Quality of Service Optimization for Vehicular Edge Computing with Solar-Powered Road Side Units

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1 Qualiy of Service Opimizaion for Vehicular Edge Compuing wih Solar-Powered Road Side Unis Yu-Jen Ku, Po-Han Chiang and Suji Dey Mobile Sysems Design Lab, Dep. of Elecrical and Compuer Engineering, Universiy of California, San Diego {yuku, pochiang, Absrac This paper shows he viabiliy of Solar-powered Road Side Unis (SRSU), consising of small cell base saions and Mobile Edge Compuing (MEC) servers, and powered solely by solar panels wih baery, o provide conneced vehicles wih a lowlaency, easy-o-deploy and energy-efficien communicaion and edge compuing infrasrucure. However, SRSU may enail a high risk of power deficiency, leading o severe Qualiy of Service (QoS) loss due o spaial and emporal flucuaion of solar power generaion. Meanwhile, he daa raffic demand also varies wih space and ime. The mismach beween solar power generaion and SRSU power consumpion makes opimal use of solar power challenging. In his paper, we model he above problem wih hree sub-problems, he SRSU power consumpion minimizaion problem, he emporal energy balancing problem and spaial energy balancing problem. Three algorihms are proposed o solve he above sub-problems, and hey ogeher provide a complee join baery charging and user associaion conrol algorihm o minimize he QoS loss under delay consrain of he compuing asks. Resuls wih a simulaed urban environmen using acual solar irradiance and vehicular raffic daa demonsraes ha he proposed soluion reduces he QoS loss significanly compared o greedy approaches. Keywords Solar power generaion, Road Side Unis, User Associaion, Mobile Edge Compuing, Qualiy of Service. I. INTRODUCTION Emerging conneced vehicles will need o suppor differen levels of assised and auonomous driving, road safey, infoainmen and collaboraion services, wih increasingly high hroughpu and low laency compuing and communicaion needs. There is significan work in progress o ensure high hroughpu wireless conneciviy beween vehicles (V2V) as well as vehicle-o-infrasrucure (V2I) using boh radiional cellular licensed specrum or ITS bands (e.g. ITS 5.9 GHz) [1]. Road-Side Unis (RSU) are evolving o play an imporan role in providing infrasrucure suppor o increase he range of communicaions as well as help provide various vehicular services. To saisfy he massive growh in communicaion demands, in paricular in urban areas, dense deploymen of small cell base saions (SBS) [2] is expeced, which can also funcion as RSUs o saisfy he high hroughpu requiremens of emerging vehicular applicaions. Furhermore, he small cell-based RSUs can be supplemened wih Mobile Edge Compuing (MEC), allowing opporunisic use of MEC resources for growing vehicular compuing needs while sill saisfying low laency requiremens. While he use of RSUs consising of SBS and MEC will make high hroughpu and low laency emerging vehicular applicaions viable, i is imporan o ake ino consideraion he energy consumpion and susainabiliy of he vehicular wireless infrasrucure. From [3], i is esimaed ha he carbon dioxide equivalen (CO 2e) and he oal energy consumpion of cellular neworks globally will escalae o 235 million ons and 120TWh per year by Alhough he power consumpion of SBS is 100x o 1000x less han he macro base saion (BS) [4], he dense deploymen of massive SBSs will sill make he accumulaed power consumpion beyond ha consumed by macro BSs. The pas few years have seen growing research on cellular neworks powered by renewable energy, in paricular solar energy [3]. While he power generaion rae of solar panels is no sufficien o be he sole source of power for macro BSs, in his paper we show ha i is sufficien o power an SBS wih a reasonably sized solar panel of a few square meers square. Hence, we propose he use of Solar-powered Road Side Unis (SRSU), consising of SBS, MEC, solar panel and baery. SRSUs will no only achieve reduced power consumpion and provide clean wireless and edge compuing infrasrucure bu enable quick and on-demand deploymens as needed in urban areas. A criical challenge of adoping solar energy in a wireless nework is heir inermien and flucuaing naure. From he solar irradiance measuremen in [5], solar generaion varies significanly on locaion and ime. On he oher hand, he vehicular daa raffic profile also