Agent-based Traffic Simulation and Traffic Signal Timing Optimization with GPU Zhen Shen, Kai Wang, Fenghua Zhu

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1 20 4th Internatonal IEEE Conferene on Intellgent Transportaton Systes Washngton, DC, USA. Otober 5-7, 20 Agent-based Traff Sulaton and Traff Sgnal Tng Optzaton wth GPU Zhen Shen, Ka Wang, Fenghua Zhu Abstrat Wth the adantage of sulatng the detals of a transportaton syste, the rosulaton of a traff syste has long been a hot top n the Intellgent Transportaton Systes (ITS) researh. The Cellular Autoata (CA) and the Mult-Agent Syste (MAS) odelng are two typal ethods for the traff rosulaton. Howeer, the oputng burden for the rosulaton and the optzaton based on t s usually ery heay. In reent years the Graphs Proessng Unts (GPUs) hae been appled suessfully n any areas for parallel oputng. Copared wth the tradtonal CPU luster, GPU has an obous adantage of low ost of hardware and eletrty onsupton. In ths paper we buld an MAS odel for a road network of four sgnalzed ntersetons and we use a Genet Algorth (GA) to optze the traff sgnal tng wth the objete of axzng the nuber of the ehles leang the network n a gen perod of te. Both the sulaton and the optzaton are aelerated by GPU and a speedup by a fator of 95 s obtaned. In the future we wll extend the work to large sale road networks. Index Ters Mrosulaton; Mult-Agent Systes; Intellgent Transportaton Systes; GPU; Genet Algorths I. INTRODUCTION raff sulaton [-2] s an portant tool for ontrol T and anageent of urban traff systes as the experents on the real traff systes are usually ery ostly. Early traff sulaton systes tended to be arosop or esosop based on hydroehans or statstal physs. Typal ethods nlude the Lghthll_Whtha_Rhards (LWR) odel [0,] and Latte Blotzann Methods (LBM) ethod [2]. These odels are good at desrbng the oerall propertes of the traff flow but lak the flexblty to desrbe the oplex rosop behaors suh as lane hangng and ehle oertakng. As the deelopent of oputers, the rosulaton ethods suh as ar followng odel [3], Cellular Autoata (CA) [4] and Mult-Agent Systes (MAS) [5, 6] beoe ore and ore popular n traff analyss and foreastng. Many rosulaton systes are Ths work s supported n part by NSFC , , , , and ; CAS 2F09N05, 2F09N06, 2F0E08, and 2F0E0. Dr. Zhen Shen, Ka Wang and Dr. Fenghua Wang are wth the State Key Laboratory for Intellgent Control and Manageent of Coplex Systes, Bejng Engneerng Researh Center for Intellgent Systes and Tehnology, Insttute of Autoaton, Chnese Aadey of Senes, No. 95 Zhongguanun East Road, Hadan Dstrt, Bejng 0090, Chna. (phone: , fax: , e-al: zhen.shen@a.a.n, ka.wang_nudt@hotal.o, fenghua.zhu@a.a.n.) Ka Wang s also wth Center for Mltary Coputatonal Experents and Parallel Systes Tehnology, and College of Mehatrons Engneerng and Autoaton, the Natonal Unersty of Defense Tehnology (NUDT), Changsha, Hunan, Chna. deeloped, for exaple [, 9, 7-9], MATS, VISSIM, TRANSIMS, TransWorld, MITSIM, MITSIMU, CORSIM, SHIVA and UTOBAHN. These systes an desrbe the rosop behaor of the ehles but has to fae a great hallenge that t s te-onsung to alulate the state eoluton of ehles. The oputaton te onsued by rosop traff flow sulaton nreases ery fast as the road network expands and the nuber of ehles nreases. Moreoer, the optzaton of the traff syste wth a rosulaton odel often noles n algorths suh as the Genet Algorths (GA) whh need to ealuate the syste any tes. There s a great hallenge n oputng when GA s appled to sole the traff sgnal tng optzaton proble [22-24]. Whle the deand for oputng power n the Intellgent Transportaton Systes (ITS) researh s growng, the oputng hardware s gong