cellular automata vs. object-automata in traffic simulation

9
International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014 www.ijrsa.org doi: 10.14355/ijrsa.2014.0401.07 61 Cellular Automata vs. Object-Automata in Traffic Simulation Saeed Behzadi *1 , Ali.A. Alesheikh 2 Department of Geographic Information System, Faculty of Geodesy and Geomatics Eng., K.N. Toosi University of Technology ValiAsr Street, Mirdamad cross Tehran, Iran 19967-15433 *1 [email protected]; 2 [email protected] Abstract Cellular Automata (CA) recently has been used in variety of fields related to continuous areas such as Geospatial Information System (GIS), traffic, air pollution, and so on. Having been used only in continuous raster-based area is the most weakness of CA, so defining the shape of the cellular and their adjacency for the study area is always a big challenge for researchers. Despite CA, agent-based modeling is complex and progressive type of intelligent object. Agent- based model is used in variety fields. Having efficiency such as moving makes it extremely distinctive from the concept of static intelligent entity. In this paper, at first, an intermediate type of object named Object-Automata (OA) was defined based on the simplicity of CA and complexity of agent which is suitable for both continues and discontinues area. Secondly, to asses and investigate the proposed OA, the simulation of traffic was implemented by OA and the model was compared with CA. As roads are defined as discrete entities, OA is much more suitable for such problem. At the end of this paper, the rules about the problem were described. Keywords Cellular Automata; Object Automata; Traffic Simulation; Geospatial Information System Introduction The investigation of traffic systems has attracted much attention recently as its results are useful in scientific scheduling transportation construction and efficient utilization of traffic resources. Many kinds of traffic models have been proposed (Shi et al., 2007), one of which is agent-based modeling and simulation. Most of these agent-based modeling and simulation are used as moving objects (cars), traffic signals and so on. Cellular Automata (Wolfram, 1986) (CA) provides a simple, flexible way for modeling. It is also suitable for computer simulations. Many interesting phenomena can be observed in such simulation, so CA leaves challenges to mathematicians. In most of the researches, CA was used as a microscopic model in which space, time and state variables were considered as discrete (Wolfram, 1986); moreover, the simple regulation reflects all kinds of factors in traffic process. The discreteness of space is suitable for high- performance computer simulations for every cell site on the road occupied by one car at most (Shi et al., 2007). CA was originally introduced by von Neumann and Ulam (under the name of ‘‘cellular spaces’’) as a possible idealization of biological systems (Von Neumann, 1951, Von Neumann and Burks, 1966). Although the concept of CA was first proposed long ago, the CA began to receive wide attention from the traffic and transportation community only after the simple formulation by Creamer and Ludwig in 1986 (Cremer and Ludwig, 1986). After that, Cellular automata models were employed to represent several traffic scenarios from rather simple ones to more complex ones. In 1992, Nagel and Schreckenberg (Nagel and Schreckenberg, 1992) proposed a one- dimensional cellular automata model to simulate traffic flow on a freeway, providing the basic principles for more complex surroundings such as city traffic flow. In 1997, they (HU, 1999) presented a more realistic one-dimensional cellular automaton model for the project TRANSIMS (Nagel et al., 1997). In traffic cellular automata model, the roadway is represented by a uniform cell lattice in which each cell belongs to a discrete set of states. The state of the cells is updated at discrete time steps with a set of update rules that combine a few vehicle motion models. The models are governed by a small set of parameters (Sun and Wang, 2007). Improvements have been made to the N-S (Nagel-Schreckenberg) model by adapting to more realistic circumstances, such as the Fukui–Ishibashi (FI) model, TT model, VDR model, VE model, and so on (Li et al., 2006, In-nami and Toyoki, 2007, Maerivoet and De Moor, 2005). Those models are single-lane ones. In the model proposed by In-nami and Toyoki (In- nami and Toyoki, 2007) a traffic flow model of cars on a two-dimensional lattice was investigated in which a

Upload: shirley-wang

Post on 01-Apr-2016

225 views

Category:

Documents


3 download

DESCRIPTION

http://www.ijrsa.org/paperInfo.aspx?ID=4833 Cellular Automata (CA) recently has been used in variety of fields related to continuous areas such as Geospatial Information System (GIS), traffic, air pollution, and so on. Having been used only in continuous raster-based area is the most weakness of CA, so defining the shape of the cellular and their adjacency for the study area is always a big challenge for researchers. Despite CA, agent-based modeling is complex and progressive type of intelligent object. Agent-based model is used in variety fields. Having efficiency such as moving makes it extremely distinctive from the concept of static intelligent entity. In this paper, at first, an intermediate type of object named Object-Automata (OA) was defined based on the simplicity of CA and complexity of agent which is suitable for both continues and discontinues area. Secondly, to asses and investigate the proposed OA, the simulation of traffic was implemented by OA

TRANSCRIPT

Page 1: Cellular Automata vs. Object-Automata in Traffic Simulation

International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014 www.ijrsa.org doi: 10.14355/ijrsa.2014.0401.07

