Inter national J our nal of Electrical and Computer Engineering (IJECE) V ol. 8, No. 5, October 2018, pp. 3149 3157 ISSN: 2088-8708 3149       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w       i                       l       c       m     Motor cycle Mo v ement Model Based on Mark o v Chain Pr ocess in Mixed T raffic Rina Mardiati 1 , Bambang R. T rilaksono 2 , Y udi S. Gondokary ono 3 , and Sony S. W ibo w o 4 1,2,3 School of Electrical Engineering and Informatics, Bandung Institute of T echnology , Indonesia 4 Department of Ci vil Engineering, Bandung Institute of T echnology , Indonesia Article Inf o Article history: Recei v ed August 9, 2017 Re vised June 25, 2018 Accepted July 7, 2018 K eyw ord: Mark o v Chain Maneuv er Intention V ehicle Mo v ement Mix ed T raf fic ABSTRA CT Mix ed traf fic systems are dynamically com ple x since there are man y parameters and v ariables that influence the interactions between the dif ferent kinds of v ehicles. Mod- eling the beha vior of v ehicles, especially motorc ycle which has erratic beha vior is still being de v eloped continuously , espe cially in de v eloping countries which ha v e hetero- geneous traf fic. T o get a better understanding of motorc ycle beha vior , one can look at maneuv ers performed by dri v ers. In this research, we tried to b uild a model of motor - c ycle mo v ement which only focused on maneuv er action to a v oid the obstacle along with the trajectories using a Mark o v Chain approach. In Mark o v Chain, the maneuv er of motorc ycle will described by state transition. The state transition model is depend on probability function which wil l use for determine what action will be e x ecuted ne xt. The maneuv er of motorc ycle using Mark o v Chain model w as v alidated by comparing the analytical result with the naturalistic data, with similarity is calculated using MSE. In order to kno w ho w good our proposed method can describe the maneuv er of mo- torc ycle, we try to compare the MSE of the trajectory based on Mark o v Chain model with those using polynomial approach. The MSE results sho wed the performance of Mark o v Chain Model gi v e the smallest MSE which 0.7666 about 0.24 better than 4 th order polynomial. Copyright c 201x Institute of Advanced Engineering and Science . All rights r eserved. Corresponding A uthor: Rina Mardiati Department of Electrical Engineering, UIN Sunan Gunung Djati Bandung Jl. A.H. Nasution No. 105 Bandung 40614, Indonesia r mardiati@uinsgd.ac.id 1. INTR ODUCTION T oday , Indonesian transportation problems are increasingly being encountered in our daily life. Se v- eral economic and social moti v ations can be rela ted to the need to minimize the time s pent in mot orc y c le for transportation and consequently their related pollution problems. An additional problem w orth mentioning is the need to reduce traf fic accidents, a human and social cost that is related not only inadequate dri ving, b ut also to the planning of the flo w conditions [1]. Due this moti v ations, the literature on traf fic phenomena is already v ast and characterized by contri b ut ions co v ering modeling aspects, statement of problems, qualitati v e analysis, and particularly de v eloped simulation generated by applications. Continuing this ef forts, there are man y litera- ture of traf fic flo w theories and models ha v e been de v eloped, b ut researcher generally agree that modeling has not yet reached a satisfying le v el. Study of traf fic flo w are become important since man y reasons behind that, such as: 1) it is necessary to de v elop traf fic model which can describes the real phenomena, 2) traf fic model can support for de v eloping intelligent transportation system (ITS) whose related with safety dri ving syste m, 3) traf fic model support for future i ssue about intelligent car [2]. So, there are man y researchers who de v eloped intelligent transportation system in order to minimize the number of traf fic accident [3] [4] [5]. Mix ed traf fic systems are dynamically comple x since there are man y parameters and v ariables t hat influence the interactions between the dif ferent kinds of motorc ycles. These interactions can be described as the beha vior occurring in traf fic. V ehicle beha vior is influenced by internal and e xternal f actors. Internal J ournal Homepage: http://iaescor e .com/journals/inde x.php/IJECE       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w       i                       l       c       m     DOI:  10.11591/ijece.v8i5.pp3149-3157 Evaluation Warning : The document was created with Spire.PDF for Python.
