Dynamic Traffic Cellular Automata Model to Express the Congestion at One Lane Highway Traffic System

Transcription

1 2012 Iteratioal Coferece o Traffic ad Trasportatio Egieerig (ICTTE 2012) IPCSIT ol. 26 (2012) (2012) IACSIT Press, Sigapore Dyamic Traffic Cellular Automata Model to Express the Cogestio at Oe Lae Highway Traffic System Ahmed AlGhamdi +, HalitEre, HarieaiPakka Electrical egieerig Departmet, Curti Uiersity. Abstract. Highway cogestios ca cause cosiderable impact o loss of time ad delays displacemet. This article itroduces a ew method of explaatio of the cogestio i cotrast to coetioal method of ehicles capacity o the highways. This method is primarily based o the Cellular Automata (CA) cocept itroduced by Nagel ad Schreckeberg i 1992 [1]. Dyamic Traffic Cellular Automata (DTCA) is also explaied with emphasis o the acceleratio, the deceleratio, ad the reactio factors. Dferet i speeds chagig ad delays i start-up are discussed for beig importat reasos of the highway cogestios. Keywords. Cellular automata (CA), Dyamic Traffic Cellular Automata (DTCA), Cogestio. 1. Itroductio For seeral years, we hae bee deelopig a geeral purpose road-traffic simulatio system to aalyse road traffic jam. This paper describes the cocept of the system usig the ruig lie model, ad a case study for geeral purpose simulatio with Dyamic Traffic CellularAutomatio model, which is mody from Cellular automata model[1]. I order to simulate cogestio of road traffic system, it is essetial to describe ehicles haig their ow decisio-makig capabilities, ad to hae detailed ad exact road coditio data o the road system[2]. Seeral studies hae bee doeto realize road traffic simulatio by a microscopicmodel. For example, there is a flattery model of aehicle by a fuzzy theory ad arious theories suchas a eural etwork work ad cellular automata[2]. The Cellular Automata model had bee suggested by Nagel ad Schreckeberg i It was first used to study the cogestio o the oe lae highways[1]. Sice the the model has bee modied to study two ad three lae highways [3-6]. Origial CA model cotais of oe-dimesioal array of L umber of cells. Each cell is 7.5m ad may be occupied or ot. The elocity of the ith ehicle, i, is a iteger betwee 0 to imum speed, V. Updatig is carried out the system cosists of the followig steps: (1) Acceleratio: the elocity i of a ehicle is lower tha V ad the distace to the ext car a head is larger tha i +1, the speed is adaced by oe [ i i +1]. (2) Slowig dow (due to other cars): a ehicle i sees the ext ehicle at site i+j, where j is the gab a head, (with j ν i ), it reduces its speed to be [ i j-1]. (3) Radomizatio: with probability р, the elocity of each ehicle ( greater tha zero) is decreased by oe [ i i -1]. (4) Car motio: each ehicle is adaced ν cells. This paper iestigates cogestios o the oe lae highway traffic system by usig Dyamic Traffic Cellular Automata (DTCA) model. [1],[3],[6],[7]. Ahmed AlGhamdi. Tel.: ; fax: address: a.alghamdi5@postgrad.curti.edu.au. 69

2 I this article a brief explaatio about Cellular Automata (CA) has bee gie i the itroductio. The follow part proides the details about A Dyamic Traffic Cellular Automata (DTCA), ad fial part claries the ew cocept o cogestio. I this article there are two reasos that create the cogestio. 2. Dyamic Traffic Cellular Automata (DTCA) A Dyamic Traffic Cellular Automata (DTCA) that has bee suggested i this paper ca be compared with the origial CA model. Basically it offers three mai dfereces: 1) I the CA the road is diided ito equal legth cells, each cell beig 7.5 m. A cell may or may ot be occupied. The CA model assumes that a ehicle is restricted by fixed positio, while the positio of the ehicle i the DTCA is ot limited with fixed cells o the highway. Howeer, the ehicle i the MCA is iewed as a cell 7.5 m moig through the highway. 2) Nagel ad Schreckeberg [1] used fix amout of acceleratio ad declaratio, equal to 1 cell (±7.5 m/s 2 ). Accordig to Basal ad Brar imum deceleratio is explaied i Equatio 1. dec ( cosθ siθ ) = G r + Where G is the graity (9.81m/s 2), r is frictio coefficiet for dry seal roads (0.6) ad θ is ehicle agle of icliatio of the plae of the horizotal. It is assumed that ε equal to 0. This equatio idicates that declaratio caot be greater tha m/s 2 while i Nagel ad Schreckeberg model assumes 7.5 m/s 2, cell legth, at all times [8].dferet deceleratios are achieed by dferet drier habits, road ad traffic codtioes. These dfreces are stated by deceleratio factor (β). β gies the proportioof the dec, ad it will be 0 β 1. dec = dec β Similarly, the imum acceleratio (acc ) is m/s 2, which is equal to km/hr 2. Maximum acceleratio leads moig the ehicle from zero to km/hr speed i first secod. I six secod with imum acceleratio the ehicle ca approach 106 km/hr, which is reasoable for most ehicles. Howeer, dferet acceleratios are achieed by dferet drier habits, road ad traffic codtioes. These dfreces are stated by acceleratio factor (α). α gies the proportioof the acc. for example α is equal 1the acc will equal to acc, ad it will be 0 α 1. acc = acc α (3) 3) The origial CA uses oe radomazatio factor (p) while MCA uses three idepedet radomazatio factors (α, β ad p d ). α is acceleratio facor, β is decleratio factor ad p is drier reactio factor. Those factore describe the driig satuatio o highways. α ad β are ery issetial to mage of zero or o momet. xi-1 xi xi+1 Vi-1 x(i-1,i)=mi(3.vi-1) Vi x(i+1)=mi(3.vi) Vi+1 Fig. 1: Relatio betwee the Velocity ad the Gabs betwee the Vehicles o the highway (1) (2) Chages i speed due to acceleratio the < V &ϕ x = + 1 ( + T acc > (4) Where i is a cell umber the sequece umber T is the fixed time ad we assume it equal to 1 secod φ is safety factor Deceleratio 70