varies wih differen ime and locaion, which ogeher wih he inermiency of solar generaion, may lead o mismaches beween solar generaion and SRSU power demands. The mismach beween power generaion and consumpion may lead o severe Qualiy of Service (QoS) loss, leading o service disrupions for he vehicular applicaions. We expec each vehicle will coninuously upload he informaion capured by is sensors, including images and video segmens recorded by is cameras, o is conneced SRSU. The MEC node in each SRSU need o process he received informaion and form conexual daa. The conexual daa should be compued and ransmied back o he vehicle wih a delay consrain o ensure driving safey. To accomplish he whole process, he SRSU should allocae o each vehicle sufficien uplink, downlink, and compuaional resources. When he power demand of SRSU canno be fulfilled by he solar generaion or sored energy in he baery, i will need o rearrange is compuing and communicaion resource allocaion, so is power consumpion can be reduced, consequenly adversely affecing he QoS experienced by he served vehicles due o delay consrain violaions. In he wors case, when here is no solar power To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

2 generaed and he SRSU baery is fully discharged, he conneced vehicles canno be served a all, leading o service ouage. We model he above challenges as a QoS loss minimizaion problem by miigaing he emporal and spaial mismach of he solar power generaion profile and SRSU power consumpion hrough baery charging/discharging managemen and vehicle associaion. We break down he problem ino hree subproblems: 1) Minimizing SRSU Power Consumpion problem (MPC) given he daa raffic demand, 2) Temporal Energy Balancing problem (TEB) as emporal allocaion of solar energy o mach he profile of solar generaion and power consumpion for individual SRSU, and 3) Spaial Energy Balancing (SEB) problem o balance solar energy among muliple SRSUs. Then, we propose he QoS Loss Minimizaion (QLM) algorihm, a join solar energy sorage and baery charging, user associaion and SRSU resource allocaion mechanism comprising hree algorihms solving he above hree sub-problems respecively. A. Relaed Work Various relevan recen works ha address he use of renewable energy o minimize grid energy in wireless cellular communicaions. In [6], he auhors opimally adjus he cell size and schedule daily solar energy of BSs o minimize grid-power consumpion in a solar-powered wireless neworks. In [6], he raffic load is balanced by modifying he ransmi power of BSs while our work manages user associaion wihou requiring o change cell size. In [7], he auhors propose a Lyapunov opimizaion framework o adap he BS resource allocaion and baery operaion o minimize grid power consumpion. However, he objecive in [7] is o minimize he grid-power consumpion while our work is o minimize he QoS loss wih RSUs powered solely by solar energy. The auhors in [8] minimize he SBS power ouage probabiliy by proposing a power availabiliy oriened user associaion sraegy under ransmission rae consrain. In [9], he auhors proposed o minimize he overall nework laency under limied solar availabiliy by downlink power conrol and user associaion managemen. The above research considers only downlink ransmission while we address he problem of boh uplink and downlink ransmissions and compuing resource in order o faciliae vehicles offloading heir compuing o he SRSU. In [10], he auhors address he problem of minimizing he execuion delay and workload failure in a single MEC-enabled BS-user link powered by solar energy. They make online ask offloading and ransmi power decision on he user side under delay and energy consrains. The auhors in [11] focus on minimizing he long-erm sysem cos, including execuion delay, downlink ransmission delay, baery depreciaion and backup diesel power consumpion, of a solar-powered MECenabled single-bs. They propose a learning-based dynamic workload offloading and MEC server auoscaling sraegy o solve he above problem. The auhors in [12] exends he work in [11] wih a muli- RSU cellular nework. In he nework, he workload can be offloaded beween MEC servers locaed in differen SBSs. Alhough he SBSs in he nework is conneced o grid power, hey apply energy budge consrains o each SBS. Regulaed by he energy budge, he problem is o minimize he overall sysem delay due o compuaion