YEAR 2006 MODELLING FOR SIMULATION OF HETEROGENEOUS TRAFFIC AT A SIGNALIZED INTERSECTION |
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This paper presents the development of a model to simulate the flow of heterogeneous traffic through a signalized intersection. Seven types of fast and slow moving vehicles are considered. Based on the field observations, a strip strategy is developed wherein the intersection approaches are divided into narrow strips of 0.5 meter width. Different types of vehicles are assumed to occupy different number of contiguous strips. Four types of dissipation processes are considered to simulate different movements. The model parameters are calibrated with field data and simulation experiments are made for different flow levels. An animation program is developed to visualize the overall system and movement of each individual vehicle with respect to arrival, queuing, dissipation of vehicles and signal settings. Simulation model can be used for optimal design of cycle length and its settings. . KEY WORDS: Simulation, animation, traffic signal, heterogeneous, intersection
Intersections are the bottlenecks on road network and their improvement generally improves the performance of entire network. Traffic signals were originally used when there was insufficient land available for enlarging a junction. Increasing sophistication in the control system has resulted in the widespread use of signalized intersections. The traffic engineer must be able to assess the likely queues and delays when changes are being made to existing intersections or new installations are being considered. The assessments can be divided into two parts: - Capacity, queues and delays
- Signal settings or timings
One of the steps in assessing the above is to have a reasonably realistic model for intersections. Due to the complexity of mixed traffic flow on Indian roads, most of the existing models of signalized intersections are not applicable to Indian conditions.
This study formulates a simulation model for signalized intersection, considering the heterogeneous traffic on Indian roads. The scope of this study is: - Development of model to simulate the flow through signalized intersections.
- Result processing program that performs analysis of simulated output and yield a set of files that serve as input to the Graphic Display program.
- Development of animation program to visualize the overall system and movement of each individual vehicle.
- Simulation experiments to understand the logic in the model and behavior of traffic flow by considering the effects of intersection.
Computer simulation model can play a major role in the analysis and assessment of the highways planning techniques. When suitable conceptual model cannot be formulated for the several components of the process and the complexity is due to the stochastic nature, computer simulation of the process may be adopted.
Intersections in Indian road networks are difficult to model because of the different types of vehicles involved in the traffic. These vehicles have different widths, speeds (both slow moving and fast moving vehicles), turning movements, etc. and it is difficult to model these with analytical methods. In order to idealize the system, various types of vehicles involved in the system are reduced to seven groups and are listed in To simplify the queuing procedure of vehicles, road is assumed to be divided into numerous strips. Different types of vehicles occupy different numbers of contiguous strips, the number of strips depend on the width of the vehicle. Figure 1 shows the representation of vehicle and road as strips.
The assumptions made in constructing the model are: - A newly arrived vehicle, searches for sufficient space to stand in queue on the left of the previously queued vehicle.
- The mathematical distributions to describe the inter-arrival time of vehicles in the traffic stream of all the approaches is assumed to be Negative Exponential Distribution (The model can easily incorporate any other distribution).
- The road is assumed to be of uniform cross section.
- Seven types of vehicles (Table 1) and three turning movements (Table 2) are considered.
- Vehicle type and turning movement are decided randomly. The probability of a vehicle being of a particular type and movement obviously depends on the proportion of such vehicles and movements in that stream.
- The road is assumed to be divided into numerous strips. Different types of vehicles are assumed to occupy different number of contiguous strips, the number of strips depends on the width of the vehicle.
The present simulation model is developed using Discrete-Event simulation technique with next-event time advancement approach i.e. the simulation clock is advanced from one event time to another (next) event time and the time interval between two successive events is highly variable. The various road, intersection and traffic characteristics are given as input. The following modules are used to develop the simulation model of the signalized intersection: - Road_Strip_module: Divides the approach roads into numerous strips of equal width. This module requires the the road width of different approaches and the desirable strip width as input.
- Initialization_module: Initializes all the statistical counters and events in the system.
- Time_Advancement_module: Compares all the events and advances the simulation clock to the time of occurrence of the chosen event type.
- Arrival_Generation_module: Generates arrival from a particular approach. Assigns values to vehicle identification number, arrival time and direction of travel.
