Referring to the Nagel–Schreckenberg’s (NaSch) model, we have studied the impact of agent and diligent driver into the micro traffic model in the case of evacuation. This study is attention to the deceleration that added in the micro traffic model. The effect of deceleration to simulation for evacuation from disaster area is considered. The traffic flow property is studied by analyzing the time-space diagram. The simulation results show that deceleration caused the evacuation time increases when we compare it by without deceleration

Kohei, Arai

Tri, Harsono

English

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The 13th Industrial Electronics Seminar 2011 (IES 2011)   Electronic Engineering Polytechnic Institute of Surabaya (EEPIS), Indonesia, October 26, 2011    ISBN: 978-979-8689-14-7  463    Deceleration in The Micro Traffic Model and Its Application to Simulation   for Evacuation from Disaster Area    Tri Harsono1,2, Kohei Arai1 1 Department of Information Science Saga University, Saga Japan 2 Electronic Engineering Polytechnic Institute of Surabaya (EEPIS), Surabaya Indonesia triharsono69@yahoo.com; arai@is.saga-u.ac.jp    Abstract  Referring to the Nagel–Schreckenberg’s (NaSch) model, we have studied the impact of agent and diligent driver into the micro traffic model in the case of evacuation. This study is attention to the deceleration that added in the  micro  traffic  model.  The  effect  of  deceleration  to simulation  for  evacuation  from  disaster  area  is considered.  The  traffic  flow  property  is  studied  by analyzing  the  time-space  diagram.  The  simulation results  show  that  deceleration  caused  the  evacuation time  increases  when  we  compare  it  by  without deceleration.  Keywords: deceleration, agent and diligent driver, micro traffic model, evacuation.   1. Introduction The  traffic  dynamics  model  has  attracted  much attention of researchers in the fields of statistical physics and applied mathematics by using the advancement of computer technology [1-5]. The models can be divided in two kinds, continuous and discrete. Some continuous models have been carried out to explain the empirical findings [6-8] [4]. While the discrete models that have simpler structure than the continuous models and have fast performance in simulating have been widely used to model traffic flow, they have used the cellular automata (CA)  approach.  In  1992,  Nagel  and  Schreckenberg (NaSch)  proposed  a  traffic  cellular  automata  (TCA) model  for  single-lane  traffic  flow  that  was  able  to reproduce  several  characteristics  of  real-life  traffic flows, e.g., the spontaneous  emergence  of  traffic  jams [9]. The NaSch model contains four consecutive steps: acceleration,  deceleration,  randomization  and  vehicle movement. The NaSch model is a minimal model in the sense that all the four steps are necessary to reproduce the  basic  features  of  real  traffic  flows.  The  additional rules  have  been  added  to  the  NaSch  model  by researchers  depending  on  their  field  of  study.  One  of extension has been conducted related with the driving behavior; it is about diligent driver [10-12]. They have reflected  diligent  driver  as  an  additional  speed  in  the micro traffic model and implemented to simulation for evacuation from disaster area to get the effect of diligent driver  towards  the  evacuation  time.  The  other extensions pay attention to the deceleration step [13-15]. They  have  assumed  that  a  vehicle  has  an  expectation effect  on  the  leading  vehicle,  so  the  velocity  is  not restricted by the current gap. In connection with the deceleration, a vehicle has a limited capability of deceleration, it can’t suddenly drop its velocity and it has to decelerate in advance to avoid a collision  with  the  leading  vehicle  [15-16].  A  model considering  the  limited  capability  of  deceleration  had been presented by [16]. They expressed the safe driving equation  in  a  complex  form.  Otherwise,  a  simple method to reflect the deceleration in advance effect had been  proposed  by  [15].  They  stated  that,  to  keep  safe driving, a vehicle has to decelerate its velocity when it drives at a higher speed than the leading vehicle. The velocity of the vehicle may be restricted by a lower value than the current space gap. In  this  study,  we  have  added  deceleration  in advance  to  the  traffic  model  in  the  previous  work  by referring  to  the  [15].  The  effects  of  deceleration  have been  considered  by  using  various  numbers  of  diligent drivers in the case of evacuation from disaster area.   