and downlink ransmission. Unlike [10] and [11] which consider only a poin-o-poin MEC-enabled link, we propose a join BS resource allocaion and user associaion echnique among muliple SBSs. Alhough [12] considers muliple SBSs, i only applies o he scenario ha he workload can be divided ino arbirary porions, and allocaed simulaneously o muliple SBSs. In our work, we consider a more pracical scenario ha he enire workload of he user can only be execued a he associaed SBS. Moreover, he long-erm energy budge consrain used in [12] canno efficienly capure he naure of high inermiency of solar power generaion. The res of he paper is organized as follows. Secion II elaboraes he sysem models used, including workload, MEC server, channel, power consumpion and baery model.the problem we are addressing is formulaed in Secion III. Secion IV describes he QLM algorihm, our proposed join solar power-aware SBS energy sorage and iner-sbs user associaion algorihm along wih SBS power minimizaion. We presen he simulaion resuls in Secion V, and conclude in Secion VI. A. Nework Model II. SYSTEM MODEL Consider a se of N SRSUs B = {1,2,, N} along a road R 1 and a se of vehicular users (UEs) I = {1,2,, Ι}. Each SRSU b has a SBS and a MEC, each of which we will also refer o as b h SBS and MEC respecively. Each SRSU is powered solely by a solar panel and equipped wih a baery. The maximum capaciy of he MEC processor in SRSU b is denoed as U b megabis per second (MIPS), and he maximum bandwidh offered by associaed SBS b for downlink and uplink ransmission any ime are W b,d and W b,u, respecively. We divide he duraion of ime equally ino T ime slos, each ime slo has duraion τ. B. Workload Model and SBS uilizaion A each ime slo, we assume ha a group of UE will pass hrough he endpoins of each roads R r, r {1,2,,6} wih predeermined ravel roues and speed, enering he nework following a Poisson process wih arrival rae λ r, while anoher group of UEs will pass hrough hese endpoins and leave he nework. The locaion and speed of he i h UE a ime slo is denoed by x i and v i respecively. x i and v i of each UE over T ime slos are assumed o be known a he sar of 1 s. This assumpion is valid given ha he raffic load difference of a single base saion beween wo consecuive days are limied [13] and by he approach in [14] [15], rouine UE movemens can be known in advance under negligible predicion error. Le a bi = {0,1} be he UE associaion indicaor, where a bi = 1 if he i h UE is conneced o b h SBS and a bi = 0 oherwise. Wihou loss of generaliy, we assume UE will iniially connec o he SBS ha provides he highes Received Signal Srengh Indicaion (RSSI) measuremen. To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

3 w bi,u iεζ (b) W b,u, b B (2) Figure 1. he workload and MEC server model The workload generaed by he i h UE a each ime slo can be represened as K i = { s i, c i, δ i, ε i, d i }, wih he noaions explained as he following. s i is he size of video and conexual sensor daa generaed a his ime slo, which is uploaded o he MEC server. The daa is uploaded once i is generaed. we assume he daa generaion rae is a consan, so he uploading rae is no less han s i /τ. The MEC server will wai for a duraion υ before saring he daa processing. The duraion υ is chosen as large as possible for he MEC server o collec as much daa as possible for analysis. The compuing resource required o process he daa uploaded by he i h UE is denoed as c i. The SBS will hen ransmi he processed informaion, which has size δ i, back o he i h UE. The delay requiremen of he analysis process and downlink ransmission is denoed as d i. Since he analysis resuls are criical o driving safey, d i is very small compared o τ and we refer o his kind of daa as delay sensiive downlink daa. Noe ha his whole process needs o be finished in one ime slo, herefore, he duraion υ along wih he compuaion and downlink delay should no be greaer han τ. Furhermore, some of he UEs migh concurrenly download exra informaion from he MEC server or he Inerne, for example, he map daa or video frames capured from oher UEs which are sored in he MEC server. The daa size and delay consrain of hese exra daa are se o be ε i and τ respecively. Since τ is much longer han d i, we refer o hese daa as delay oleran downlink daa. The overall workload and MEC compuing model is shown in Fig. 1. Each K i will uilize a combinaion