through a reoluton. Releant graphs dee opanes propose the onept of general purpose oputng based on the nnate haratersts of data parallel oputng of Graphs Proessng Unts (GPUs) [25-3]. GPU s a spealzed rut orgnally desgned to offload graphs tasks fro the CPU wth the ntenton of perforng the faster than the CPU an do. In a personal oputer, GPU usually appears on the deo ard or the other board. Usually t has exellent floatng pont perforanes wth any ores workng together to draw trangles and polygons on the sreen. Beause of ths, people began to use t for sentf oputng. Howeer, people had to ap ther applatons nto probles that draw graphs and progra wth graphs prograng languages lke Open Graphs Lbrary (OpenGL) and Cg. NVIDIA, a great GPU produer, realzed the potental to use GPU for general purpose oputng, and deeloped General-Purpose GPU (GPGPU) and Copute Unfed Dee Arhteture (CUDA). Wth CUDA, people an progra wth hgh-leel languages suh as C, C++ and Fortran. The GPGPU dea and CUDA ake the objets proessed by GPU onerted fro pxels on sreen to dfferent knds of sentf data. There hae been any suessful applatons of GPGPU, suh as oleular dynas [26], oputatonal flud dynas [27], bonforats [28] and shedulng [29]. GPU an ake onsderable speedups opared wth CPU and s uh affordable than other knds of oputer hardware that hae the sae oputng perforane. Lately soe efforts hae already been ade n rosop traff sulaton usng CUDA [20,2] that opened up a new way for pleentaton and parallelzaton of rosop traff sulaton. Just as the deelopent of CPU akes the terate algorths prealng, we belee that the deelopent of GPU an ake the parallel algorths n an terate fashon prealng. In ths paper, we report soe prelnary work on //$ IEEE 45

2 usng GPU for the traff rosulaton and optzaton. We buld a parallel MAS odel for a road network wth four sgnalzed ntersetons. Ths odel bulds a GPU based MAS odel of traff sulaton enronent followng the work by Dad Strppgen [20,2], and then we apply GPU-adapted parallel Genet Algorth (GA) [22] to optze the traff sgnal tng onfguratons. By usng NVIDIA GTX 470 we obtan a speedup by a fator of 95 opared wth a anstrea CPU of AMD Athlon TM 64 X2 Dual Core proessor The ontrbuton of the paper s that we use GPU to parallelze the rosulaton and optzaton of a traff syste and show that ths ntegraton of GPU wth MAS and parallel terate algorths an help sole real probles ore pratally. The reanng parts of the paper are organzed as follows. In Seton II, we ge a reew on GPU and the rosulaton and optzaton of the traff systes. In Seton III, we ge the forulaton of the proble and show how to pleent the parallel traff sulaton and optzaton odel wth GA on GPU. In Seton IV we show the experent results. In Seton V we onlude the paper and dsuss the future researh. alled grd and the other s alled blok. One grd an onsst of at ost bloks and eah blok an onsst of at ost 52 threads. Then the grd s alloated to GPU for parallel oputng wth bloks alloated to dfferent SMs n the GPU and threads alloated to dfferent SPs n the SM. Eah SM has ts own eory alled shared eory that all threads n t an aess sultaneously, and all SMs share the global eory, onstant eory and texture eory of GPU. Aong all knds of eores aessed by threads n the grd, the shared eory has the lowest eory aess lateny whle the global eory has the hghest lateny. Fg. llustrates the GPU parallel oputng. TABLE I KEY SPECIFICATIONS OF GEFORCE GTX 470 Nuber of SPs (ores) 448 Proessor Clok (MHz) 25 Meory Bandwdth (GB/s) 33.9 Vdeo Meory (MB),280 II. REVIEW A. GPU, Fer and CUDA Currently, llons of personal oputer users are usng NVIDIA GPUs for arous dfferent purposes, ost of whh are related