3150 ISSN: 2088-8708 f actors are the status of the motorc ycle such a s dri v er psychology , motorc ycle position, steering angle, speed, etc. Meanwhile, e xternal f actors are en vironmental conditions such as the position of other v ehicles, road borders, pedestrians, etc. Modeling the beha vior of the motorc ycle is still being continuously de v eloped, especially in de v el- oping countries which ha v e the characteristics of mix ed traf fic. T o get a better understanding of motorc ycle beha vior , one can look at maneuv ers performed by dri v ers. Maneuv er here can also be called as a mo v ement performed by the motorc ycle which is a part of motorc ycle’ s mo v ement to change a lane and also to a v oid obstacles or slo wer v ehicle in front of him. Modeling the maneuv er t hat can adequately simulate actual situations has man y benefits, especially to solv e problems in t he field of transportation. M odeling of maneuv ers can also describe ho w a dri v er interacts within a traf fic system. In order to reach this goal, v arious methods ha v e been de v eloped to obtain a model that can adequately simulate actual situations. Based on the literature, se v eral methods ha v e been proposed for modeling v ehicle mo v ement, such as: Rule Based Model [6], Cellular Automata [7] [8] [9], and Social F orce Model [10] [11] [12]. Each method has its o wn deficiencies and adv antages. Rule Based Model is quite good at describing v ehicle maneuv ers in traf fic b ut it only w orks well at lo w traf fic density . Problems will occur when Rule Based Model is implemented on high-density traf fic systems, making the simulation beha v e in an unrealistic manner . Celullar Automata (CA) describes v ehicle maneuv ers better than the rule-based system b ut has the disadv antage that its position updating rules are deterministic. Lately , Social F orce Model (SFM) has been applied to describe v ehicl e maneuv ers and it performed better than both Rule Based Model and Celullar Automata. SFM can describe the mo v ement of v ehicles based on a v ector -based approach. In SFM, which includes a mo v ement model and the decision-making process of the dri v er , v ehicle beha vior is described by the sum of se v eral v ector forces (acceleration force, repulsi v e force and attracti v e force). Although SFM can describe v ehicle mo v ement better than Rule Based or CA, this method does not input some parameters that ha v e a lar ge ef fect on ac h i e ving a realistic model, such as dri v er psychology or a probabilistic model for dri v er characteristics. Mark o v Chain w as broadly use for modeling traf fic for dif ferent purposes, such as to reduce v ehicle emission [13], short-term traf fic flo w forecasting [14], modeling the multi-traf fic signal-control synchronization [15], traf fic state prediction [16], tra v el time estimation [17], etc. Ho we v er , no one has modeled the motorc ycle maneuv er using the Mark o v Chain model. In this research, we tried to b uild a model of motorc ycle mo v ement which only focused on maneuv er action to a v oid the obstacle along with the trajectorie s using a Mark o v Chain approach. In Mark o v Chain, the maneuv er of motorc ycle will described by state transition. The state transition model is depend on probability function which will use for determine what action will be e x ecuted ne xt. The maneuv er of motorc ycle using Mark o v Chain model w as v alidated by comparing the analytical result with the naturalistic data, with similarity is calculated using MSE. In order to kno w ho w good our proposed method can describe the maneuv er of motorc ycle, we try to compare the MSE of the trajectory based on Mark o v Chain model with those using polynomial approach that has been done in pre vious research [18]. This paper is or g anized as follo ws. In Section 2, modeling motorc ycle maneuv ers using a Mark o v chain process is presented. The simulation and analysis of applying this model are discussed in Section 3. Finally , in Section 4 this paper is concluded by stating that the Mark o v chain