of compuing and communicaion resources of he SRSU where i is offloaded. We assume ha he MEC sever can concurrenly serve muliple workloads from differen UE using echniques such as Virual Machine(VM) [16]. Le u bi be he CPU processor s capaciy allocaed o he i h UE by he b h MEC server; w bi,u be he uplink bandwidh allocaed o he i h UE by he b h SBS respecively. For downlink ransmission, we denoe w bi,ds and w bi,dt as he downlink bandwidh allocaed o he i h UE by he b h SBS for delay sensiive and delay oleran daa respecively. Since he resource of a SBS is limied, we have he following compuing and communicaion resource consrains [17]: ( w bi,ds iεζ (b) + w bi,dt ) W b,d, b B (3) where ζ (b) I is he se of UEs which are associae o he b h SBS a ime. C. Channel and Delay Model We se boh of he ransmi power densiy of SBS and UE o be fixed and denoed hem as p B and p I respecively. The downlink ransmission rae from he b h SBS o he i h UE per 1 Hz is r bi,d = log 2 (1 + η bi ), (4) where η bi = (p B g bi /N 0 ) is he signal-o-noise raio (SNR) wih g bi denoes he downlink channel gain and N 0 is he noise power densiy. We assume he iner-cell inerference (ICI) from oher SBSs can be ignored since our approach requires informaion of UE locaion and associaion condiion o be shared among SBSs, in he meanime, SBSs can obain he channel esimaion of each UE and eliminae ICI by implemening Coordinaed Mulipoin (CoMP) [18] Similarly, he uplink ransmission rae from i h UE o b h SBS per 1 Hz is given by r bi,u = log 2 (1 + p Ig bi ). (5) N 0 For simpliciy, we assume ha here is no video buffer in UE sides, which means each video frame will be uploaded immediaely afer i is capured. The uploading ransmission rae of he i h UE should be greaer han he video size per ime slo. Consequenly, for each UE, he allocaed uplink bandwidh should saisfy he consrain: a bi r bi,u w bi,u τ a bi s i, iϵi. (6) while he consrain of he allocaed downlink bandwidh for delay oleran ransmission is: a bi r bi,d w bi,dt τ a bi ε i, iϵi. (7) The overall delay of he delay sensiive downlink daa can be expressed as he compuaion delay of offloaded applicaion ask processing plus he downlink ransmission delay. To he i h UE, he consrain on he allocaed processing speed and downlink bandwidh for delay sensiive daa can be expressed as: a bi ( c i u bi + δ i r bi,d w bi,ds ) a bi d i, iϵi. (8) iεζ (b) u bi U b, b B (1) To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

4 D. Power Consumpion Model Since our work focuses on he solar power allocaion sraegies of SRSU, we will omi he energy consumpion of UE in our model. The power consumpion of he b h MEC server can be calculaed by [16] = E S,IDLE + (E S,MAX E S,IDLE ) u iεζ(b) bi, (9) U b E b,s where E max is he power consumpion when he server is fullyuilized and E S,IDLE as he power consumpion when he server is idle. Transmission power is he major facor for SRSU power consumpion. The downlink power consumpion of he b h SBS can be modeled as E b,d = p d ( w bi,ds iεζ (b) = p d ( δ i r bi,d iεζ (b) δ i r bi,d w bi,ds + τ w bi,dt iεζ (b) + τ w bi,dt iεζ (b) ) (10) ), (11) where p d is he overall downlink ransmission power densiy: p d = (p B + p c,d ) wih p c,d is he circui power densiy needed o realize a downlink ransmission, for example, i can be he power consumpion of modulaion as well as channel encoding [19] [20]. Similarly, he power consumed for receiving uplink daa from all he associaed UEs will be = p c,u τ w bi,u. (12) E b,u iεζ (b) Denoing E b,idle as he idle power of he SBS, he oal power consumpion of SRSU b a ime slo is herefore E b = E b,s + E b,d E. Solar Energy and Baery Model + E b,u + E b,idle. (13) Each SRSU is accompanied wih a solar panel as energy harvesing module and a baery as energy sorage module. A each ime slo, he solar panel of he b h SRSU will generae J b joules of energy. Le BAT b be he b h SRSU baery level a slo. BAT b is conrolled by a baery charging sraegy under zero loss on charging, discharging and depleion wih he following consrain: 0 BAT b = J b E b =1 =1 (14) where 1 T, which ensures ha he baery canno be discharged afer he sored energy has been exhaused. Alhough he solar power generaion flucuaes wih ime and locaion, our previous work has shown ha i can be prediced several hours in advance wih very high accuracy [21]. Therefore, we assume advanced knowledge of he solar