61

Cellular Automata vs. Object-Automata in Traffic Simulation Saeed Behzadi *1, Ali.A. Alesheikh 2

Department of Geographic Information System, Faculty of Geodesy and Geomatics Eng., K.N. Toosi University of Technology ValiAsr Street, Mirdamad cross Tehran, Iran 19967-15433 *[email protected]; [email protected] Abstract

Cellular Automata (CA) recently has been used in variety of fields related to continuous areas such as Geospatial Information System (GIS), traffic, air pollution, and so on. Having been used only in continuous raster-based area is the most weakness of CA, so defining the shape of the cellular and their adjacency for the study area is always a big challenge for researchers. Despite CA, agent-based modeling is complex and progressive type of intelligent object. Agent-based model is used in variety fields. Having efficiency such as moving makes it extremely distinctive from the concept of static intelligent entity. In this paper, at first, an intermediate type of object named Object-Automata (OA) was defined based on the simplicity of CA and complexity of agent which is suitable for both continues and discontinues area. Secondly, to asses and investigate the proposed OA, the simulation of traffic was implemented by OA and the model was compared with CA. As roads are defined as discrete entities, OA is much more suitable for such problem. At the end of this paper, the rules about the problem were described.

Keywords

Cellular Automata; Object Automata; Traffic Simulation; Geospatial Information System

Introduction

The investigation of traffic systems has attracted much attention recently as its results are useful in scientific scheduling transportation construction and efficient utilization of traffic resources. Many kinds of traffic models have been proposed (Shi et al., 2007), one of which is agent-based modeling and simulation. Most of these agent-based modeling and simulation are used as moving objects (cars), traffic signals and so on. Cellular Automata (Wolfram, 1986) (CA) provides a simple, flexible way for modeling. It is also suitable for computer simulations. Many interesting phenomena can be observed in such simulation, so CA leaves challenges to mathematicians. In most of the researches, CA was used as a microscopic model in

which space, time and state variables were considered as discrete (Wolfram, 1986); moreover, the simple regulation reflects all kinds of factors in traffic process. The discreteness of space is suitable for high-performance computer simulations for every cell site on the road occupied by one car at most (Shi et al., 2007). CA was originally introduced by von Neumann and Ulam (under the name of ‘‘cellular spaces’’) as a possible idealization of biological systems (Von Neumann, 1951, Von Neumann and Burks, 1966). Although the concept of CA was first proposed long ago, the CA began to receive wide attention from the traffic and transportation community only after the simple formulation by Creamer and Ludwig in 1986 (Cremer and Ludwig, 1986). After that, Cellular automata models were employed to represent several traffic scenarios from rather simple ones to more complex ones. In 1992, Nagel and Schreckenberg (Nagel and Schreckenberg, 1992) proposed a one-dimensional cellular automata model to simulate traffic flow on a freeway, providing the basic principles for more complex surroundings such as city traffic flow. In 1997, they (HU, 1999) presented a more realistic one-dimensional cellular automaton model for the project TRANSIMS (Nagel et al., 1997). In traffic cellular automata model, the roadway is represented by a uniform cell lattice in which each cell belongs to a discrete set of states. The state of the cells is updated at discrete time steps with a set of update rules that combine a few vehicle motion models. The models are governed by a small set of parameters (Sun and Wang, 2007). Improvements have been made to the N-S (Nagel-Schreckenberg) model by adapting to more realistic circumstances, such as the Fukui–Ishibashi (FI) model, TT model, VDR model, VE model, and so on (Li et al., 2006, In-nami and Toyoki, 2007, Maerivoet and De Moor, 2005). Those models are single-lane ones. In the model proposed by In-nami and Toyoki (In-nami and Toyoki, 2007) a traffic flow model of cars on a two-dimensional lattice was investigated in which a

Page 2: Cellular Automata vs. Object-Automata in Traffic Simulation

www.ijrsa.org International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014

62

car had an origin and a destination. In this model, the destination was determined when the car was created, and the car then determined a path randomly among the shortest paths. If a car arrived at its destination, the car was deleted and a new car was created. Furthermore, CA has been generalized to slow-to-start phenomena (Takayasu and Takayasu, 1993, Benjamin et al., 1996, Schadschneider and Schreckenberg, 1997), rule and the extension from single lane to multilane models (Nagel and Paczuski, 1995, Takayasu and Takayasu, 1993, Li et al., 2001, Rickert et al., 1995), traffic with high speed vehicles (Schadschneider and Schreckenberg, 1997), signalized intersection, multi-class traffic flow (Daganzo, 1994, Simon and Nagel, 1998, Nagel, 1996), inhomogeneous mixed traffic flow (Lo and Hsu, 2009), simulation of lane reduction scenarios (Nassab et al., 2006), aggressive lane changing vehicle behavior (Li et al., 2005, Li et al., 2006). In paper proposed by (Li et al., 2006), the aggressive lane-changing behavior of fast vehicle and the effect of different lane-changing probability were investigated. In this paper, a new set of lane-changing rules was proposed (Li et al., 2006). The simulation of mixed traffic was also investigated by CA (Plan et al., 2006, Meng et al., 2007, Lan et al., 2010). Passenger cars and motorcycles were introduced by the cell width parameter (Spyropoulou, 2007) as motorcycles would use less lateral space than passenger cars. Lan, Chiou et al. proposed a sophisticated CA model to explain the erratic motorcycle behaviors in mixed traffic contexts, the conventional moving forward, and lane-change rules. The sophisticated CA model also explained the lateral drift behavior for cars moving in the same lane, the lateral drift behavior for motorcycles breaking into two moving cars, and the transverse crossing behavior for motorcycles through the gap between two stationary cars in the same lane.