process can b e implemented in modeling motorc ycle mo v ement trajectories for certain maneuv ers. 2. THE PR OPOSED METHOD This research tries to b uild a model of maneuv er beha vior along with the trajectories using a Mark o v Chain approach. In a Mark o v Chain process, the dri v er will mak e decisions to determine what actions will be carried out in a certain en vironment. V ehicle will be in a certain position, mo ving at a certain speed and steering angle at time t , denoted as motorc ycle state (internal information). Ne xt, motorc ycle will recei v e e xternal information from its en vironment, s uch as the positions and v elocities of v ehicles around it, for further processing to determine what action is to be tak en by motorc ycle . There are se v eral steps must be e x ecuted to b uild a motorc ycle maneuv er model using Mark o v Chain: 1) Define set of states and actions, 2) Define the transition probability function, and 3) State mapping function. 2.1. Set of States and Actions A state is the condition or status of motorc ycle agent, which is a function of position ( x; y ) , speed ( v ) and direction of steering maneuv ers ( ). Meanwhile, action is described by a function of the maneuv er m 2 IJECE V ol. 8, No. 5, October 2018: 3149 3157   Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3151 f 0,1,2 g with 0, 1, and 2 corresponds to no maneuv er , right maneuv er , and left maneuv er respecti v ely . Simi larly , acceleration a 2 f 0,1,2 g with 0, 1, and 2 corresponds to fix ed speed, acceleration, and deceleration. In the Mark o v Chain process, the action of the motorc ycle is determined by the probability of a transition states. There are ten states to describe the mo v em ent of motorc ycle, along with nine actions. The set of actions ( A i ) and states ( S i ) that are used for the motorc ycle maneuv ers can be seen in T able 1. T able 1. Set of States and Actions States Definition Actions Definition S 0 V ehicle with speed 0 km/h A 1 Increases speed with no maneuv er S 1 V ehicle with speed 3 km/h A 2 Increases speed with right maneuv er S 2 V ehicle with speed 6 km/h A 3 Increases speed with left maneuv er S 3 V ehicle with speed 9 km/h A 4 Decreases speed with no maneuv er S 1 L V ehicle at a speed of 3 km/h with left steering angle A 5 Decreases speed with right maneuv er S 2 L V ehicle at a speed of 6 km/h with left steering angle A 6 Decreases speed with left maneuv er S 3 L V ehicle at a speed of 9 km/h with left steering angle A 7 Decreases speed with right maneuv er S 1 R V ehicle at a speed of 3 km/h with left steering angle A 8 Fix ed v elocity with right maneuv er S 2 R V ehicle at a speed of 6 km/h with left steering angle A 9 Fix ed v elocity with left maneuv er S 3 R V ehicle at a speed of 9 km/h with left steering angle 2.2. T ransition Pr obabilities A maneuv er is the mo v ement to change the direction of a v ehicle to mo v e from one lane to another . Maneuv ers in this study are infl u e nced by se v eral parameters, including the internal state of the v ehicle as well as the e xternal conditions, as sho wn in Figure 1. d αβ v β d β 1 D B r D B l v β 1 w β D O V D O H V ehicle β V ehicle β 1 V ehicle α W R Figure 1. Illustration of Maneuv er’ s P arameters The parameter in Figure 1 are d  ; v ; w ; d 1 ; d 2 ; : : : ; d n ; v 1 ; v 2 ; d B r ; d B l ; D O H ; D O V ; and W R . Where d  is a distance between motorc ycle and v ehicle , v is speed of v ehicle , w is the width of v ehicle ; ( d 1 ; d 2 ; : : : ; d n ), distance between motorc ycle and v ehicles to the left and right, v 1 is a speed of v ehicle to the left, v 2 is speed of v ehicle to the right, d B r is the distance between v ehicle and the right border , d B l , distance between v ehicl e and the left border , D O H is a horizontal of fset distance to objects that are in front of the v ehicle, D O V is the v ertical of fset distance to v ehicles to the left or the right of the v ehicle, and W R is the width of road. There are tw o steps performed to b uild the transition probability function. Firstly , to model the prob- ability of maneuv erability function of the rider . Secondly , to model the probability of maneuv ering direction (left or right) to be tak en by the motorc ycle. 2.2.1. T ransition Pr obability of V ehicle Maneuv ers The biggest f actor that influenced the maneuv er is if there is an obstacle in front of the motorc ycle. As function to model the desire of maneuv ering of the dri v er , ne g ati v e e xponential function can be used to obtain a great v alue for small distances and a small v alue for lar ge distances . In addition, a critical distance f actor ( D c ) should be added, which represents the critical distance where the motorc ycle must do maneuv er . If a maneuv er V ehicle Mo vement Model Based on Mark o v Chain Pr ocess in Mixed T r af fic (Rina Mar diati) Evaluation Warning : The document was created with Spire.PDF for Python.