power generaed a SRSUs: {J b 1, J b 2,, J b T } b B. III. PROBLEM FORMULATION Noe ha since he solar power is limied and changes emporally, SRSU migh suffer power deficiency in some ime slos. For he b h SRSU, he power deficiency happens a ime slo when he energy drained from baery BAT 1 b BAT b plus he generaed solar energy J b is less han he SRSU power consumpion E b. Under his condiion, he SRSU mus reduce E b by eiher re-associaing he UEs in ζ (b) o oher SRSUs or dropping heir service. If here exiss any UE ha canno be reassociaed o any SRSU a ime slo, he offloaded applicaion of his UE in his ime slo will be dropped, leading o a QoS loss since UE canno offload is daa processing applicaion o SRSU. Such QoS loss is denoed by C drop, which is defined o be equal o he oal number of UEs experiencing his ype of QoS loss a ime slo. C drop I B = (1 a bi i=1 b=1 ). (15) Moreover, SRSU migh hand over is UE o oher SRSUs afer he end of curren ime slo, making his UE fail o receive he processed informaion corresponding o he daa ha is uploaded afer duraion υ. We refer o his informaion loss as a QoS loss from handover, C handover, which is defined as he oal number of UEs suffering such QoS loss a ime slo muliplied 1 by a scaling facor κ = 1 υ/τ. We se C handover = 0, and for 2, C handover I = κ a bi (1 a bi a bi i=1 B b=1 1 ) (16) Given he solar power generaed J b a each ime slo over he whole day for each SRSU b and he daa raffic demand profile {K i, x i, v i } for each UE, we focus on minimizing he QoS loss specified by (15) and (16). Our objecive is o opimally deermine he user associaion A i = {a 1i, a 2i,, a Bi }, iεi and allocae solar energy o each ime slo o minimize he overall average QoS loss during imeslos T, while saisfying he workload compuaion and ransmission delay, communicaion resource, compuing resource and solar generaion consrains. The overall average QoS loss is defined as he overall QoS loss divided by he accumulaed oal number of UE in he nework a each ime slos. The problem can be formulaed as: min A i,iεi,1 T T =1(C drop T =1 ) + C handover I s.. (1) - (3), (6) - (8), (14).. (17) where I is he number of UEs in he nework a ime slo. Problem (17) is difficul o solve since SRSU can generae differen solar power and experience disinc daa raffic demand a differen ime slo. Moreover, differen SRSU will have diverse solar power generaion and daa raffic a he same ime slo. Therefore, we propose o heurisically break down (17) ino 3 sub-problems: 1) Minimizing SRSU Power Consumpion (MPC) problem aims o minimize single SRSU power To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

5 consumpion given he workload and provides a feasible SRSU compuing and communicaion resource allocaion, 2) Temporal Energy Balancing (TEB) problem addresses he problem of miigaing he mismach beween energy generaion and power consumpion over ime for individual SRSU, and 3) Spaial Energy Balancing (SEB) problem is formulaed o balance he workload raffic and solar power among all he N SRSUs. In he following paragraphs, we will explain hese hree sub-problems in deail. 1) MPC Problem: Subjec o he limied power supply of solar panel, SRSU should minimize is power consumpion E b given is associaed UE se ζ (b) a each ime slo by opimally allocaing he communicaion and compuing resources. Therefore, we formulae MPC as {w bi,ds min,w bi,dt,u bi,wbi,u },iε ζ (b) E b (18) s.. (1) - (3), (6) - (8). The allocaion of processing power and channel bandwidh should saisfy consrains (1) - (3) o ensure he allocaed SRSU resource will no exceed he resource limiaion of he SBS. Meanwhile, he allocaion of SRSU communicaion and compuing resources saisfy consrains (6) - (8) o avoid violaing he boh he daa raffic ransmission and UE applicaion ask compuaion delay requiremens. 2) TEB Problem: Le { M 1 b, M 2 b,, M T b } be he solar energy allocaed o he b h SRSU over he T imeslos. Since SRSU allocaes solar energy o any ime slo hrough baery charging and dischargin sraegies, he allocaion sraegy should saisfy baery consrain, in oher words, M b = BAT 1 b BAT b + J b. The objecive of TEB is o minimize he mismach beween allocaed solarenergy M b and power consumpion E b for all ime slos. Defining he allocae-usagepower-raio (AUPR) o be π b = M b /E b, he problem can be expressed as max min π { M 1 b,mb 2,,Mb T b (19) } 1 T s.. M b E s,idle + E b,idle, 1 T (20) (14). The consrain on M b in (20) guaranees ha SRSU will never be shu down because of he lack of generaed solar power and fully discharged baery. 