RECENT advancements in vehicular communication and

Transcription

1 Reliabiliy-oriened Opimizaion of Compuaion Offloading for Cooperaive Vehicle-Infrasrucure Sysems Jianshan Zhou, Daxin Tian, Senior Member, IEEE, Yunpeng Wang, Zhengguo Sheng, Xuing Duan, and Vicor C.M. eung, Fellow, IEEE Absrac Compuaion offloading is criical for mobile applicaions ha are sensiive o compuaional power, while dynamic and random naure of vehicular newors maes i challenging o guaranee he reliabiliy of vehicular compuaion offloading. In his leer, we propose a reliabiliy-oriened sochasic opimizaion model based on dynamic programming for compuaion offloading in he presence of he deadline consrain on applicaion execuion. Specifically, a heoreical lower bound of he expeced reliabiliy of compuaion offloading is derived, and hen an opimal daa ransmission scheduling mechanism is proposed o maximize he lower bound wih consideraion of randomness in vehicle-o-infrasrucure V2I communicaions. Experimenal resuls demonsrae ha our mechanism can ouperform he convenional scheme and benefis vehicular compuaion offloading in erms of reliabiliy performance in sochasic siuaions. Index Terms Cooperaive vehicle infrasrucure sysem CVIS, vehicular communicaion, mobile edge compuing, compuaion offloading, dynamic programming. I. INTRODUCTION RECENT advancemens in vehicular communicaion and neworing are empowering he inegraion of moving vehicles and road-side infrasrucures sensing, compuing and sorage capaciies [], which has spawn a new echnological paradigm for vehicular elemaics and infoainmen applicaions, called Cooperaive Vehicle Infrasrucure Sysems CVIS. In CVIS, full or parial compuaion offloading mechanisms play a ey role in boosing he cooperaion beween vehicles and infrasrucures. Nowadays, here exis exensive research effors such as [2] [9] ha have been made on compuaion offloading in a variey of mobile cloud/edge compuing scenarios. Mos of hese curren wors focus on he issue of energy-aware or/and laency-aware opimizaion for mobile applicaions, since smar mobile devices e.g., smar This research was suppored in par by he Naional Naural Science Foundaion of China under Gran Nos. 6822, and , he scholarship under he Sae Scholarship Fund No , Royal Sociey-Newon Mobiliy Gran IE692 and The Engineering, and Physical Sciences Research Council EPSRC EP/P25862/. J. Zhou, D. Tian, Y. Wang and X. Duan are wih Beijing Advanced Innovaion Cener for Big Daa and Brain Compuing, Beijing Key aboraory for Cooperaive Vehicle Infrasrucure Sysems & Safey Conrol, School of Transporaion Science and Engineering, Beihang Universiy, Beijing 9, China. jianshanzhou@foxmail.com, dian@buaa.edu.cn Z. Sheng is wih Deparmen of Engineering and Design, he Universiy of Sussex, Richmond 3A9, UK. z.sheng@sussex.ac.u V. eung is wih Deparmen of Elecrical and Compuer Engineering, The Universiy of Briish Columbia, Vancouver, B.C., V6T Z4 Canada. vleung@ece.ubc.ca Fig.. Cooperaive Vehicle-Infrasrucure Compuing Scenario. phones, ables, wireless sensors, ec. are commonly energyhungry. Many oher effecive offloading mechanisms can also be found in some sae-of-he-ar surveys [] [5], which mainly concern abou he resource opimizaion or/and load balancing in communicaion and compuaion aspecs. owever, lile or no aenion has been paid o reliabiliyoriened opimizaion of compuaion offloading for vehicular users, which is he main focus of his leer. Essenially differen from many mobile users, vehicles are usually equipped wih powerful energy, such ha energy consumpion issue is no he main concern in heir sysem design. Insead, many vehicular