3152 ISSN: 2088-8708 cannot be carried out for e xample because there are v ehicle s to the right and left, then the action is decelerate the speed. The maneuv er intention probability of motorc ycle stated as P can be e xpressed as follo ws. P = ( e k 1 ( d  D c ) ; for d  > D c 1 ; for d  D c (1) Where d  is the distance between motorc ycle and the v ehicle in front of it (v ehicle ), D c is represents the critical distance where the motorc ycle must do maneuv er or decelerate the speed, k 1 is a constant that sho ws an increased slope rate of a ne g ati v e e xponential curv e as a function of the distance between the tw o v ehicles. Ph ysically , a small v alue of k 1 indicates that the dri v er w ants to maneuv er despite the distance to the v ehicle in front still being quite lar ge (alert dri v er), while a high v alue of k 1 indicates that the dri v er w ants to maneuv er when the distance to the v ehicle in front is already v ery small (a dri v er who is reluctant to maneuv er unless pressed). 2.2.2. Pr obability Estimation of Maneuv er Dir ection When the decision to maneuv er based on P e xceeds a certain threshold v alue, the ne xt step is mod- eled the optimum maneuv er direction. The possible directions for the maneuv er are determined by the condition of the road, the borders to the right and left, and other v ehicles in the vicinity . In this subsection, we b uild ma- neuv er direction probability model for six scenarios that commonly occur in traf fic, as sho wn in Figure 2. This scenario is stil l possible to be de v eloped further in a follo w-up study , which will be tailored to observ ations in the field and processing the data obtained. The deri v at ion process of the probability model has been done in a pre vious research [18]. T able 2. Maneuv er Direction Probabilities Scenario Pr obability of Maneuv er Dir ection There are no obstructions on the left nor right P L = e k 3 ( d B l d C l ) W R k 2 l P R = e k 3 ( d B r d C r ) W R k 2 r There is an obstruction to the right of the motorc yle P L = e k 3 ( d B l d C l ) W R k 2 l P R = ( 1 e k 4 ( d 1 d 1 C ) , for d 1 > d 1 C 0 , for d 1 d 1 C There is an obstruction to the left of the motorc ycle P L = ( 1 e k 5 ( d 1 d 1 C ) , for d 1 > d 1 C 0 , for d 1 d 1 C P R = e k 3 ( d B r d C r ) W R k 2 r There are obstruction to the right and to the left of the motorc ycle P L = ( 1 e k 5 ( d 1 d 1 C ) , for d 1 > d 1 C 0 , for d 1 d 1 C P R = ( 1 e k 4 ( d 1 d 1 C ) , for d 1 > d 1 C 0 , for d 1 d 1 C There is a border on the left or on the right P L = 0 P R = 1 There are boarders and obstructions P L = e k 3 ( d B l d C l ) W R k 2 l P R = ( 1 e k 4 ( d 1 d 1 C ) , for d 1 > d 1 C 0 , for d 1 d 1 C T able 2 sho ws the maneuv er direction probability function. P L denotes the probability of a left direction maneuv er and P R denotes the probability of a right direction maneuv er , with k 2 ; k 3 ; k 4 and k 5 as constants. P arameter denotes as a function of horizontal of fset distances to objects that are in front of motorc ycle ( D O H l ; D O H r ) , where w = d O H l + d O H r , l = D O H l D O H l + d O H r and r = D O H r D O H l + D O H r . d C r and d C l denotes critical distance with motorc ycle on the left and right. The v alue can be set to the v alue that describes the habits of maneuv ering direction of Indonesian dri v er . IJECE V ol. 8, No. 5, October 2018: 3149 3157 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3153 2.3. State-Mapping Function After the transiti on probability function were de termined, then we need to b uild a mapping func- tion which describes the state-action mapping of decision making beha vior of dri v er . Mathematically , this is e xpressed by P( S t +1 j S t ; S 1 ; S ; S 3 ; ; m; a ) = P( S i +1 j S t ; m; a ) (2) with P( S i +1 j S i ; m i ; a i ) denotes probability function of maneuv er and acceleration at time t . (a) (b) (c) (d) (e) (f ) Figure 2. T raf fic Scenario 3. RESEARCH METHOD The research method consists of three main steps: 1) Data preprocessing, 2) Simulation, and 3) Com- paring the simulation results with actual data. Data preprocessing w as be gin with doing the naturalistic obser - v ation using video streaming which ensures that the normal beha vior can be observ ed and the data collected are not af fected by the presence of researchers. Ne xt, in order to obtained pix el coordinate which represents motorc ycle’ s trajectory , coordinates transformation to con v ert the pix el coordinate to real-w orld coordinate as we seen on Figure 3. The preprocessing of data in this research is similar to those in our pre vious research [18]. (a) (b) (c) Figure 3. The flo w of data preprocessing, (a) T ar geted motorc ycle; (b) Maneuv ers trajectory; (c) Photo coordi- nate in a pix el 4. SIMULA TION RESUL TS AND DISCUSSION The simulation results sho w that motorc ycle mo v ement modeling based on a Mark o v Chain process w as successf ully implemented. The Mark o v Chai n model w as e v aluated by looking at a plotti ng diagram. There are three diagrams in Figure 4 which describes that Mark o v Chain w as successfully implemented to modeled the manue v er of motorc ycle (a maneuv er diagram, a state transition diagram, and an acceleration diagram). In Figure 4 (a), the changes of each state and speed for e v ery v ehicle during the simulation period can be seen clearly . The blue motorc ycle change his state in order to get a sa v ely dri ving. Besides, Figure 4 (c), we can see the beha vior of the blue motorc ycle making three times maneuv er during simulation time, at the 5 th , the 19 th , and the 40 th time step of the duration. In that time, the blue motorc ycle sees a v ehicle in front of V ehicle Mo vement Model Based on Mark o v Chain Pr ocess in Mixed T r af fic (Rina Mar diati) Evaluation Warning : The document was created with Spire.PDF for Python.
3154 ISSN: 2088-8708 him and try to a v oid the v ehicle by making a maneuv er , while considering the border beside him to calculate the maneuv er probability . The performance of Mark o v Chain model is v erified by comparing actual maneuv er trajectory with the trajectory from Mark o v Chain model. Figure 5 (a) sho ws the actual trajectory data of ten motorc ycle’ s that has tak en independently at dif ferent time b ut plotted in one figure. It is interesting to note that there are dif ferent types of maneuv er style in that trajectory , for e xample motorc ycle 1 mak es a comple x maneuv er pattern as to a v oid the obstacle. In the other hand, motorc ycle 3 and motorc ycle 6 tak e a simple maneuv er with considerable distance to complete this maneuv er . Figure 5 (b) sho ws the track of Mark o v Chain model using (a) (b) (c) Figure 4. Mark o v Chain simulation, (a) State-transition diagram; (b) Acceleration diagram; (c) Maneuv er decision diagram that only accommodate one maneuv ering angle which is 45 . W e observ ed in this figure that Mark o v Chain model successfully follo w the trend of actual maneuv er b ut cannot produce a smooth pattern. T o impro v e the situation, in Figure 5 (c), we add additional states of maneuv er s teering angle which are 22 : 5 ; 45 ; 62 : 5 to accommodate a smoother trajectory pattern which is v ery close to the actual one. As a comparison we plot the curv e fitting of the track using static polynomial fitting which are 2 nd order polynomial, 3 r d order polynomial, and 4 th order polynomial as sho wn in Figure 5 (d) (e) (f). In those figures, we observ ed that polynomial can fit the actual trajectory as f ar as the trajectory is short and simple curv e such as the maneuv er of motorc ycle 2, 4, and 9. Ho we v er , polynomial fitting has dif ficulty to track a comple x maneuv er such as the maneuv er of motorc ycle 1. This polynomial fitting also cannot track the slight maneuv er such as maneuv er of motorc ycle 7 and 10. IJECE V ol. 8, No. 5, October 2018: 3149 3157 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3155 (a) (b) (c) (d) (e) (f) Figure 5. Manually track of ten dif ferent motorc ycle’ s maneuv er , (a) actual motorc ycle’ s maneuv er