will change from the left lane to the right lane as long as conditions on the right lane are safety.

>=
i n gap (14) ) The same changing rules above are used for stopping buses which will change lane in order from bus stop to the right lane (or bus lane) when the dwell time is satisfied. If a stopping bus can not change to the destination lane, it will stop and wait for opportunity to change in order.
The periodic boundary condition is used in the simulations. In each time step, the position of the last vehicles on each lane is checked when the update of all vehicles is finished. If the position of the leading vehicle is beyond the length of the road, it will be move to the end of the queue on the certain lane as the lane-changing rule mentions above and its following vehicle becomes the new leader.

III. RESULTS AND DISCUSSIONS
The standard simulations set-up in this paper is described for the following observations. The road with length 7.5km is divided into According to the Transit Co-operative Research Program Report 19(1996) [16], the average peak-period dwell time exceeds 30 second per bus, so s T s 30 = in this section. One of the most basic measurements in traffic flow model is the fundamental diagram, which represents a relation between the three macroscopic variables: average velocity v , flow q and density ! .For the two types section, the relationship between cars flux and density with different R is shown in Fig. 2. And the relationship between cars velocity and density is shown in Fig.3. Since buses and cars are separated running on the bus lane section, the cars flux and velocity only be affected by density but not be affected by the bus ratio.
From Fig.1 and Fig.2, it can be seen that:   It is found that, the length of bus stop has more influence on the bus lane section than on the general traffic section. And the flux of buses can be effective improved by increasing length of bus stop on the section which set a bus lane.
However the length of bus stop can not immeasurably increased in reality. In the above results, buses enter the off-line bus stop in order and there is no special facility in bus stop. In addition, with the different of predominant passenger movement, the buses dwell times are different between boarding predominates which services run overloaded or alighting predominates (or express services) which those services run nearly empty [17].
Considered two types of buses in the ratio 1:1, a short dwell time  Fig.6.
It can be seen a clustering phenomenon in the upstream section of the bus stop. In downstream section of the bus stop, there is no hindrance for the buses which waiting for stop to proceed. Thus, the queue at the entry of the bus stop is accumulate by the increase of buses dwelling time in the bus stop. However some of the buses finish their stopping procedure at the stop already cannot leave out of the bus stop because the first bus in the bus stop is not finish the procedure because of the buses entry and exit the bus stop must be in ordered. To improve the throughput of bus stop, a bus stop layout and operating regimes is introduced in this section which is familiar in the form of bus priority in many countries [17]. Fig.7 shows a 3-bay off-line bus stop with bus overtaking facilities in the bus stop area. It is different with the general off-line bus stop which all bays can be provided for all stop buses; there is a special bay C which can only be allocated to limited stop. The boarding predominate buses can only be allocated to bay A or Bay B. The alighting predominate buses may either be allocated to specific bay C or use any bay.  Change the position update rules for the stopping buses as follow.
(1)For the boarding predominate bus, it will enter the bus stop in order, and move from Bay B to Bay A if Bay A is empty in its dwelling time. If Bay A and Bay B are occupied by other buses, it will queue to access the stop. All of the boarding predominate buses will stay at Bay A to waiting for exit the bus stop until the dwelling time and safe condition are satisfied.
(2)For the alighting predominate bus, it will be allocated preferentially to Bay C if the Bay C is empty, no matter the Bay A and B empty or not. And then exit the bus stop from Bay C. Else if Bay C has been occupied, the bus will enter the Bay A or Bay B if any of them is empty. Then it will change lane from bus stop to the right lane as well as the dwell time and safety conditions are all satisfied.  Fig.8, the simulation indicates that the queue at the entry of bus stop becomes shorter and fades out quicker than that of in the Fig.6. This suggests that for the conditions studied, the provision of overtaking bays is likely to reduce the delays of the buses in the stop.   According to the analysis, the traffic of road is light and the bus ratio is small, it is not very necessary to set bus lane. If the traffic is very high or with large bus ratio, bus lane can improve the flux and velocity significantly. In order to further improve the performance and decrease the time for waiting enter or exit the bus stop, extending the bus stop length is considered. Then provision of overtaking facilities at bus stops is an especially effective way to increase flux and decrease the unnecessary dwelling time in bus stop. These implications may provide suggestions on the design of public traffic.