3) SEB Problem: Due o he spaial diversiy of daa raffic profile, some SRSUs migh experience high workload raffic when is allocaed solar power is low. Conversely, due o he spaial diversiy of solar power generaion, some SRSUs may have more solar power generaion han is need, resuling in solar power surplus. Noe ha if SRSU is under power deficiency, namely π b 1, i forces SRSU o reduce is power consumpion E b by dropping or re-associaing is conneced UE o he feasible SRSU saisfyiny consrains (14) (20). When UE is offloaded o a new SRSU by changing he user associaion, he workload is re-direced o his new hos. This provides us he oppuruniy o reduce he QoS loss. Therefore, SEB is formulaed as a problem in (21), which is o achieve he Figure 2. Breakdown of he QLM algorihm minimum QoS loss by maximizing he possible workload balancing across he SRSUs for each ime slo. min C { A 1,A2,,AI drop + κc handover (21) } s.. π b 1, b B (22) a bi η bi a bi η h. (23) (1)~ (3), (6)~ (8). The firs consrain (22) requires every SRSU has is allocaed solar power higher han is power consumpion. Consrain (23) saes ha he SNR beween i^h UE and he SRSU i is re-associaed o should be greaer han a hreshold η h o saisfy he minimum RSSI requiremen of he SBS nework. Consrains (1) o (3) ensure ha SRSU s communicaion and compuing resource allocaion afer he change of UE associaion sill saisfies is resource limi. Moreover, for he associaed UE, he delay consrains of he workload should never be violaed, as saed in consrains (6) o (8). Since problem (17) is divided ino hree sub-problems, in he nex secion, we will firs presen our proposed soluion o hese hree sub-problems and hen inroduce an opimal join solar energy sorage and user associaion echnique by adoping hese hree soluions. IV. ALGORITHM DESIGN In his secion we inroduce he QoS Loss Minimizaion (QLM) algorihm o solve (17). As shown in Fig. 2, QLM leverages he soluion of MPC, TEB and SEB problems. A he beginning of every ime slo, each UE is associaed wih he SBS which provides he bes SNR η bi. Each SRSU will firs minimize is power consumpion and find he resuling feasible user se ζ (b). The soluion of MPC will opimally allocae he compuaion and communicaion resource o he associaed UE for each SRSU o minimize he power consumpion. Under consrains (1) o (3) SRSU will need o drop some UEs if here is no available communicaion or compuing resources. Afer he energy consumpion of each SRSU a each ime slo has been esimaed by MPCA, he Temporal Energy Balancing Algorihm (TEBA) is proposed o solve TEB problem, which decides how o schedule he generaed solar over T ime slos for each SRSU. Based on he resul of he TEBA, he To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

6 Spaial Energy Balancing Algorihm (SEBA) will balance he offloaded UE applicaion among all SRSUs considering he raio of allocaed green energy and power consumpion by UE offloading echnique o minimize number of UEs experiencing offloaded applicaion QoS loss by dropping or hand over. Since he resul of SEBA will change SRSU s esimaed power consumpion, and hence affecs he resul of TEBA, he TEBA and SEBA will be ieraively execued unil he opimum is achieved. A. The MPCA algorihm Noe ha E b in (13) is a linear combinaion of resource allocaion indicaors w bi,ds, w bi,dt, u bi, w bi,u,iε ζ (b). Since he consrains on w bi,dt and w bi,u are independen of oher variables and E b is sricly increasing wih w bi,dt and w bi,u, by (6) and (7), he opimal value of w bi,dt and w bi,u should be w bi,u = s i r bi,u τ, w bi,dt = ε i r bi,d τ, iε ζ (b). (24) On he oher hand, since E b is independen of he value of w bi,ds, he resource allocaion problem in (18) is equivalen o minimizing he MEC server power consumpion (9) subjec o he processor speed consrain (1), downlink bandwidh limiaion (3) and workload delay requiremen (8). Noe ha since (1), (3), (8), (9) are convex funcions when u bi > 0 and > 0, he opimal soluion can be achieved by analyzing w bi,dl Temporal Energy Balancing Algorihm (TEBA) Inpu: {E b, J b ห1 T, b B} Oupu: {M b ห1 T, b B} Iniialize M b J b, b, E E s,idle + E b,idle ; for b = 1 o N do for = T 1 o 1 do for = + 1 o T do γ b = max(ρҧe b M b, 0) ; θ b = max(e M b, 0); end for calculae γ sum = T γ i= b, θ sum = T θ i= b ; calculae ρ, b πb ; If θ sum > M b E calculae θ spare = max(m b E, 0) ; calculae γ spare = 0; else calculae θ spare = θ sum ; calculae γ spare = max(m b θ spare ρҧe b, 0) ; endif for = + 1 o T do If γ sum 0: M b = M γ b + γ b spare ; endif γ sum If θ sum 0: M b = M b + θ spare θ b end for M b = M b ε spare ; end for end for Figure 4. TEBA algorihm θ sum ; endif is Karush Kuhn Tucker (KKT) condiions. The proof is similar o Boyd in [22], which is omied for breviy. To show he opimal resul in (26), we define he following erms for all i h UE in ζ (b), γ i = δ i r bi,d c i d, σ i = γ i i d, π b = w bi,dt, i iεζ (b) Q iεζ σ i b = (b) W b,d π i, y iεζ (b) γ i = c i i d + γ i d i Q i d b. (25) i Then he opimal resource allocaion for u bi and w bi,dl is u bi = y i c i, w bi,ds = y i γ i d i, iε ζ (b). (26) Q b However, he above analysis is under he condiion ha ζ (b) is a feasible se for he b h SRSU. When ζ (b) is no feasible, MPCA will drop he UE which consumes he mos communicaion and compuing resource unil consrains of (18) are saisfied. B. The TEBA algorihm Given he minimized power consumpion of each SRSU a each ime slo from MPCA, solar energy generaion and power consumpion of a single SRSU are mached by solving he TEB problem. The soluion is provided by TEBA, as shown in Fig. 4. To make he smalles AUPR π b among all ime slos as large as possible, he idea of TEBA is o allocae he curren generaed solar energy J b o fuure ime slos + 1 o T. In he beginning of TEBA, he allocaed solar energy M b for each ime slo is iniialized o be equal o J b. To saisfy consrain (14), TEBA will sar he allocaion process from he las slo o he firs slo. Since all SRSU has o remain on a all ime, he algorihm will firs check if here exiss any ime slo beween + 1 o T which has M b < E s,idle + E b,idle. If yes, TEBA will allocae par of M b o unil no such exiss or M b iself reaches he lower limi, namely E s,idle + E b,idle. π b is recalculaed by he residual M b, if he updaed π b is greaer han he average AUPR ρ b afer ime slos, where ρ b is calculaed as: ρ T i M b = i= b, (27) T E i i= b TEBA will le π b equal ρ b by reducing M b. The redundan M b will be allocaed o ime slos, >, wih π b < ρ b by a value proporional o he solar energy required o make π b = ρ. b TEBA will repea he above process unil all of he ime slos are processed. C. The SEBA algorihm Based on he resul of TEBA, we propose he algorihm SEBA shown in Fig. 5 o balance he solar energy among differen SRSUs. SEBA has hree seps: 1) choose he SRSU which has he smalles AUPR wih is value less han 1, namely he allocaed solar power is less han is esimaed power consumpion; 2) drop or offload associaed UEs of he above SBS unil is AUPR is a leas 1. 3) ieraively apply above seps o oher SRSUs unil all SRSUs have AUPR greaer han 1. A each ime slo, SEBA will firs sor all SRSUs by heir AUPR in an ascending order. Following he sored lis, SEBA To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

7 Spaial Energy Balancing Algorihm (SEBA) Inpu: Time slo, {E b, M b, ζ (b) ห b B}, {K i, A i หi I}, u bi, w bi,u, w bi,ds, w bi,dt ห i I, b B, U b, E S,MAX, α, p d, p c,u, τ Oupu: {A i หi I}, {E b, ζ (b) ห b B}, u bi, w bi,u, w bi,ds, w bi,dt ห i I, b B. Iniialize Ω bi {u bi, w bi,u, w bi,ds, w bi,dt }; Sor SRSU by π b in an ascending order, sore he index in D. while D is no empy do b D(1). Λ b { max(b 1,1), min(b + 1, N)}; Sep 1: Divide ζ (b ) ino subses S 1, S 2, S 3 Sor UE in each group S i by he corresponding power consumpion in a descending order, le he sored index be H 1, H 2, H 3 respecively. H {H 1, H 2, H 3 }; Sep 2: change associaion saus of UEs while π b 1 do i M H(1). sor all SRSUs b Λ b \{b } by η b i M in descend order, le he sored index be Z; f drop rue; for b = 1 o Λ b \{b } do b m Z(b ), ζ (b m ) v ζ (b m ) { i M } calculae (Ω bm i M ) by (23), (25) use ζ (b v m ) v if ζ (b m ) v and (Ω bm i M ) saisfy (1) - (3), (6) - (8), v and (E bm ) M v bm do ζ (b m ) ζ (b m ) v, ζ (b ) ζ (b )\{ i M } a b i M 0, a bm i M 1, Ω bm i M (Ω bm i M ) v updae Ω b i, i ζ (b ) by (24), (26) use ζ (b ) updae E bm, E b by (13), updae π bm, π b ; H H\{H(1)}; f drop false; break; end if end for if f drop == rue do ζ (b ) ζ (b )\{ i M }, a b i M 0, updae Ω b i, i ζ (b ) by (24), (26) use ζ (b ) updae E b, updae π b ; H H\{H(1)}; end if end while D D\{D(1)}; end while