track (b) approximation of maneuv er’ s track using Mark o v Chain with = 45 (c) approximation of maneuv er’ s track using Mark o v Chain with = 22 : 5 ; 45 ; 62 : 5 (d) approximation of maneuv er’ s track using 2 nd order polynomial (e) approximation of maneuv er’ s track using 3 r d order polynomial (f) approximation of maneuv er’ s track using 4 th order polynomial Performance of each fitting method is sho wn in T able 3. In T able 3, we observ ed that Mark o v Chain model gi v e the s mallest MSE which 0.7666 about 0.24 better than 4 th order polynomial. Ev en though in most cases the Mark o v Chain model using 22.5, 45, 62.5 has better MSE b ut in particular case, for e xample in motorc ycle 6, the performance of this model is w orse than polynomial fitting, since the maneuv er is v ery comple x. T able 3. Mean Square Error of Motorc ycle Maneuv er T rajectory T racking V ehicle 2 nd order 3 r d order 4 th order = 45 = 22 : 5 ; 45 ; 62 : 5 1 2.7076 2.6887 2.1865 1.8073 0.6907 2 0.0849 0.0640 0.0626 0.4998 0.1472 3 1.0267 0.8822 0.8655 1.6302 0.4086 4 0.2525 0.2521 0.2509 0.9108 0.4336 5 0.8472 0.8092 0.6743 1.1847 0.2783 6 1.7213 1.3810 1.2796 3.8066 2.3199 7 1.9405 1.9405 1.9344 2.0455 0.6516 8 1.4145 1.4056 1.3684 2.0102 0.5179 9 0.2622 0.2022 0.1966 2.0889 0.7340 10 2.1705 1.6028 1.2978 3.8687 1.4841 A v erage 1.2428 1.1228 1.0117 1.9853 0.7666 5. CONCLUSION In this research, a simple model based on a Mark o v Chain process w as implemented to descr ibe motorc ycle maneuv er using ten states and nine actions. Besides, the probability function of maneuv er intention V ehicle Mo vement Model Based on Mark o v Chain Pr ocess in Mixed T r af fic (Rina Mar diati) Evaluation Warning : The document was created with Spire.PDF for Python.
3156 ISSN: 2088-8708 w as introduced in six scenarios which inte grated to the state-mapping function of Mark o v Chain Model. The maneuv er of motorc ycle using Mark o v Chain model w as v erified by comparing the analytical result with the naturalistic data which gi v e small MSE. This methods also compare with static polynomial fitting to kno w ho w good is Mark o v Chain can describe a motorc ycle maneuv er mo v ement. As a result, we found that MSE of Mark o v Chain model is smaller than static polynomial fitting approach. A CKNO WLEDGMENT The authors w ould lik e to thank the Indonesia Endo wment Fund for Education (LPDP Indonesia) and the Indonesian Ministry of Religious Af f airs for their financial support of this study . REFERENCES [1] N. Bellomo and C. Dogbe, “On the modeling of traf fic and cro wds: A surv e y of models, speculations, and perspecti v es, SIAM Re vie w , v ol. 53, no. 3, pp. 409–463, 2011. [Online]. A v ailable: https://doi.or g/10.1137/090746677 [2] R. Mardiati, N. Ismail, and A. F aroqi, “Re vie w of microscopic model for t raf fic flo w , ARPN J ournal of Engineering and Applied Sciences , v ol. 9, no. 10, pp. 1794–1800, October 2014. [3] K. Gopalakrishna and S. Hariprasad, “Real-time f atigue analysis of dri v er through iris recognition, In- ternational J ournal of Electrical and Computer Engineering (IJECE) , v ol. 7, no. 6 , pp. 3306–3312, 2017. [4] S. K. V enkata, An intelligent online v ehicle tyre pressure monitoring system, International J ournal of Electrical and Computer Engineering , v ol. 2, no. 3, p. 301, 2012. [5] T . S. Guna w an, A. Mutholib, and M. Kartiwi, “Performance e v aluation of automatic number plate recog- nition on android smartphone platform, International J ournal of Electrical and Computer Engineering , v ol. 7, no. 4, p. 1973, 2017. [6] L. Chong, M. M. Abbas, A. M. Flintsch, and B. Higgs, A rule-based neural net- w ork approach to model dri v er naturalistic beha vior in traf fic, T r ansportation Resear c h P art C: Emer ging T ec hnolo gies , v ol. 32, pp. 207 223, 2013. [Online]. A v ailable: http://www .sciencedirect.com/science/article/pii/S0968090X12001210 [7] Y . Zhang and H. Duan, “Modeling mix ed traf fic flo w at crossw alks in microsimulations using cellular automata, Tsinghua Science and T ec hnolo gy , v ol. 12, no. 2, pp. 214–222, April 2007. [8] J. X. Ding, H. J. Huang, and Q. T ian, A mix ed traf fic flo w m od e l based on a modified cellular automaton in tw o-lane system, in 2009 International J oint Confer ence on Computational Sciences and Optimi za- tion , v ol. 