applicaions, especially safey-ype applicaions such as danger recogniion and on-line diagnosis, are reliabiliycriical and laency-consrained. A his poin, he reliabiliy and efficiency of vehicular communicaions can have a grea influence on he performance of offloading compuaion ass o nearby service infrasrucures. Moreover, due o high mobiliy and randomness in propagaion channel fading, V2I communicaions may be randomly inermien, which presens a challenge o opimizaion design and implemenaion of reliable vehicular compuaion offloading. Toward his end, in his leer, we ae ino accoun he dynamic and random characerisics of V2I communicaions, and presen a reliabiliy-oriened sochasic opimizaion model for V2I-based compuaion offloading. We derive he successful probabiliy of compuaion offloading wih consideraion of deadline-consrained applicaion profile. Moreover, we obain a lower bound of he opimal expeced offloading reliabiliy as well as an opimal daa ransmission scheduling mechanism by ransforming he sochasic opimizaion ino a dynamic programming paradigm. To he bes of our nowledge, his wor firs presens reliabiliy-oriened sochasic opimizaion for V2I-based compuaion offloading. Our mechanism can

2 2 Fig. 2. Iniialize he coundown ime index as =T Iniialize he residual daa volume as lt=d If = No Yes Offload all he residual daa a, l Sop Sense he SNR sae of he V2I channel a SNR Apply Theorem 2 o deermine he opimal daa size o be offloaded a, S=S * l, SNR SNRT Offload he opimal daa size a, S Updae he residual daa volume a - l-=l-s Updae he coundown ime index as - Inpu applicaion consrains. Deadline: T 2. Inpu daa size: D Iniially specify a reliabiliy hreshold for local execuion: r Apply Theorem 2 o deermine he maximum lower bound of he overall expeced reliabiliy of compuaion offloading: exp-ȉd,t Yes Perform compuaion offloading If exp-ȉd,t >r No Perform local execuion Reliabiliy-oriened Vehicular Compuaion Offloading. be used o design a hreshold-based decision-maing policy for compuaion offloading in sochasic siuaions, which may faciliae a paradigm shif from he local vehicular compuing o cooperaive vehicle-infrasrucure compuing in CVIS. A. Mobile Applicaion Model II. SYSTEM MODE Following much exising lieraure such as [2], [6], we can use wo ey parameers o characerize he profile of a mobile applicaion: i The inpu daa size D ha is he oal number of daa bis as he applicaion inpu. These D-bi daa can be pariioned and offloaded o a roadside infrasrucure as he cloud edge for remoe execuion. ii The applicaion compleion deadline T ha denoes he maximum number of successive ime slos before which he mobile applicaion mus be compleed. In addiion, we use o represen he index of a ime slo, and hese D-bi daa can also be pariioned ino a series of smaller pieces s [, D], where s denoes he number of daa bis ha should be ransmied o he infrasrucure in he -h ime slo. B. Vehicle-o-Infrasrucure Transmission Channel Model We ae ino accoun dynamic naure and randomness of he V2I communicaions from he physical-layer perspecive. Since vehicle mobiliy and many environmenal facors, such as rees, buildings and nearby moving vehicles as he obsacles in he signal propagaion pah, can lead o sochasic variaion of signal-o-noise raio SNR condiion in V2I communicaions, we presen sochasic modeling on he V2I channel. In order o capure he randomness, we adop a wo-sae Marov chain model o characerize he SNR. I is also worh poining ou ha he Marov modeling approach has been widely used o characerize a sochasic channel in many oher wors, such as Gilber-Ellio channels [2] and Rayleigh channels [7]. Specifically, we consider ha here are wo raversable saes of he V2I ransmission channel, which include a high-snr sae and a low-snr sae. The SNRs corresponding o hese wo saes are denoed by SNR and SNR, respecively. e SNR be he SNR level of he ransmission channel in ime slo. Thus, SNR {SNR, SNR }. We denoe by p he sae ransiion probabiliy ha he nex channel sae has a high SNR given ha is curren sae has a high SNR and by p he probabiliy ha he nex channel sae has a low SNR given ha is curren sae has a low SNR. Addiionally, he ransiion probabiliy ha he channel changes from he curren sae wih a high SNR o ha wih a low SNR can be calculaed by p = p, and he ransiion probabiliy from a low-snr sae o a high-snr sae can be p = p. The proposed wo-sae Marov model is represened by he diagram in Figure. Based on he wo-sae Marov model, he mean duraions represened by he number of ime slos of being in he high-snr sae and in he low-snr sae can be esimaed by T = p and T = p, respecively. Given he fading coefficien of he V2I channel as g V2I and he corresponding fading variance as σ 2, we can express he channel capaciy beween he vehicle and he wireless access poin of he infrasrucure by I V2I = log 2 SNR g V2I 2 Generally, here is usually no dominan line-of-sigh os propagaion pah beween a mobile communicaion erminal and an access infrasrucure e.g., a basesaion in urban environmens ha are heavily buil-up. In such siuaions, Rayleigh fading model has been widely used o represen he characerisics e.g., pah loss of radio signal propagaion. ence, we also employ Rayleigh fading model for V2I communicaions, in which g V2I 2 is a random variable following an exponenial disribuion wih parameer σ 2. Accordingly, he successful probabiliy of ransmiing s -bi daa in a ime slo hrough he V2I channel can be calculaed by p s, SNR = Prob {I V2I > s } = exp 2s 2 III. STOCASTIC OPTIMIZATION MODE FOR V2I DATA TRANSMISSION SCEDUING We consider he opimizaion of ransmission scheduling of D-bi applicaion daa in T ime slos. For simpliciy, we arrange he ime slo index,, in descending order, i.e., = T, T,...,. Tha is, is used as a coundown imer, and he iniial ime slo is indexed by = T. We also denoe by s = [s T, s T,..., s ] T a feasible scheduling soluion and by S he corresponding feasible region. Then, since SNR are random variables, we propose he opimizaion model for V2I ransmission scheduling based on 2 wih he goal o maximize he expeced successful probabiliy of compuaion offloading: max s S :E s.. [ T ] [ T p s, SNR = E exp = { T = s = D; s. = ] In fac, i is difficul or even impracical o solve 3. Thus, we consider o bound he expeced overall successful probabiliy of compuaion offloading. The resul is given in Theorem. Theorem : For he expeced overall successful probabiliy of compuaion offloading in 3, i always holds ha E [ exp T = ] exp E [ T = ] 3. 4 Proof: I is noed ha exp x is a convex funcion wih respec o x. Thus, applying Jensen s inequaliy o he convex funcion exp x can immediaely derive Theorem.

3 3 Accordingly, o maximize he objecive funcion in 3 as much as possible, we can urn o solve he following model raher han he original model 3: [ T ] min :E s S = { T 5 = s.. s = D; s. From 5, he opimal soluion depends on he SNR of he channel in he iniial ime slo = T, i.e., SNR T = SNR or SNR T = SNR. To solve 5, we denoe he number of daa bis ha are remained o be offloaded a he beginning of he ime slo by l. Thus, we can have l = l s for = T, T,..., 2, and l T = D. We also denoe he opimal number of daa bis o be scheduled in ime slo under he condiion SNR T = SNR by s l, SNR SNR and ha under SNR T = SNR by s l, SNR SNR. e ϕd, T SNR and ϕd, T SNR be he opimal value of he objecive funcions in 5 under hese wo condiions, respecively. Now, we derive he opimal daa bis o be ransmied in each ime slo by using dynamic programming and sochasic analysis as in Theorem 2. Theorem 2: For he opimizaion model of V2I ransmission scheduling 5, he opimal ransmission scheduling is s l, SNR SNR = l, = ; l log 2 log 2 SNR, 2 = under he condiion SNR T = SNR, where is = p p ; 7 SNR SNR and s l, SNR SNR = l, = ; l log 2 log 2 SNR, 2 = under SNR T = SNR, where is = p p. 9 SNR SNR The opimal values of he objecive funcion in 5 under SNR T = SNR and SNR T = SNR are T 2 l T T T T = ϕd, T SNR = σ 2 T σ 2 T 2 l T T T T = ϕd, T SNR = σ 2 T σ 2 respecively, where l T = D. The minimum expeced objecive funcion in 5, denoed by ΦD, T, is ΦD, T = 6 8 T T ϕd, T SNR ϕd, T SNR. T T T T 2 Proof: Recall l = l s for 2. Applying he dynamic programming principle o 5, we can rearrange he opimizaion model ino a series of recursive equaions, i.e., he Bellman equaion [8], as follows f l, SNR = 2 σ 2 SNR, { 2 s } = ; min s [,l ] E [f l s, SNR ], 2. 3 Firs, we prove he heorem under he condiion SNR T = SNR by adoping mahemaical inducion as follows. i When =, he whole remaining daa bis, l, mus be ransmied in he las ime slo o mee he deadline imposed on he compuaion offloading. Thus, he opimal number of daa bis scheduled in ime slo = is s l, SNR SNR = l. Besides, given ha he SNR level of he V2I ransmission channel is high in ime slo = 2, i.e., SNR 2 = SNR, we can calculae he expeced opimal objecive funcion in ime slo = by [ 2 l ] E [f l, SNR SNR ] = E = 2l p σ 2 p SNR SNR σ 2 SNR = 2l σ 2, 4 which is in accordance wih by seing T = under SNR T = SNR. ii Suppose ha 6, 7 and hold for and 3. Based on he inducion hypohesis, we can presen 3 as f l, SNR SNR = min s [,l ] 2 l s. = σ 2 σ 2 5 iii e gs denoe he objecive funcion in 5. Now, o obain he opimal soluion for 5, we solve he equaion dgs ds =, which is equivalen o solving 2 l s ln 2 ln 2 = σ 2 SNR σ 2 =. 6 Solving 6 can direcly ge s l, SNR SNR as in 6. By subsiuing s l, SNR SNR ino 5, we can derive 2 l f l, SNR SNR = Noing ha E[ SNR = σ 2. 7 SNR = SNR ] = as given in 7, we can derive he mahemaical expecaion 2 l = E [f l, SNR SNR ] = σ 2 σ 2, 8 which can lead o by seing = T. Therefore, we can prove 6, 7 and under he condiion SNR T = SNR.

4 Fig. 3. Opimal V2I ransmission Fig. 4. The lower bound of he Fig. 5. Reliabiliy performance com- Fig. 6. Reliabiliy performance comscheduling wih D = 4 bis, T = expeced reliabiliy, exp ΦD, T, parison wih D = 4 bis, T = parison wih D = 4 bis, T = 5 and SNR T = SNR. 5, p =.9 and p =.2. wih p =.9 and p =.2. 5, p =.9 and p =.2. The proof of 8, 9 and under SNR T = SNR can also be achieved by following he same inducion logic, which is omied here for he sae of breviy. In he seady sae, he probabiliy ha he channel has a high SNR or a low SNR is TTT and TTT, respecively. Thus, we can derive 2 based on and. Proposiion : Given he applicaion profile D, T, he expeced overall successful probabiliy of compuaion offloading in 3 is no less han exp ΦD, T. Proof: The proposiion is proven by combining Theorems and 2. In addiion, we furher presen an implemenaion framewor of he reliabiliy-oriened vehicular compuaion offloading based on he dynamic programming approach as in Figure 2. Under he framewor, a vehicular node is able o dynamically schedule is daa ransmissions wihin he imposed deadline of he applicaion, such ha he overall expeced reliabiliy of he compuaion offloading can be well guaraneed in he sochasic V2I communicaion