CA rules have also been used to simulate pedestrian (Blue and Adler, 2001, Burstedde et al., 2001). Nagatani (2009a) and Nagatani (2010) also presented a bi-directional CA model for facing traffic of pedestrians. Blue et al. (1997) proposed a pedestrian movement model for large scale open areas. Muramastu et al. (1999) developed a pedestrian movement model based on stochastic processes. Blue and Adler (2000) then developed a four-directional pedestrian crosswalk model and a year later proposed a bi-directional pedestrian crosswalk model (Blue and Adler, 2001). The focus of Yi and Houli (Yi and Houli, 2007) was on the behavior of pedestrians, the influence of pedestrians’ behavior on the vehicle flow, pedestrian flows, and the vehicle waiting time.

Therefore, in this paper, a pedestrian cross-street model was described under the traffic light control based on CA. The paper proposed by Lo and Hsu (Lo and Hsu, 2009) concentrated on car gap which was defined to be the distance between two successive vehicles, and Tian (Tian, 2009) and Nagatani (Nagatani, 2009b) concentrated on mathematical rules of CA.

The papers mentioned here showed the variety used of CA in traffic. Being used in continues area is one of most weakness of CA. So, in this area, defining the structure of CA is the only challenge of designer; however, in discrete area such as traffic not only the structure of CA but also modification of CA must be considered. To overcome this problem, a microscopic traffic CA model based on road network grids was proposed by (Sun and Wang, 2007) to overcome the low spatial and temporal resolutions of traditional traffic CA models. In this model, spatial resolution can be changed by setting different grid size for lanes and intersections before or during simulation. Temporal resolution can be defined according to simulation needs to model different drivers’ reaction time, whereas the vehicular movement models were still traditional CA models.

Recently, CA has been used for simulation models along with multi-agent technique. Such simulation models were constructed for traffic simulation (Wahle and Schreckenberg, 2001, Wahle et al., 2002), and pedestrian simulation (Dijkstra et al., 2000). Usually, agent is considered as a complex intelligent object which is used in multifaceted system as a sensitive, smart, decision making object. Defining agent as an environment is rarely brought into play, because in this situation, most of the capability of agent must be diminished. In this paper, to deal with these difficulties, a new type of intelligent object was investigated to overcome the disadvantages of CA while there is no need to define complex intelligent objects as agent.

In this paper, at first the concept of CA was briefly stated, then based on these concepts, a new type of intelligent entity named object-automata (OA) was introduced. Next, the proposed OA was used in traffic simulation and the result was compared with CA.

Cellular Automata

Cellular Automaton (CA) is a discrete dynamic system in which space is divided into regular spatial cells, and time progresses in discrete steps. Each cell in the

Page 3: Cellular Automata vs. Object-Automata in Traffic Simulation

International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014 www.ijrsa.org

63

system has one of a finite number of states. The state of each cell is updated according to local rules. The state of a cell at a given time depends on its own state and the states of its neighbors at the previous time step (Liu, 2009, Wolfram, 1984).

According to this definition, CA consists of five basic elements (Liu, 2009):

The cell is considered as the basic spatial unit in the cellular space. Cells in a cellular automaton are arranged in a spatial tessellation which can be one, two or three dimensional.

The state defines the attributes of the system. Each cell can take only one state from a set of states at any one time.

The neighborhood is a set of cells with which the cell in question interacts. In a two-dimensional space, there are two basic types of neighborhoods: the von Neumann Neighborhood (four cells), and the Moore Neighborhood (eight cells).

The transition rule defines how the state of one cell changes in response to its current state and the states of its neighbors. This is the key part of CA because these rules represent modeling of the system, thus they are essential to the success of a good modeling practice (White, 1998).

The time specifies the temporal dimension in which CA exists. According to the definition of cellular automata, the states of all cells are updated simultaneously at all iterations over time.

Object-Automata

In this section, based on the concept of CA, the principle of OA is affirmed. The lattice and neighborhood properties of OA are independent on the situation of the problem, but rules and states properties of OA depend on the problem. Therefore, at first, two properties are mentioned, and then the two late principles are explained based on the specifics problem for one type of OA.