Computer Science and Engineering, Information Systems Technologies and Applications 464 2. Model As we said in the previous section that the NaSch model [9] is one kind of the discrete model for traffic flow. By using CA, they presented a simple traffic flow model for one lane of traffic. The road is divided into L cells on a one-dimensional array in which each cell can be either empty or occupied by a vehicle. The velocity of each vehicle is v = 0, 1, …, or vmax. All vehicles move from  the  left  to  the  right  with  periodic  boundary conditions. At each discrete time step  1   t t , all the vehicles simultaneously update their states according to three  consecutive  rules  [17]  (note  that  the  original formula of NaSch  model  [9]  had  four  rules,  they  had separated acceleration and breaking):   (R1) acceleration and braking   ) ( , , 1 ) ( min ) 1 ( max t gs v t v t v i i i                     (1) (R2) randomization   1 ) ( , 0 max ) 1 (    t v t v i i                             (2) with probability p (R3) vehicle movement ) 1 ( ) ( ) 1 (     t v t x t x i i i                                     (3) In which vi and xi denote the velocity and position of the ith  vehicle  respectively;  while  vmax  is  the  maximum velocity; gsi = xi+1 – xi – 1 denotes the number of empty cells  in  front  of  the  ith  vehicle;  and  p  is  the randomization probability (sometimes called slowdown probability), it has the meaning that if a random number [0:1] is lower than p, the randomization occurs. Based on [15], a vehicle will decelerate in advance when its velocity is  higher  than  the  leading  one.  The driver  estimates  the  velocity  differencee v  ,  when e v  > 0 means that the current (following) vehicle is approaching  the  leading  one.  If  the  velocity  of  the follower and the leader do not change, the gap should be gsi(t) - e v    at time step t + 1. They proposed that the driver will decelerate in advance when e v  > 0, so the gap at time step t + 1 should be lower than gsi(t) and larger than gsi(t) - e v  . Then the estimated gap at time step  t+1  is  determined  by    eiei v t gs t gs     ) ( , 0 max ) ( .  In  which  the  floor function    x   is defined by the largest integer no larger than x;     denotes a constant value and in this study, we  use   =0.5.  The  velocity  of  the  following  vehicle will be restricted by the estimated gap. If the condition is e v    ≤ 0, it means that the leading vehicle is driving away; the follower does not have to decelerate. Referring to the estimated gap above, for two lanes of  traffic,  a  modified  NaSch  model  by  considering deceleration  in  advance  is  proposed  by  the  following rules: (1) acceleration   max , , , 1 ) ( min ) 1 ( v t v t v j i j i          (4) (2) determine the estimated gap If (ej i v ,  > 0),     ej iej i v t gs t gs     ) ( , 0 max ) ( , , , else  ) ( ) ( t gs t gs iei         (5) where   =0.5; (2) deceleration/braking   ) ( , , 1 ) ( min ) 1 ( max , , t gs v t v t vei j i j i        (6) (3) randomization   1 ) ( , 0 max ) 1 ( , ,    t v t v j i j i       (7) with probability p (4) vehicle movement (i)  with  lane-changing:  determine  probability  of lane-changing Plc; a security criterion = [-vmax : v+1].   ) ( ) 1 (0 ) ( ) (, 1 , 2] 1 : [ , , 2 , 1 ; maxt x t xt x v t gj i j iv v j i j i s          (8) or ) ( ) 1 (0 ) ( ) (, 2 , 1] 1 : [ , , 1 , 2 ; maxt x t xt x v t gj i j iv v j i j i s          (9) Then vehicle movement: ] 1 : 0 [ ) 1 ( ) ( ) 1 ( , , ,      t v t x t x j i j i j i           (10a) ) 1 ( ) ( ) 1 ( , , ,     t v t x t x j i j i j i             (10b) where  (10a)  and  (10b)  denote  vehicle movement  for  a  diligent  and  ordinary  driver, respectively. (ii) without lane-changing: Vehicle  movement  such  as  in  Equation  (10a) and (10b).  3. Time-Space Diagram In  the  time-space  diagram,  horizontal  axis  shows the space and vertical one is the time. All vehicles move from left to right. Each new line shows the traffic line after  one  further  complete  velocity-update  and  just before  the  vehicle  motion.  The  time  axis  shows  the evacuation time, its value increases from up to bottom. In Figure 1, two pictures on the top is time-space diagram  without  deceleration  in  advance.  While  two pictures on the bottom  show  time-space  diagram  with deceleration  in  advance.  In  this  time-space  diagram, time (vertical) and space (horizontal) axes are oriented from  the  top  to  the  bottom  and  the  left  to  the  right, respectively. As time advances, vehicles move from the left  to  the  right  (to  the  lower  right  corner),  whereas congestion  waves  move  to  the  upper  left  corner,  i.e., Computer Science and Engineering, Information Systems Technologies and Applications 465 backwards in space. This simulation for the low vehicle density  k  =  0.2,  slowdown  probability  p  =  0.1,  and diligent driver dd = 0.8.    Lane150 100 150 200 250 300 350 400 450 50050100150200250300350 Lane250 100 150 200 250 300 350 400 450 50050100150200250300350 Lane150 100 150 200 250 300 350 400 450 50050100150200250300350400450 Lane250 100 150 200 250 300 350 400 450 50050100150200250300350400450 Figure 1 Time-space diagram of the traffic using density k = 0.2; lane-changing lc = 1; diligent driver dd = 0.8; and slowdown probability p = 0.1. Two Top sides: without deceleration (for lane 1 and 2 respectively); Two Bottom sides: with deceleration (for lane 1 and 2 respectively). Lane150 100 150 200 250 300 350 400 450 50050100150200250300350 Lane250 100 150 200 250 300 350 400 450 50050100150200250300350  Lane150 100 150 200 250 300 350 400 450 500100200300400500600 Lane250 100 150 200 250 300 350 400 450 500100200300400500600  Figure 2 Time-space diagram of the traffic using density k = 0.2; lane-changing lc = 1; diligent driver dd = 0.8; and slowdown probability p = 0.2. Two Top sides: without deceleration (for lane 1 and 2 respectively); Two Bottom sides: with deceleration (for lane 1 and 2 respectively).  