siuaion. IV. N UMERICA R ESUTS We conduc differen simulaion experimens where we se SNR = 5 db and SNR = 2 db o simulae he good and he bad SNR condiions of he V2I channel, respecively, and le σ = 3. In Figure 3, we illusrae he opimal daa ransmission scheduling s in differen specified cases of he channel sae variaion. From wo exreme cases See he red solid and he blue dashed lines, we can see ha he number of daa bis o be ransmied in each decreases as ime proceeds when he SNR is always high, while i will increase when he SNR always says low. The main reason is ha since he expeced SNR in he nex ime slo is lower given ha he curren SNR is high, he daa bis o be ransmied in he nex ime slo should be reduced in order o guaranee he offloading reliabiliy. In conras, given he curren channel is a a low-snr level, he expeced SNR in he nex ime slo is higher, such ha he daa bis o be ransmied in he nex ime slo should be larger. This proposiion can also be confirmed in oher wo specific cases where he ransiion chain consiss of mixed saes. I is worh poining ou ha since an opimal scheduling soluion for he sochasic opimizaion model 5 is obained from he opimal expecaion perspecive, i may no be he bes for a specific and deerminisic case. For insance, in Figure 3, in he exreme case where he SNR is always low, he corresponding scheduling soluion is no he bes soluion for ha case, and may even perform worse han a simple soluion ha schedules equal daa bis in each ime slo. Noneheless, in acual implemenaion, we can decide o performance local execuion insead of compuaion offloading when he lower bound of he opimal expeced successful probabiliy of compuaion offloading associaed wih an opimal scheduling soluion, exp ΦD, T, is lower han a given hreshold. Moreover, we show he profile of exp ΦD, T under differen applicaion profiles in Figure 4. A finie region wih high reliabiliy of compuaion offloading where exp ΦD, T is more han.9 does exis. Nex, we compare our mechanism based on dynamic programming mared as DP wih wo oher offloading mechanisms, one of which mared as Uniform schedules equal daa bis in each ime slo while he oher mechanism mared as Random randomly creaes he daa pariions by following he uniform disribuion. Exensive Mone Carlo simulaions have been carried ou wih replicaions per iniial sae condiion. The numerical resuls are given in Figure 5, where he average level of he successful probabiliy of compuaion offloading is illusraed wih he corresponding sandard deviaion. Besides, in Figure 6, we se p = p and vary p from. o.99 o simulae differen randomness. Figure 6 also gives he average resul as well as he sandard deviaion inerval. From hese wo figures, i can be seen ha he proposed mechanism can achieve he highes performance under differen iniial channel saes and differen channel randomness. This confirms he advanage of our proposed mehod in dynamic and sochasic communicaion siuaions. V. C ONCUSION A ND F UTURE W ORK In his leer we explore he problem of reliabiliy-oriened opimizaion of compuaion offloading in dynamic and sochasic V2I communicaions. We have proposed an opimal V2I ransmission scheduling mechanism based on dynamic programming, he goal of which is o improve he reliabiliy in compuaion offloading by maximizing he lower bound of he expeced successful probabiliy of daa ransmissions. Numerical resuls verify he effeciveness and advanage of our mehod in erms of guaraneeing he reliabiliy performance. In he fuure, we will exend our mehod o a highly reliable cooperaive compuing framewor where vehicles and infrasrucures are coordinaed o process disribued applicaions.