As seen in CA section, to define the OA, four properties of CA must be stated for OA. 1) Lattice: lattice is a space of similar object with the same geometry. In OA, the lattice can be one of the three groups of objects: space of points: all objects in the area are points, space of lines: only line objects are located in the area, and space of polygon: polygons are only ones in the area. 2) Neighbor: in each group, based on the type of lattice defined, the neighbor of

objects can also be defined, so for each type, the neighborhood property is defined as follow:

Neighbor in Point-based Space: in this case, the only points exist in the space. To specify the neighborhood points around each object and their direction, two parameters must be defined: the radius of buffered area (r) around each point, and the number of pieces area around each point object (n). In CA, the size of pixel can be varied and depends on the conditions of the area. In point-based automata, r performs the rule of pixel size, so if it is small, neighborhood area around each point will be small and versus. Parameter n divides the circle around the point to n part. These two parameters depend on the situation of the problem and the decision maker’s criteria. Similar CA, if n is equal to 4, “von Neumann” neighbor is obtained, and if n is equal to 8, “Moor” neighbor is obtained (Figure 1). The overall rule for neighborhood around point is shown in Equation 1.

Neighbor = {r, n} (1)

Where, r is the radius of circle around object, and n is the number of sectors of the circle. Points in the distance less than r are in the neighbors of point; based on being in the specific sector, the directions of neighbor points are specified.

(A) (B)

FIG. 1 THE NEIGHBOR OBJECTS AROUND POINT (A) “VON NEUMANN” NEIGHBOR (B) “MOOR” NEIGHBOR

Neighbor in line-based space: in this case, all objects in the area are lines. Each object in the area is defined as follow: “an object is a line whose connection to the other objects is only made by one or both ends.” If two lines intersect each other, then each line creates two objects which meet each other at their ends. In this case, the neighbors of a line object are some line objects which connect to the end of the line by their ends. In Figure 2, some line objects in line-based space are shown.

(A) (B)

FIG. 2 THE LINE OBJECT AUTOMATA (A) THE LINE LOCATED IN THE AREA (B) LINE OBJECT AUTOMATA WITH THEIR

NEIGHBORHOODS EXTRACTED FROM LINE

Page 4: Cellular Automata vs. Object-Automata in Traffic Simulation

www.ijrsa.org International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014

64

Neighbor in Polygon-base space: in this case, all objects in the area are polygons. An object in this area is defined as follow: “Polygon A is an object in the area, while it has is no overlay with the other objects in the area.” In this case, if a polygon overlays with another one, more than two objects are defined for these two polygons; one object for each polygon, and one or more objects for the overlay area between two polygons. In Figure 3, polygons and objects obtained from the polygons are shown.

(A) (B)

FIG. 3 THE POLYGON OBJECT AUTOMATA (A) TWO POLYGON WITH OVERLAY AREA (B) THREE POLYGON OBJECTS

EXTRACTED FROM THESE TWO POLYGONS

In this case, the neighbors of an object are the objects which have the same boundary with the specific object. Like CA, “von Neumann” and “Moor” neighbors can also be defined for this object. The neighbor objects are divided into two parts: the objects which meet the specific object only in one-point and the objects whose boundary with the specific object is more than one point. If the neighbor objects have one-point adjacency, they are considered as “von Neumann” neighbors. If the neighbor objects have more than one-point adjacency, they are considered as “Moor” neighbors (Figure 4).

(A) (B)

FIG. 4 THE NEIGHBORHOOD OBJECT IN THE AREA FILLED WITH POLYGONS (A) “MOOR” NEIGHBORHOOD (B) “VON

NEUMANN” NEIGHBORHOOD

The 3) state and 4) rules defined for objects, are based on the condition and situation of the problem. So there are no explicit definitions for rules and states; therefore, these two properties are defined in OA based on the problem.

Object-Automata Traffic Simulation

Recently, traffic simulation and modeling are interested for many researchers (Shi et al., 2007). In addition, CA is used as a simple and effective method

for simulation and modeling in many researches. Although this model is suitable for continues area, it has also been used in traffic simulation and modeling. The most important part of traffic is road which is always considered as an object because road is not a continues area, and there is always no road everywhere (deBy et al., 2001). In this case, defining the structure of pixels makes a big challenge for designer (Sun and Wang, 2007). By using an inter-mediate tool such as object-automata, the difficulty in designing the structure of cell is resolved. Then, in each object, CA is defined simply. At first, the network is divided into some objects; next, each object is split into many cells; and the rules among objects and cells are defined based on OA, and CA rules, respectively. In the following, the process of creating line object automata from road of the network is probed.

All roads in the network are considered as line. These entities must be changed to some line object-automata. Next, the neighbor of each object must be defined. After that, the state of each object must be defined. Different types of states can be defined based on the situation of the problem, some of which are exposited based on the condition of the network. So, to define the state of each object, two different types of traffic simulations are considered. First of all, only one car in the network is looked into. In this case, one car exists and moves in the network, so the state of each road in the network is assessed based on its moving. Secondly, many cars in the network are evaluated.