to aeleraton of graphs renderng or sentf oputaton. GPU s the ore of the dsplay ard and s ontrolled by CPU. In hardware, a GPU has any ores workng together. The ores are alled Streang Proessors (SP), and seeral ores (8 or 32 typally) are organzed nto a Streang Mult-proessor (SM). In software, a typal GPU progra onssts of two parts: one part s the CPU odes that ontrol the proess of the whole progra and does the sequental work, and the other s the GPU part that does the parallel work. Wth CUDA, the prograers an use C style odes to use the oputng resoures proded by GPU and the prograng on GPU has no uh dfferene fro usng Applaton Prograng Interfaes (APIs). Sne 2006, NVIDIA has ntrodued three generatons of hardware arhtetures of GPU: G80, GT200, and Fer. The latest Fer arhteture akes great nnoatons and offers draatally nreased prograablty and opute effeny. Copared to GT200, soe key features of Fer are: ) Eah SM has 32 SPs that s 4 tes oer GT200. 2) The peak double preson floatng pont perforane s 8 tes oer GT200. 3) Eah SM ould hae a 64KB shared eory that s 4 tes oer GT200. We ge soe key perforane ndators of one Fer GPU naed GeFore GTX 470 n Table I. A funton that exeutes on the GPU s typally alled a kernel [25]. When a kernel s launhed, ultple threads on GPU organzed by two leels are atated. The top leel s CPU thread Fg.. GPU parallel oputng One bg aheeent of the GPU s that Tanhe-A, the seond fastest oputer n the world (oertaken by the K oputer n Jun. 20), uses 7,68 NVIDIA Tesla M2050 GPUs and 4, 336 CPUs. It would requre ore than 50,000 CPUs to deler the sae perforane, and the power onsupton would nrease fro 4.04 egawatts to ore than 2 egawatts [30]. Ths shows learly the adantage of GPU. B. Traff rosulaton and optzaton In the rosulaton, the road network and the ehle trael are two eleentary parts. Usually a graph s used to desrbe the topology of the road network. The nodes and the lnks represent the ntersetons and roads. And a queue sulaton algorth an be used to sulate the behaors of ars traellng along the lnks. When not onsderng the lane hangng or ehle oertakng, the relatonshp between two sequental ehles an be desrbed by a GM-type ar-followng odel [32], β n( t+ τ n) an( t+ τn) = α [ n ( t) n( t)], γ () [ xn ( t) xn( t)] where n s used to ndex ehles. The (n )-th ehle s n 46

3 front of the n-th ehle. an () t, n () t and xn () t are the aeleraton, speed and poston of ehles at the te t, τ n s the drer s reaton te of the ehles, α, β and γ are onstant paraeters that need to be estated fro the real ar-followng data. Many rosulaton systes are based on the aboe ethods of desrbng the road network and the ehle trael. As the oputer deelops, the perforane of rosulaton systes beoes better and better. For exaple, MATS has a ult-ore erson of ts so-alled Deternst, Eent-based Queue-Sulaton (DEQS), and by usng a Beowulf Cluster (wth 8 nodes) t an sulate the traff flow of Swtzerland onsstng of about 20,000 nodes and 60,000 lnks for one whole day (24 hours) wthn 7 n [7]. Howeer, the Ethernet network latenes stll ake t dffult to gan speedup by addng ore lusters [20,2]. The GPU an be used to aelerate the rosulaton. It s reported n [20] that a speedup of up to 67 tes opared aganst the hghly optzed jaa erson MATS on a CPU was aheed. Besdes traff sulaton, there are any optzaton probles n the ITS researh. In [23] GA s used to sole the proble of traff sgnal tng optzaton wth a 34% proeent oer the utually onsstent soluton of the proble. It has been hallengng for the rosulaton, not to enton the optzaton based on the rosulaton. Ths s why we belee that GPU s a neessary and prosng tool for the traff rosulaton and optzaton. Fortunately, GA