- Vehicle_characteristics_module: Decides the vehicle type and turning movement.
- Vehicle_Queueing_module: Calls a particular queueing pattern module depending on approach number and flow characteristics. When the simulation starts, the vehicles on the approaches, having GREEN signal, start moving and on the remaining approaches, vehicles start queuing. Three types of queuing patterns are mentioned in the simulation model.
(i) Queuing Pattern 1: In this queuing pattern, depending on the width of the strip, four strips on the right most part of the road are allocated for the right turning vehicles. Four more strips immediately on the left side of these right turning strips are allocated for CAR, HMV vehicle types. The remaining strips are allocated for the remaining vehicle groups mentioned in the model. Vehicles arrived in the RED period, and sometimes, arrived in GREEN period occupy these strips forming queue. A newly arrived vehicle searches for space on the left side of the previously queued vehicle of same category. If it finds sufficient number of strips to queue-up, then it occupies those strips. Otherwise it stands behind the first vehicle of the previous row, forming a new row. The process of queuing is explained with the help of a simple example in Figure 2. (ii) Queuing pattern 2: In this queuing pattern, through and right turning vehicles do not queue-up separately. Irrespective of the turning movement, all the vehicles are mixed and the newly arriving vehicle always searches for sufficient space to stand in queue, on the left of the previously queued vehicle. If it does not find space, it occupies the position behind the first vehicle of the previous row. This queuing pattern is adopted only when the four wheeler traffic is much less as compared to the two wheeler and three wheeler traffic. In this case also, left turning vehicles are allowed to move freely. The queuing pattern 2 is depicted in Figure 3. - Vehicle_processing_module: Corresponding to the three patterns described in the previous subsection, four vehicle dissipation modules are specified in this model.
(i) Dissipation module 1: This module allows only through vehicles into the intersection, when the signal turns GREEN. And is considered only when the queuing pattern 1 is adopted. It treats the CAR, HMV vehicle types, forming a single queue, as one group and the remaining vehicle types as another group. This module goes through a vehicle record and checks its turning type. If the turning type is RIGHT, it skips the vehicle record and moves the pointer to the next record. If the turning type is STRAIGHT, checks the vehicle type and calculates the entry time. (ii) Dissipation module 2: This module is to allow only RIGHT turning vehicles into the intersection and is considered only when the Queuing pattern 1 is adopted i.e. when the right turning volume is less. It treats all types of vehicles in similar manner. This module skips the vehicle record if the turning type of vehicle is STRAIGHT. (iii) Dissipation module 3: This module treats both RIGHT and STRAIGHT vehicles alike i.e. it dissipates both right turning and through vehicles at a time. This dissipation process is considered only when the queuing pattern 2 is adopted. (iv) Dissipation module 4: This module follows the same logic as Dissipation module 1, except that this module dissipates both right turning and through vehicles at a time with same logic. After dissipation or processing a vehicle, all these modules calculate the queuing_delay of the vehicle as the difference of entry_time and arrival_time. Depending on the direction, from which the vehicle has arrived, these modules calculate the vehicle’s position on the graphics screen. - Queue_Updating_module: Updates the remaining vehicles in queue(s) immediately after the completion of GREEN period.
- Signal_Phase_Changing_module: Decides the next phase and thus decides the vehicles to be dissipated.
- Result_Processing_module: Reads the vehicle records of all the approaches, summarizes the output and prepares the input to the Graphic Display program.
Figure 5 presents pictorially the interconnection of different modules and the primary output obtained from different modules
The model gives the following output, derived from the basic output:
Video recording of traffic data is used to observe the following parameters. For the present study, the intersection at Bara Chauraha, Kanpur is selected. The video camera is placed over an elevated position i.e the General Post Office building, Kanpur. To have a clear idea about the intersection, first the intersection with movements of vehicles of all the approaches are videotaped for thirty minutes. Now, in order to collect the data for individual approaches, the camera is focused only on one approach at a time and the events are videotaped for thirty minutes. The main concentration is on arrival of vehicle, vehicle queuing and dissipation, turning movement of vehicle whenever the signal turns GREEN. Later the events on remaining approaches are also videotaped.