We  see  that  both,  with  and  without  deceleration  in advance,  there  is  congestion  wave  with  the  opposite direction to the vehicle movement. Computer Science and Engineering, Information Systems Technologies and Applications 466 In  these  results,  the  evacuation  time  without  and with deceleration in advance is found at 186 and 377 respectively. Thus, with deceleration in advance in this case, the evacuation time increases about double when it is compared by the result without deceleration. Figure  2  also  sees  the  time-space  diagram  using different p (this result by p = 0.3 and value of the other parameters  are  same  with  Figure  1).  We  found  that when  the  value  of  p  increases,  congestion  wave  also increases that shown by the black area in diagram. This happens  in  both,  with  and  without  deceleration  in advance.  4. Simulation Results Regarding with the real situation on Sidoarjo Porong roadway, the distance of the road from start position of the evacuation to the destination area (safe area) is 3500 m, it is as a road length L. In this work, L is assumed to be 500, so that the length of one site is set to 7 m. By referring to [9], one time step approximately corresponds to 1 second in real time.   The  following  section,  we  show  relations  between the evacuation time T and diligent driver dd without/with deceleration in advance, using selected vehicle density k and different of slowdown probability p.  4.1. For the vehicle density k = 0.2  For the low vehicle density k = 0.2; parameters  v  and sd for the initial velocity of each vehicle are 4 and 1, respectively. Figure 3 on the top side for  lc  =  0.3,  we obtain that by the increase of dd from 0% to 100%, T decreases either without or with deceleration in advance. The  evacuation  time  with  deceleration  in  advance  for each value of dd is larger than that the evacuation time without deceleration in advance. The same condition is also experienced for both: lc = 0.5  and  0.8.  When  dd  increases,  we  find  T  decreases either without or with deceleration in advance (Figure 2 on the middle and the bottom side for lc = 0.5 and 0.8 respectively). We also find that the evacuation time with deceleration  in  advance  for  each  value  of  dd  is  larger than that the evacuation without deceleration in advance.  4.2. For the vehicle density k = 0.5  For  the  intermediate  vehicle  density  k  =  0.5; parameters  v   and  sd  for  the  initial  velocity  of  each vehicle are 3 and 1, respectively. For lc = 0.3, we find that  T  decreases  as  dd  increases  from  0%  to  100%,  T decreases either without or with deceleration in advance (Figure 4 on the top side). As condition occurred in the low vehicle density, in this vehicle density also happen that the evacuation time with deceleration in advance for each  value  of  dd  is  more  increase  than  that  the evacuation time without deceleration in advance. When we use the value of lc = 0.5 and 0.8, the same trend of the evacuation time is obtained. It means that by the increase of dd, we find T decreases either without or with deceleration in advance (Figure 3 on the middle and the bottom side for lc = 0.5  and  0.8  respectively).  We also can see that the evacuation time with deceleration in advance  for  each  value  of  dd  is  larger  than  that  the evacuation without deceleration in advance.   0501001502002503000 10 20 30 40 50 60 70 80 90 100dd (%)evacuation time Twithout deceleration with deceleration 0501001502002500 10 20 30 40 50 60 70 80 90 100dd (%)evacuation time Twithout deceleraion with deceleration 0501001502002500 10 20 30 40 50 60 70 80 90 100dd (%)evacuation time Twithout deceleration with deceleration Figure 3 Relationship between diligent driver dd and evacuation time T without/with deceleration in advance, using k = 0.2;  v   = 4; sd = 1; A = 5. From the top side to the bottom side: using lc = 0.3, 0.5, and 0.8 respectively.    Computer Science and Engineering, Information Systems Technologies and Applications 467 5. Conclusion Deceleration  in  advance  parameter  has  been incorporated into the micro traffic model besides agent and diligent driver. A modified NaSch model has been proposed by  adding  the  deceleration  in  advance  in  the previous work. Traffic flow property has been presented by time-space diagram. In the context of its application to  simulation  for  evacuation  from  disaster  area, relationships  between  the  evacuation  time  and  diligent driver are investigated without and with deceleration in advance. 0501001502002503000 10 20 30 40 50 60 70 80 90 100dd  (%)evacuation time Twithout deceleration with deceleration 0501001502002503000 10 20 30 40 50 60 70 80 90 100dd  (%)evacuation time Twithout deceleration with deceleration 0501001502002503000 10 20 30 40 50 60 70 80 90 100dd  (%)evacuation time Twithout deceleration with deceleration Figure 4 Relationship between diligent driver dd and evacuation time T without/with deceleration in advance, using k = 0.5;  v   = 3; sd = 1; A = 5. From the top side to the bottom side: using lc = 0.3, 0.5, and 0.8 respectively.  The simulation results found the effect of deceleration in advance with respect to the evacuation time. 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Deceleration in The Micro Traffic Model and Its Application to Simulation for Evacuation from Disaster Area

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Deceleration in The Micro Traffic Model and Its Application to Simulation for Evacuation from Disaster Area

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