has been odfed nto a parallel erson adapted to GPU. In [29], the authors use the parallel GA algorth to sole the Quadrat Assgnent Proble (QAP) and ahee a speedup fator of 3 to 2 by GTX 285 opared to the Intel proessor. Ths parallel GA s the ethod that we use n ths paper for solng the traff sgnal tng optzaton proble. We ndex the ntersetons n the road network arbtrarly fro to N. The road network used n ths paper s shown n Fg. 2. For eery road there are seeral lanes. We assue that there are ehles fro both dretons on a road and we do not onsder ehle oertakng or lane hangng n ths paper. For eery nterseton, there are seeral phases of the traff lghts, shown n Fg. 3. We assue that there are M = 4 phases and that the sequenes of phases are the sae for all the ntersetons. The M phases onsttute a yle and we assue that all ntersetons share the sae yle te, denoted by. We take the -st nterseton as the referene nterseton and the offset te of yles of the ntersetons s denoted by a etorψ = [ ψ, ψ2, L, ψ ] T M. Obously ψ = T 0. We denote θ = [ θ, θ2, L, θn] ( =, 2,..., M) wth θn (n =, 2,, N) as the green te of the -th phase of the n-th nterseton. The proble an be forulated as follows, ax f(, ψθ,, θ2, L, θm ) st.. n ax (2) 0 ψ en, θ θn, en, =, 2, L, M, where f(, ψθ,, θ2, L, θ M ) s the funton of the nuber of ehles that leae the road network durng the gen te, n and ax are the nu and axu alues of the yle te, en s a olun etor of N oponents all beng ones, θ n, ( =,2, L, M ) s the nu green te for the -th phase. Fg. 3. Phase sequene of the traff lghts III. FORMULATION AND IMPLEMENTATION A. Proble Forulaton and the Oerall Ipleentaton In ths paper we axze the nuber of ehles leang a road network n a gen te perod. Ths proble s portant n that the perforane s proed by software wthout upgradng the hardware. Ths proble s a typal proble n the ITS researh [23]. Fg. 2. The road network Fg. 4. Oerall pleentaton There are two an parts n the pleentaton: one s the 47

4 traff flow sulator, and the other s the traff sgnal tng optzer. Eery ehle s ewed as an agent. The operatons for the agents are slar. Also, the operatons for the hroosoes n GA are also slar. These ake the parallel pleent on GPU possble, please see Fg. 4. B. Traff Flow Sulator The road s dded nto seeral lanes. We use the GM-type ar-followng odel [32] to desrbe the oeents of the ehles as t has a lear physal eanng, please see (). In ths odel, ehles are queued n a lane and the state of a ehle at a sulaton te step an be oputed by the states of tself and the ehle n front of t at the preous sulaton te step. We assue that the arral of the ehles s subjet to Posson dstrbuton wth the arral rate λ for eah lane of the road network. The rando nubers u, u2,..., u n whh obeys the unfor dstrbuton are generated by a Mersenne Twster (MT) generator [33]. Ths ethod an be appled easly on GPU. Eah lane of the roads n our sulator has ts own ehle generator. We use a queue to represent the ehles n a lane. We assue that when the dstane between a ehle and the one at ts front s less than 25 eters, the behnd one oes n a ar-followng ode [34]; otherwse, t traels wth a desred speed of ts drer. For ehle agents n a queue, the ost front s dfferent fro the others as there s no ehle at ts front. Its oeent s totally deterned by the states of traff lght and ts dstane fro the stop lne. We assue that the ost front ehle has an ntal speed whh obeys a noral dstrbuton. When a ehle arres at an nterseton, t ay go forward, or turn left or turn rght. No atter whh aton t takes, we assue that t hooses the new lanes wth an equal probablty. C. Traff Sgnal Tng Optzer ) Parallel GA odel GA s an terate searhng