Only one car in the network: In this case, the state of each object can be defined as Boolean number. If the car is in the road, the state value of the road is considered one; if not, the state value of the road is considered zero. In this case, only one road in the network has the state of one and the others have zero value for their states. Beside the state of the roads, another parameter named “saturation” must be defined. This value shows the percentage of road which the car passed. In this case, only the road whose state is one has this parameter. To change the state of entities (cells or objects), some rules must be defined. In this problem, only one rule is needed which is defined as:

Rule: if the state of road is one and the ‘saturation’ reaches one, the state changes to ‘0’. In this case, the state of the neighbor object changes to ‘1.’ The saturation of both origin and destination roads also change to ‘0’.

The destination road of the car can be specified based on the path of the car and the connected roads in the

Page 5: Cellular Automata vs. Object-Automata in Traffic Simulation

International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014 www.ijrsa.org

65

network.

Many cars in the network: In this case, the state of each road is specified as a real number between ‘0’ to ‘1’. The state of each road is calculated by dividing the number of cars in the road into the sum of all cars in the network. The state of each road shows the percentage of total number of cars which the road has. Like the previous case, the “saturation” is calculated for each car. Saturation shows the percentage of road that car passed. Similar to the previous case, only one rule is needed which is defined as:

Rule: If the saturation of each car reaches ‘1’, the car changes the road. In the case, the states of origin and destination road are changed. When a car changes the road, the state of both origin and destination roads are changed. For origin road, the new state is defined as:

( ) 1( )

oldnew

S the number of carsS

the number of cars× −

= (2)

For destination road the new state is defined as: ( ) 1

( )old

newS the number of cars

Sthe number of cars× +

= (3)

Where, Sold and Snew are respectively the state of road before and after the car changes the road.

(A) (B) (C)

FIG. 5 (A) TWO ROADS OF THE NETWORK, (B) CA OF THE ROADS, (C) OA OF THE ROADS

Cellular-Automata Defined in Line Object-automata

The most reason of defining OA was the difficulty in defining a suitable structure for CA. As object can have different shape, the studied area is divided into objects easily. Based on the conditions of the problem, each object is divided into some cells. In this case, there is no need to define CA exactly fit to the shape of the object. It is possible to change the shape of objects and define CA in these objects. Although CA is defined in OA, the shape of object is not important. However, topology structure must be considered. In this paper, the network contains complex roads for which defining CA was difficult. So the network is divided into some objects based on the line OA method. By using this process, the complexity of the

network is removed. Regardless of the shape of object, each object can be divided into a set of cells. In this case, the shape of each object can be considered as a straight line, so the cells are easily used for each object. The comparison between defining only CA and the combination of CA and OA for roads network is shown in Figure 5.

Comparison between CA and OA in Traffic

CA has been used in many studied related to traffic, but in most of which the structure of the network was simple, so CA was easily used in these problems. However, more complex is the environment, less capability has CA. For example, in freeway intersection (Wahle et al., 2001) shown in Figure 6, there is no CA defined for eight parts of the networks, because it is hard to define cells agreeable with the other cells. So these eight parts were not considered in that study, while in reality it might happen some events in those areas. The lack of flexibility of CA was the most important reason of not being used in many fields. To overcome this shortage, OA is defined. So OA has the ability to change the shape and structure of CA, while keeping the topology structure of cellular. To show the efficiency of OA, the free way intersection is implemented by OA. Based on the concept of creating OA, the network is divided into some automata objects. In this case, twelve objects are obtained from the network. So each object is considered as a separate straight line (shown in Figure 6), then CA easily implemented for each part.

(a) (b)

FIG. 6 THE CA OF THE NETWORK ONLY FOR FOUR ROADS (Wahle et al., 2001), (B) CORRESPOND OA OF CA

FOR ALL ROADS

Implementation

To assess the efficiency of OA, two mentioned type of line object automata were implemented in the simulated network. At first, only one car moves from the origin point to its destination. The position of car in all snapshots is shown in Figure 7. In this case, two parameters (state and saturation) are considered for each road. In Table 1, these two parameters are

Page 6: Cellular Automata vs. Object-Automata in Traffic Simulation

www.ijrsa.org International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014

66

calculated for three roads through which the car passed. These two parameters are considered as zeros for the other roads. These two values are not zero only for roads in which the car is. In this case, only one road has nonzero state and saturation at each snapshot, which is illustrated in Table 1.