3 the ϕ x ( ( T dec or x ( / T ) + 1 = ϕ Radomizatio the > 0 with probability β = + 1 Car motio x + 1 = x + T T dec (5) (6) (7) 2.1 Simulatio We cosider kcars moig o a strait road, with o icliatio, perfect weather ad road coditios. The boudary coditio adopted i this work is periodic. Sice real traffic data ca be well described by the parameters V = 110 km/h or 30.6 m/s, p = 0.5 ad α ad β=n(0.4, 0.2). We assume these parameters i our implemetatio. The legth of the eolutio time is 2000s. 3. Cogestio Best way to obsere the cogestio is lookig at the: = accd ( t) acc( t) Where decs is deceleratio stregth, d ( t) d( t = dt dt Where V d ( t) V d ) d( t) = 0 dt accd is acceleratio to desired elocity (8) (9) (10) Fig. 2: cogestio loos From the Figure (2) the black cure shows decs (t). There are two thigs could get it from decs(t) cure: 1) the limits of cogestio (where the cogestio starts ad where it fiishes). 2) Obserig who the stregth of cogestio is ad whe that happeed. Aother factor eeds to otice is losig (LOSS) LOSS = t e t0 V d ( t)dt (11) 71

4 Where t 0 is the time startig cogestio ad we will assume it as 0, ad t e is the time of fiishig of cogestio. While V d V LOSS = t e 0 V ( t)dt ( x( t ) x( )) LOSS = V e LOSS = t 0 x( t e ) (12) (13) (14) Figure (3) illustrates the oeriew of traffic system i the simulatio. It shows the shape ad behaiour of cogestio i time o the highway. The global obseratio of the cogestio lets us to iestigate the reasos why cogestios take place ad how they are dispersed. I this figure the moemet of ehicle o the highway ca be recogized by time ad the positio at the road. From Figure (3A), it ca be obsered that the ehicle (1), (Bolded), moemet durig the experimet ad it ca be recogized the moemet through the cogestio. Focusig o just small part of Figure (3A) to be appear i Figure (3B), which helps to uderstad the cluster of ehicles ad how each of them ca impacts o the ext oe, also by spotlight o oe ehicle ad how is it moig with the cluster to uderstad the reasos of creatig of cogestios, as well as peakig i demad ad a bottleeck regardig to peter [9]. Figures (3 A&B) expressig the essetial reasos of cogestio, which are speed coflict ad delay of start-up moemet. Fig.2: A: cogested Highway, B: cogested High way foucusig o the cogestio Referrig to Figure (2) shows the ehicle (1), i the Figure 3A, moemet i two scearios: 1) durig the cogestio ad 2) durig freeway. From the Figure (2), it ca be see the positio dferece. Cogestio i this figure ca be explaied as time ad positio delay compariso to desired positio at the same time. The gap betwee the cures of cogested ad desired ehicles is expadig from startig the cogestio to be ed. It is also ca be obsered the stregth of cogestio for idiidual ehicle ad it is losig. 4. Coclusio I this article, Dyamic Traffic Cellular Automata has bee discussed cooperatio with Nagel ad Schreckeberg CA model.fidig the time ad distace loss equatio as result of compressio betwee cogested ad free highways.defied acceleratio ad deceleratio factors respectiely. 72

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