algorth that s the proess of natural eoluton. Its an dea s that the better ndduals are ore lkely to pass the genes to next generatons. Reently, there has been a growng nterest n pleentng parallel GA wth GPU [29, 3]. Here we eploy the parallel GA algorth wth the GPU desgned n [30] whh an sole the quadrat assgnent proble (QAP) effently. In ths parallel GA, two pools P and W of the sae sze are used to store urrent and newly generated offsprng ndduals. The algorth flow s as follows, Step : Generate an ntal populaton of ndduals of P. Step 2: Ealuate the ndduals n P. Step 3: For eah nddual I n P, selet another nddual I j ( j) n P randoly. Apply rossoer to I and I j wth the probablty P. If the rossoer happens, put the hld I nto W; otherwse, opy I nto W. Step 4: For eah nddual I n W, apply the utaton wth the probablty P. Step 5: Ealuate ndduals n W. Step 6: For eah nddual I n P and ts orrespondng hld or opy I n W, opare the ftness alues. If I has a hgher ftness, replae I n P wth I n W. Step 7: If the ternaton rtera are et, ternate the algorth. Otherwse, go to Step3. The steps 2 to 6 all hae the sae operatons on hroosoes. Ths s why ths GA an be parallelzed. 2) Ftness funton The ftness funton s used to easure how good a soluton s. In ths paper we hoose the nuber of ehles leang the road network n the gen te perod as the ftness easure [23]. It s just the objete funton n (2). 3) Chroosoe enodng and deodng We use a bnary enodng that the yle te, the offset and the duraton of green te of the phases an be enoded n one hroosoe that s shown n Table II. Cyle te, Offset ψ TABLE II CHROMOSOME ENCODING Traff sgnal tng for the ntersetons No. No. 2 No. N duraton of green te of phase, θ duraton of green te of phase M, θ 8 bts 8 bts 8 bts 8 bts We need (M + 2) 8-bt odes for an nterseton wth the frst two for the yle te and the offset and the reanng M for the M phases. For the deodng, for any nterseton, we defne a appng fator φ as follows, 7 k φ= 2 bk, =,2, L, M + 2, (3) k = 0 where b k s the alue of the k-th bt of the -th 8-bt bnary ode. The deodng ethod s shown n Table III. TABLE III MAPPING BINARY CODES TO DECIMAL ax n Cyle te = n + φ 255 Offset ψ n = φ pax pn pn = pn + φ+ 2, =,2,..., M 255 Duraton of the green M pn te for -th phase θn = θn, + ( θn, ),,2,..., M M = = pn = In Table III, n s used as the ndex for the nterseton, and p n s the paraeter to deterne the green te for the -th phase of the n-th nterseton, wth p n and p ax as ts nu and axu alues. 4) Crossoer and utaton The one-pont rossoer operator and the one-pont utaton operators are wth the probabltes of rossoer P and utaton P respetely. M 48

5 D. Data Strutures and Coputng Resoures Alloaton The data of ehle agents s organzed fro top to botto n fe leels: the traff lghts onfguratons, ntersetons, roads, lanes, and ehles. Please see Fg. 5. Before we launh the kernel funton on GPU, the data of ehle agents and traff lghts are oped to eores on GPU. The ehle data s oped to the global eory of GPU and then oped to the shared eory of the SMs as the aess to the shared eory s faster. Traff lght data are oped to the onstant eory as the ehles ontrolled by the sae traff lghts onfguraton need t and the onstant eory an be read by all the threads n the grd wth lower eory aess lateny than the global eory. As Fg. 5 shows, a blok handles the ehles n the sae lane, and eah thread n t handles a sngle ehle on the lane. Eah row of bloks n the grd handles a replaton of the oputng of the traff lghts onfguraton. For eah onfguraton, we sulate for T ndependent replatons to redue the unertanty. For GA, the nuber of ndduals for eah generaton s C = 500. The replatons for ealuatng a onfguraton s