5 5 REFERENCES [] J. A. Guerrero-ibanez, S. Zeadally, and J. Conreras-Casillo, Inegraion challenges of inelligen ransporaion sysems wih conneced vehicle, cloud compuing, and inerne of hings echnologies, IEEE Wireless Communicaions, vol. 22, no. 6, pp , 25. [2] W. Zhang, Y. Wen, K. Guan, D. Kilper,. uo, and D. O. Wu, Energyopimal mobile cloud compuing under sochasic wireless channel, IEEE Transacions on Wireless Communicaions, vol. 2, no. 9, pp , Sepember 23. [3] O. Muoz, A. Pascual-Isere, and J. Vidal, Opimizaion of radio and compuaional resources for energy efficiency in laency-consrained applicaion offloading, IEEE Transacions on Vehicular Technology, vol. 64, no., pp , Oc 25. [4] S. agn, A. Pascual-Isere, O. Muoz, and J. Vidal, Energy efficiency in laency-consrained applicaion offloading from mobile cliens o muliple virual machines, IEEE Transacions on Signal Processing, vol. 66, no. 4, pp , Feb 28. [5] E. Baccarelli, N. Cordeschi, A. Mei, M. Panella, M. Shojafar, and J. Sefa, Energy-efficien dynamic raffic offloading and reconfiguraion of newored daa ceners for big daa sream mobile compuing: review, challenges, and a case sudy, IEEE Newor, vol. 3, no. 2, pp. 54 6, March 26. [6] C. You, K. uang,. Chae, and B. Kim, Energy-efficien resource allocaion for mobile-edge compuaion offloading, IEEE Transacions on Wireless Communicaions, vol. 6, no. 3, pp , March 27. [7] G. i, J. e, S. Peng, W. Jia, C. Wang, J. Niu, and S. Yu, Energy efficien daa collecion in large-scale inerne of hings via compuaion offloading, IEEE Inerne of Things Journal, pp., 28. [8] X. Chen,. Jiao, W. i, and X. Fu, Efficien muli-user compuaion offloading for mobile-edge cloud compuing, IEEE/ACM Transacions on Neworing, vol. 24, no. 5, pp , Ocober 26. [9] K. Zhang, Y. Mao, S. eng, Q. Zhao,. i, X. Peng,. Pan, S. Maharjan, and Y. Zhang, Energy-efficien offloading for mobile edge compuing in 5g heerogeneous newors, IEEE Access, vol. 4, pp , 26. [] P. Mach and Z. Becvar, Mobile edge compuing: A survey on archiecure and compuaion offloading, IEEE Communicaions Surveys Tuorials, vol. 9, no. 3, pp , hirdquarer 27. [] W. Yu, F. iang, X. e, W. G. acher, C. u, J. in, and X. Yang, A Survey on he Edge Compuing for he Inerne of Things, IEEE Access, vol. 6, pp , 28. [2] D. Xu, Y. i, X. Chen, J. i, P. ui, S. Chen, and J. Crowcrof, A survey of opporunisic offloading, IEEE Communicaions Surveys Tuorials, vol. 2, no. 3, pp , hirdquarer 28. [3] S. Wang, X. Zhang, Y. Zhang,. Wang, J. Yang, and W. Wang, A survey on mobile edge newors: Convergence of compuing, caching and communicaions, IEEE Access, vol. 5, pp , 27. [4] Y. Mao, C. You, J. Zhang, K. uang, and K. B. eaief, A survey on mobile edge compuing: The communicaion perspecive, IEEE Communicaions Surveys Tuorials, vol. 9, no. 4, pp , Fourhquarer 27. [5] R. Mahmud, R. Koagiri, and R. Buyya, Fog Compuing: A Taxonomy, Survey and Fuure Direcions. Singapore: Springer Singapore, 28, pp [Online]. Available: hps://doi.org/. 7/ [6] Z. Sheng, C. Mahapara, V. C. M. eung, M. Chen, and P. K. Sahu, Energy efficien cooperaive compuing in mobile wireless sensor newors, IEEE Transacions on Cloud Compuing, vol. 6, no., pp. 4 26, Jan 28. [7] Q. Zhang and S. A. Kassam, Finie-sae marov model for rayleigh fading channels, IEEE Transacions on Communicaions, vol. 47, no., pp , Nov 999. [8] M. Sniedovich, Dynamic programming: foundaions and principles. Boca Raon: CRC Press, 2.