FIG. 7 ALL SNAPSHOTS OF MOVING ONE CAR

TABLE 1 THE STATE AND SATURATION OF ROADS IN NETWORK IN FIGURE 7 FOR ALL SNAPSHOT

Snapshot No Road State =1 Road State =0 Saturation 1 R1 R2, R3, R4 0.257582673 2 R1 R2, R3, R4 0.346772024 3 R1 R2, R3, R4 0.435961375 4 R1 R2, R3, R4 0.525150726 5 R1 R2, R3, R4 0.614340077 6 R1 R2, R3, R4 0.703529428 7 R1 R2, R3, R4 0.792718779 8 R1 R2, R3, R4 0.88190813 9 R1 R2, R3, R4 0.97109748 10 R2 R1, R3, R4 0.0477628 11 R2 R1, R3, R4 0.118423887 12 R2 R1, R3, R4 0.189084975 13 R2 R1, R3, R4 0.259746063 14 R2 R1, R3, R4 0.330407151 15 R2 R1, R3, R4 0.401068239 16 R2 R1, R3, R4 0.471729327 17 R2 R1, R3, R4 0.542390415 18 R2 R1, R3, R4 0.613051502 19 R2 R1, R3, R4 0.68371259 20 R2 R1, R3, R4 0.754373678 21 R2 R1, R3, R4 0.825034766 22 R2 R1, R3, R4 0.895695854 23 R2 R1, R3, R4 0.966356942 24 R3 R1, R2, R4 0.047422394 25 R3 R1, R2, R4 0.137943634 26 R3 R1, R2, R4 0.228464874

Secondly, many cars are put in the network. In Figure 8, the positions of all cars are shown at one snapshot. The roads of the network are converted into line objects. In the experienced network, one hundred road objects are in the network, so the state and the saturation are calculated for each object. The calculation of these two parameters for this snapshot is shown in Table 2. As seen in Figure 8 and Table 2, the maximum value of state belongs to road number 9 (shown as dashed box). This road also has approximately great value for its saturation. By assessing two parameters of road number 9, it can be

specified that most of the cars in this road are in the stoplight of the intersection, while in the opposite side of this intersection (Road number 26) there is no car in that road. These two parameters are worthwhile criteria for assessing the performance of traffic system of the network. They are also valuable value for traffic manager to make a right decision for transportation of the vehicles in the network.

TABLE 2 THE STATE AND SATURATION OF ROADS IN NETWORK OF FIGURE 8 FOR ONE SNAPSHOT

Id State Saturation Id State Saturation 1 0.0221 0.6455 51 0.0098 0.6290 2 0.0098 0.5464 52 0.0123 0.8475 3 0.0172 0.5832 53 0.0049 0.6590 4 0.0270 0.6101 54 0.0172 0.7224 5 0.0245 0.6160 55 0.0074 0.5447 6 0.0245 0.3444 56 0.0245 0.5152 7 0.0025 0.2286 57 0.0221 0.5847 8 0.0098 0.6122 58 0.0123 0.4827 9 0.0294 0.7658 59 0.0098 0.6602 10 0.0049 0.9113 60 0 0 11 0.0123 0.5909 61 0.0098 0.4132 12 0.0098 0.7903 62 0.0123 0.7318 13 0.0025 0.8157 63 0.0123 0.8849 14 0 0 64 0.0147 0.7085 15 0.0098 0.7235 65 0.0074 0.8543 16 0.0074 0.6185 66 0.0074 0.6917 17 0.0098 0.5219 67 0.0147 0.2660 18 0.0270 0.7331 68 0.0074 0.7305 19 0.0049 0.8942 69 0.0025 0.4657 20 0.0074 0.5185 70 0.0147 0.4884 21 0.0196 0.9000 71 0.0098 0.6285 22 0.0025 0.5562 72 0.0147 0.4418 23 0.0049 0.8824 73 0.0025 0.0790 24 0.0049 0.6137 74 0 0 25 0.0074 0.8668 75 0.0123 0.5301 26 0 0 76 0.0074 0.5821 27 0.0245 0.8597 77 0.0123 0.6218 28 0.0123 0.2908 78 0.0172 0.4724 29 0 0 79 0.0025 0.0068 30 0.0074 0.4785 80 0.0172 0.4812 31 0.0098 0.6459 81 0.0098 0.8517 32 0.0025 0.7562 82 0.0025 0.4109 33 0.0172 0.6186 83 0.0074 0.7756 34 0.0074 0.3815 84 0.0098 0.4426 35 0.0245 0.7428 85 0.0098 0.5040 36 0.0123 0.3761 86 0.0123 0.4946 37 0.0123 0.5832 87 0 0 38 0.0147 0.6361 88 0.0025 0.8406 39 0.0074 0.6332 89 0.0049 0.6362 40 0.0074 0.5707 90 0.0123 0.4535 41 0.0123 0.3288 91 0.0098 0.5404 42 0.0221 0.5676 92 0.0025 0.5949 43 0.0049 0.5132 93 0 0 44 0.0074 0.4593 94 0.0049 0.5724 45 0.0245 0.4035 95 0.0074 0.3807 46 0.0025 0.4108 96 0.0074 0.6505 47 0.0049 0.7218 97 0.0049 0.6205 48 0.0074 0.4060 98 0.0098 0.0593

Page 7: Cellular Automata vs. Object-Automata in Traffic Simulation

International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014 www.ijrsa.org