T = 0. The probabltes for the rossoer and the utaton are P = 0.99 and P = We set GA for,000 generatons. We use a PC wth one AMD Athlon TM 64 X2 Dual Core proessor and an NVIDIA GeFore GTX470 GPU. We use CUDA drer and SDK wth the erson 3.2. The results of a typal run of GA are shown n Fg. 6. Table IV shows the output of the GA. The nuber of ehles that leae the road network s orrespondng to Fg. 6 s We ge the te onsupton for one teraton of GA for the CPU + GPU pleentaton and opare t wth the pleentaton of CPU only n Table V. The results are based on 30 runs ndependently for both pleentatons. The whole proess of the CPU + GPU pleentaton takes about 9,044s and t would be 3,79,976s (about 43. days) on CPU wth a speedup fator of 95. The data of one generaton transferred fro the an eory to the GPU eory takes about 20 MB deo eory. Please note that the road network used n ths paper (Fg. 2) s syetr, and the results n Table IV erfy the syetry. Fg.6. Results of a typal run of GA Fg. 5. Data strutures and oputng resoures alloatons IV. EXPERIMENTS In ths paper, we use the road network shown n Fg. 2. The nuber of ntersetons s N = 4. For eah road, there are 6 lanes wth 3 at ether sde. The rght sde lane s used for turnng rght, the left for turnng left and the ddle s used for gong forward. When gong past the stop lne, the ehle hooses new lanes wth equal probabltes,.e., /3. The dstane between two neghborng ntersetons s = 024, wth 4 as the aerage length of a ehle. The ehle arral rate for eah entry lane n the road network shown n Fg. 2 (24 entry lanes altogether) s λ = 0.2 ehle per seond. The ntal speed of the ar obeys the noral dstrbuton N(60 k/h, 0), and the desred speed s 80 k/h. The paraeters n the ar-followng odel are α= β= γ =. The nuber of phases s M = 4. The axu and the nu of the yle te are ax = 240sand n = 60s. The paraeters for phases are pn = 0, pax = 00 and θ n, = 6s ( =, 2,, M). The te step for the sulaton s s. We sulate for 3,600s. TABLE IV TRAFFIC SIGNAL TIMING CONFIGURATION OUTPUT by GA Green Green Green Green Inter- Cyle te of te of te of te of seton Offset/s te /s Phase Phase 2 Phase 3 Phase 4 No. /s /s /s /s TABLE V TIME CONSUMPTION OF ONE ITERATION IN GA CPU ONLY GPU+CPU Speedup Aerage Te/s Standard Deaton N/A V. CONCLUSION AND FUTURE RESEARCH In ths paper, we propose a fraework of an agent-based traff flow sulator and a traff sgnal tng optzer based on GPU usng NVIDIA s CUDA. The GM type ar-followng odel and the parallel GA are used. We obtan a speedup by a fator of 95 opared wth the pleentatons on CPU only. Our results show the power of GPU on the transportaton sulaton and optzaton. In the future, we wll go on the researh on the followng ponts, ) Iproe the rosulaton odel to ake t ore pratal. We use a ery sple odel n ths paper to deonstrate and erfy the power of GPU. In the future, 49

6 we wll ake the odel ore pratal by learnng fro ature software suh as MATS. 2) Sole large sale probles. The road network n the paper has only 4 ntersetons. A real network ontans hundreds of ntersetons of any types. We plan to use GPU lusters to takle the large sale probles. 3) Iproe the optzaton ethod. GA s not the only hoe for the traff sgnal tng optzaton proble. We ay onsder GA wth soe loal searh algorths to proe the perforanes. 4) Dfferent rtera should be onsdered. We hose the nuber of ehles leang the road network as the objete to optze. Other objete funtons an be onsdered, suh as the ean trael te of the ehles, the ean length of the queues, or the ean stop tes of the ehles. Moreoer, we should onsder the rtera together and sole the ult-objete optzaton proble. 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