The primary observation in queuing is that the vehicles are occupying the width of the road completely by moving aside of the previously queued vehicle. it is observed that vehicles arriving in the red period are always trying to occupy top position in queue. In this process, they are searching for sufficient space among the vehicles in queue. From the observations it is clear that a newly arrived vehicle (other than HMV and CAR) always tries to reach the nearest point to the stop line, from the left side of the vehicles already queued up. On the approaches having considerable proportion of four-wheeler traffic (CAR or HMV), it is observed that these form queue by standing one behind the other. Even though, this is often leading to the formation of lengthy queue, they are not trying to form another queue and are also not trying to join queues formed by other vehicles. On the approaches having separate dissipation process for right turning vehicles, it was observed that these right turning vehicles are forming queues on the right most part of the road. The width of the road occupied is differing depending on their volume level. 5.2 OBSERVATIONS OF ARRIVAL AND DEPARTURE OF VEHICLES Vehicles arriving before the vehicles in queue get completely dissipated are finding gaps among the vehicles and entering the intersection by overtaking the slow moving vehicles. - Vehicles arriving after the dissipation of queue and before the end of GREEN period are accelerating to enter the intersection, thus moving without delay, before the end of GREEN period.
It is observed that due to large volume of slow moving vehicles like cycles, cycle rickshaws and other vehicles like push carts, bullock carts, the delay to the traffic stream is more and the starting delay of vehicles like CAR and HMV is increasing. With these observations a primary logic to the model is developed. The queuing of vehicles on the width of the road was the primary initiation to develop and implement the strip logic.
As the arrival of vehicles is occurring randomly on all approaches of the intersection, it is assumed that the arrivals follow Poisson distribution. The Chi-square test is used to assess statistically the likelihood that the measured distributions have the attributes of mathematical distribution. Since the Poisson distribution is applicable to the arrivals, the distribution of time intervals between the arrivals follows the ‘Negative Exponential Distribution’. It was proved that for all approaches, the time intervals between the arrivals follow Negative Exponential Distribution.
The traffic flow characteristics of a road stretch are a function of various parameters including road geometry, traffic composition and flow level. The present study is intended to test the model logic and its working. Two simulation runs are taken with different simulation times and similar composition of traffic. The flow levels for the four approaches are given in Table 3. The simulation results for Straight and right turning movements are presented in Table 4 and Table 5. The variation of queue length on different approaches is presented in Table 6. Table 7 presents the delays for the complete system. Two more simulation runs are made with flow levels of 1600, 900, 1600 and 600 vph on first, second, third and fourth approach respectively and is presented in Table 8.
The output files of simulation model are of big size and contain large amount of data. It is very difficult to analyze and visualize the traffic flow behavior by going through the event files. Event files contain the data event times only, which make the study of traffic flow behavior at any arbitrary time instant or time interval impossible. So, a Graphic display program is written in TURBO C++ to visualize the traffic flow considering the uniform flow intervals.
This study formulates a simulation model for signalized intersection, considering the heterogeneous traffic on Indian roads. For this purpose, field observations are made at an intersection. Depending on the observations, seven types of vehicles and three turning movements are defined. The connecting-legs of the intersections are divided into numerous strips and different types of vehicles are assumed to occupy different number of contiguous strips depending on their width and strip width considered. This strip strategy is developed purely based on the field observations. Keeping the queuing patterns and phases in view, four types of dissipation processes to dissipate (i) only through vehicles, (ii) only right turning vehicles, (iii) both through and right turning vehicles irrespective of the vehicle type, (iv) both through and right turning vehicles considering the vehicle type as a factor, are defined. The model updates the queue after the dissipation process is over and moves to the next phase. The final out-come is queuing delay to each vehicle and number of vehicles in queue in each cycle. A Graphic Display program is also written to visualize the arrival of vehicles, queueing of vehicles, dissipation of vehicles, signal settings and vehicle turning movements. In another sense, this Graphic Display program shows the traffic flow behavior, giving clear idea about the system and its components.
[1] Darroch J.N. (1961), On the Traffic Light Queue, Annals Math. Stat. Vol. 35, pp 380-388. |
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