67

49 0 0 99 0.0074 0.3908 50 0.0074 0.3463 100 0.0025 0.8927

FIG. 8 ALL CARS SHOWN IN ONE SNAPSHOT

Conclusion

In this paper, at first the concept of CA was briefly expressed. Then a new type of entity automata named object-automata was introduced based on CA. Object-Automata removed CA limitation such as structure. Object-Automata did not have complexity of agent. Three types of object-automata were introduced based on the type of objects. For each type, some rules about the structure, neighbor, and so on were represented. Despite simplicity of CA, CA has two disadvantages. Firstly, the shape of CA is steady such as square, triangle and so on. Therefore, defining and fitting CA in many studies makes a big challenge. Secondly, CA is usually used in continuous environment. In this paper these two disadvantages of CA were resolved by defining OA. So, flexible entities are introduced which play the rule of CA with more capabilities.

In addition, the line-type of object-automata was implemented for traffic. The state and rules of object-automata were introduced based on the situation of the problem. Then the proposed method was implemented on experimental area. The state and rules defined for this problem were simple; however, it can be used by designer for making traffic decision. For example, the saturation introduced as additional states of OA can be used for managing the traffic signals of roads in the network. To improve the efficiency of OA, it is also possible that some complex state and rules are defined for the problem based on OA.

REFERENCES

BENJAMIN, S., JOHNSON, N. & HUI, P. 1996. Cellular

automata models of traffic flow along a highway

containing a junction. Journal of Physics A: Mathematical

and General, 29, 3119-3127.

BLUE, V. & ADLER, J. 2000. Modeling four-directional

pedestrian flows. Transportation Research Record:

Journal of the Transportation Research Board, 1710, 20-27.

BLUE, V. & ADLER, J. 2001. Cellular automata

microsimulation for modeling bi-directional pedestrian

walkways. Transportation Research Part B:

Methodological, 35, 293-312.

BLUE, V., EMBRECHTS, M. & ADLER, J. Year. Cellular

automata modeling of pedestrian movements. In, 1997.

BURSTEDDE, C., KLAUCK, K., SCHADSCHNEIDER, A. &

ZITTARTZ, J. 2001. Simulation of pedestrian dynamics

using a two-dimensional cellular automaton. Physica A:

Statistical Mechanics and its Applications, 295, 507-525.

CREMER, M. & LUDWIG, J. 1986. A fast simulation model

for traffic flow on the basis of Boolean operations.

Mathematics and computers in simulation, 28, 297-303.

DAGANZO, C. 1994. The cell transmission model: A

dynamic representation of highway traffic consistent

with the hydrodynamic theory. Transportation Research

Part B: Methodological, 28, 269-287.

DEBY, R. A., KNIPPERS, R. A., SUN, Y., ELLIS, M. C.,

KRAAK, M.-J., C.WEIR, M. J., GEORGIADOU, Y.,

RADWAN, M. M., VANWESTEN, C. J., KAINZ, W. &

SIDES, E. J. 2001. Principles of Geographic Information

System, The Netherlands, ITC.

DIJKSTRA, J., TIMMERMANS, H. & JESSURUN, A. 2000. A

multi-agent cellular automata system for visualising

simulated pedestrian activity. Bandini and Worsch [1],

29–36.

HU, Y. 1999. A New Cellular Automaton Model for Traffic

Flow. Communications in Nonlinear Science &

Numerical Simulation, 4, 264-267.

IN-NAMI, J. & TOYOKI, H. 2007. A two-dimensional CA

model for traffic flow with car origin and destination.

Physica A: Statistical Mechanics and its Applications, 378,

485-497.

LAN, L., CHIOU, Y., LIN, Z. & HSU, C. 2010. Cellular

automaton simulations for mixed traffic with erratic

motorcycles' behaviours. Physica A: Statistical Mechanics

and its Applications.

LI, K., GAO, Z. & NING, B. 2005. Cellular automaton model

for railway traffic. Journal of Computational Physics, 209,

179-192.

Page 8: Cellular Automata vs. Object-Automata in Traffic Simulation

www.ijrsa.org International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014

68

LI, X., JIA, B., GAO, Z. & JIANG, R. 2006. A realistic two-

lane cellular automata traffic model considering

aggressive lane-changing behavior of fast vehicle.

Physica A: Statistical Mechanics and its Applications, 367,

479-486.

LI, X., WU, Q. & JIANG, R. 2001. Cellular automaton model

considering the velocity effect of a car on the successive

car. Physical Review E, 64, 66128.

LIU, Y. 2009. Modeling Urban Development with

Geographical Information Systems and Cellular

Automata, New Yourk, Taylor & Francis Group.

LO, S. & HSU, C. 2009. Cellular automata simulation for

mixed manual and automated control traffic.

Mathematical and computer modelling.

MAERIVOET, S. & DE MOOR, B. 2005. Cellular automata

models of road traffic. Physics Reports, 419, 1-64.