2, April 2009, pp. 124–126. [9] Z. dong Zhang, Y . f ang yang, W . Qi, A. Chariete, and X. xiang Lin, A cellular automata traf fic flo w model considering b us lane changing beha vior wit h scheduling parameters, Discr ete Dynamics in Natur e and Society , v ol. 2015, p. 7 pages, januari 2015. [10] T . Ming and J. Hongfei, An approach for calibration and v alidation of the social force pedestrian model, 2011, kalibrasi dan V alidasi P arameter pada SFM. [11] D. N. HUYNH, M. BOL TZE, and A. T . VU, “Modelling mix ed traf fic flo w at signalized intersectionusing social force model, J ournal of the Eastern Asia Society for T r ansportation Studies , v ol. 10, pp. 1734– 1749, 2013. [12] W . Zeng, H. Nakamura, and P . Chen, A modified social force model for pedestrian beha vior simulation at signalized crossw alks, Pr ocedia - Social and Behavior al Sciences , v ol. 138, pp. 521 530, 2014. [Online]. A v ailable: http://www .sciencedirect.com/science/article/pii/S1877042814041536 [13] J. Sun, C. Li, J. Ding, J. Y ang, and Z. Liu, A mark o v chain based traf fic flo w control model for re- ducing v ehicles’ co 2 emissions, in V ehicular Electr onics and Safety (ICVES), 2015 IEEE International Confer ence on . IEEE, 2015, pp. 250–255. [14] S. Sun, G. Y u, and C. Zhang, “Short-term traf fic flo w forecasting using sampling mark o v chain method with incomplete data, in Intellig ent V ehicles Symposium, 2004 IEEE . IEEE, 2004, pp. 437–441. [15] J. B. Clempner and A. S. Pozn yak, “Modeling the multi-traf fic signal-control synchronizat ion: A mark o v chains g ame theory approach, Engineering Applications of Artificial Intellig ence , v ol. 43, pp. 147–156, 2015. [16] C. Antoniou, H. N. K outsopoulos, and G. Y annis, “T raf fic state prediction using mark o v chain models, in Contr ol Confer ence (ECC), 2007 Eur opean . IEEE, 2007, pp. 2428–2435. [17] J. Y eon, L. Elefteriadou, and S. La wphongpanich, “T ra v el time estimation on a free w ay using discrete IJECE V ol. 8, No. 5, October 2018: 3149 3157 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3157 time mark o v chains, T r ansportation Resear c h P art B: Methodolo gical , v ol. 42, no. 4, pp. 325–338, 2008. [18] R. Mardiati, B. R. T rilaksono, Y . S. Gondokaryono, and S. S. Sulaksono, “Mot orc ycl es trajectory tracking model based on polynomial least-squares approximation, Advanced Science Letter s , v ol. 23, no. 5, pp. 4537–4541, 2017. BIOGRAPHY OF A UTHORS Rina Mardiati recei v ed her Bachelor de gree in Mathematics Education from Uni v ersitas Pen- didikan Indonesia (UPI) in 2006 and Master de gree in Electrical Engineering from Institut T eknologi Bandung (ITB) in 2009. She is no w a PhD student at the School of Electrical Engi- neering and Informatics, ITB. Her research is in the fields of mathematical modeling, simulation, traf fic modeling and intelligent systems. She is af filiated with IEEE as a student member . Bambang Riyanto T rilaksono recei v ed his Bachelor de gree in Electrical Engineering from ITB, and Master and Doctorate de gre es from W aseda Uni v ersity , Japan. He is no w a professor at the School of Electrical Engineering and Informatics, ITB. His research interests include rob ust control, intelligent contr ol & intelligent systems , discrete e v ent systems, control applications, telerobotics, embedded control systems, and robotics. Y udi Satria Gondokary ono Gondokaryono recei v ed his Bachelor de gree in Electrical Engineering from ITB, and Master and Doctorate de gree from Ne w Me xico State Uni v ersity . He is no w an Assistant Professor in School of Electrical Engineering and Informatics at School of Electrical Engineering and Informatics, ITB. His resea rch interests include human computer interaction, real- time, and embedded systems. Sony Sulaksono W ibo w o recei v ed his Bachelor and Master de grees in Ci vil Engineering from ITB, and Doctorate de gree from Chualalangk orn Uni v ersity . He is no w an assistant professor at the Department of Ci vil Engineering, ITB. His research interests include tra v el beha vior , public trans- portation and transport planning, non-motorized transportation, transportation and the en vironment. V ehicle Mo vement Model Based on Mark o v Chain Pr ocess in Mixed T r af fic (Rina Mar diati) Evaluation Warning : The document was created with Spire.PDF for Python.