MENG, J., DAI, S., DONG, L. & ZHANG, J. 2007. Cellular

automaton model for mixed traffic flow with

motorcycles. Physica A: Statistical Mechanics and its

Applications, 380, 470-480.

MURAMATSU, M., IRIE, T. & NAGATANI, T. 1999.

Jamming transition in pedestrian counter flow. Physica

A, 267, 487–498.

NAGATANI, T. 2009a. Freezing transition in bi-directional

CA model for facing pedestrian traffic. Physics Letters A.

NAGATANI, T. 2009b. Traffic states and fundamental

diagram in cellular automaton model of vehicular traffic

controlled by signals. Physica A: Statistical Mechanics

and its Applications, 388, 1673-1681.

NAGATANI, T. 2010. Jamming and freezing transitions in

CA model for facing pedestrian traffic with a soft

boundary. Physics Letters A.

NAGEL, K. 1996. Particle hopping models and traffic flow

theory. Physical Review E, 53, 4655-4672.

NAGEL, K. & PACZUSKI, M. 1995. Emergent traffic jams.

Physical Review E, 51, 2909-2918.

NAGEL, K. & SCHRECKENBERG, M. 1992. A cellular

automaton model for freeway traffic. J. Phys. I France, 2,

2221-2229.

NAGEL, K., STRETZ, P., PIECK, M., DONNELLY, R. &

BARRETT, C. 1997. TRANSIMS traffic flow

characteristics. Arxiv preprint adap-org/9710003.

NASSAB, K., SCHRECKENBERG, M., BOULMAKOUL, A.

& OUASKIT, S. 2006. Effect of the lane reduction in the

cellular automata models applied to the two-lane traffic.

Physica A: Statistical Mechanics and its Applications, 369,

841-852.

PLAN, S., COMMITTEES, S., COMMITTEES, P.,

PERFORMANCE, L., BOARD, M., COVERAGE, T. &

SERIALS, T. 2006. Formation of Spatiotemporal Traffic

Patterns with Cellular Automaton Simulation.

Transportation Research, 11, 26AM.

RICKERT, M., NAGEL, K., SCHRECKENBERG, M. &

LATOUR, A. 1995. Two lane traffic simulations using

cellular automata. Arxiv preprint cond-mat/9512119.

SCHADSCHNEIDER, A. & SCHRECKENBERG, M. 1997.

Traffic flow models with'slow-to-start'rules. Arxiv

preprint cond-mat/9709131.

SHI, X., WU, Y., LI, H. & ZHONG, R. 2007. Second-order

phase transition in two-dimensional cellular automaton

model of traffic flow containing road sections. Physica A:

Statistical Mechanics and its Applications, 385, 659-666.

SIMON, P. & NAGEL, K. 1998. Simplified cellular

automaton model for city traffic. Physical Review E, 58,

1286-1295.

SPYROPOULOU, I. 2007. Modelling a signal controlled

traffic stream using cellular automata. Transportation

Research Part C: Emerging Technologies, 15, 175-190.

SUN, T. & WANG, J. 2007. A traffic cellular automata model

based on road network grids and its spatial and temporal

resolution's influences on simulation. Simulation

Modelling Practice and Theory, 15, 864-878.

TAKAYASU, M. & TAKAYASU, H. 1993. 1//noise in a traffic

model. Fractals, 1, 860-866.

TIAN, R. 2009. The mathematical solution of a cellular

automaton model which simulates traffic flow with a

slow-to-start effect. Discrete Applied Mathematics, 157,

2904-2917.

VON NEUMANN, J. 1951. The general and logical theory of

automata. Cerebral mechanisms in behavior, 1–41.

VON NEUMANN, J. & BURKS, A. 1966. Theory of self-

reproducing automata.

WAHLE, J., BAZZAN, A., KLÜGL, F. & SCHRECKENBERG,

M. 2002. The impact of real-time information in a two-

route scenario using agent-based simulation.

Transportation Research Part C: Emerging Technologies,

Page 9: Cellular Automata vs. Object-Automata in Traffic Simulation

International Journal of Remote Sensing Applications Volume 4 Issue 1, March 2014 www.ijrsa.org

69

10, 399-417.

WAHLE, J., NEUBERT, L., ESSER, J. & SCHRECKENBERG,

M. 2001. A Cellular automaton traffic flow model for

online simulation of traffic. Parallel Computing, 27, 719-

735.

WAHLE, J. & SCHRECKENBERG, M. Year. A multi-agent

system for on-line simulations based on real-world data,

in'. In, 2001. Citeseer.

WHITE, R. 1998. Cities and cellular automata. Discrete

Dynamics in Nature and Society 2, 111–125.

WOLFRAM, S. 1984. Cellular automata as models of

complexity. Nature, 311, 419–424.

WOLFRAM, S. 1986. Theory and applications of cellular

automata.

YI, Z. & HOULI, D. 2007. Modeling Mixed Traffic Flow at

Crosswalks in Micro-Simulations Using Cellular

Automata. TSINGHUA SCIENCE AND TECHNOLOGY,

12, 214-222.