Figure 5. SEBA algorihm will check if he every SRSU s AUPR is less han 1. For such SRSU, SEBA separaes UEs in ζ (b) ino hree subses: S 1, S 2, and S 3. S 1 includes he UEs ha are handed over o he b h SRSU from oher SRSUs a curren ime slo; S 2 includes he UEs ha previously have no connecion o any SRSUs and he UEs ha are previously associaed o he b h SRSU is included in S 3. The raionale of he grouping is ha changing he associaion of UEs in S 1 will no increase he value of C handover since hese UEs already suffer he QoS loss from handover. On he oher hand, alhough dropping he UEs in S 2 and S 3 will boh Figure 6. (a) above, a neighborhood around Flabush Avenue in Brooklyn. (b) below, nework opology showing deploymen of roads and SBSs. increase C drop, re-associaing he UEs in S 2 will no increase C handover. Therefore, SEBA will sar o change he associaion saus of UEs in S 1,followed by UEs in S 2 and S 3. In each subse, he UE ha accouns for he highes power consumpion, which is calculaed by he compuing and communicaion resource allocaed o UE will be firs chosen by SEBA. Whenever SEBA is going o change he associaion saus of a UE, i will check if he wo neighbor SRSUs can accommodae his UE wihou violaing consrains (1) - (3) and keep heir own π b < 1. If no, SEBA will drop his UE. Since E b for each SRSU will be modified afer he UE offloading process, TEBA needs o be applied o find he new opimal solar energy allocaion. The sysem will ieraively run TEBA and SEBA unil he cos canno be furher decreased. We use a hreshold shown in Fig. 2 o erminae he ieraions. V. EXPERIMENTAL RESULT In his secion, we firs inroduce our MATLAB-based simulaion framework and simulaion parameers. We furher presen he effecs of MCPA, TEBA and SEBA algorihms on he final power consumpion and UE associaion resul o SRSUs. In he end, we compare he performance of our overall QLM algorihm wih wo Greedy SRSU Energy Managemen (GSEM) sraegies. A. Simulaion Framework The objecive of our simulaion framework is o observe he effecs of differen solar energy managemen and UE associaion sraegies on QoS loss of he offloaded applicaion wih realworld environmen. Therefore, our simulaion environmen consiss of he solar phoovolaic (PV) model, he SRSU power consumpion model, he channel model, he user locaion and raffic model, he vehicular applicaions workload model and he MEC server model. The sysem parameers are summarized in Table I. We choose o sudy he srees in a neighborhood in Brooklyn, New York Ciy, shown in Fig. 6(a), so ha we can uilize hisorical raffic daa for he srees colleced by New York Sae Deparmen of Transporaion and available in [23]. In our simulaion environmen, we implemen he opology of he srees wih he placemen of SRSUs as shown in Fig. 6(b). The opology comprises of a bidirecional long road R 1, crossed by 5 shor bidirecional srees {R 2, R 3,, R 5 }, dividing R1 ino 6 bidirecional segmens {S 1, S 2,, S 6 }. The SRSUs are se along R 1, each separaed by 400 meers. The oal bandwidh of each SBS of each direcion in our To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

8 Table I. Simulaion Parameers Parameer Descripion Value N Number of SRSUs 8 τ Duraion of a ime slo 1 (s) U b Compuing resource limi 4744 (MIPS) W b,u UL bandwidh limi (MHz) W b,d DL bandwidh limi (MHz) p B SBS anenna power densiy 20 (dbm/mhz) p I UE anenna power densiy 17 (dbm/mhz) p c,u UL a SBS circui power densiy 15.6 (mw/mhz) p c,d DL b SBS circui power densiy 15.6 (mw/mhz) N 0 Noise power densiy -184 (dbm/mhz) E b,idle SBS power consumpion in idle 6 (W) Channel model g bi Pah loss log10(R), R in kilomeers, R is he disance beween SBS and UE Shadowing 8 (db) a UL: Uplink, b DL: Downlink simulaion is 5MHz, which is furher divided ino 25 resource blocks. Noe ha he minimum bandwidh available o a UE is equal o he bandwidh of a resource block, namely 0.18 MHz. We model he power consumpion and compuing resource profile of he MEC server as Raspberry Pi 2 Model B, which has been shown o be a feasible soluion for low-power cloud servers [24]. The power consumed for he MEC server a idle and fully uilized mode is 4.8W and 6.25W respecively. For solar generaion profile, we use he solar irradiance daa in [5], which provides emporal variaion a each SRSU as well as spaial variaion across he SRSUs. We choose o simulae for 24 hours from 9AM o 9AM, so ha SRSUs can leverage he solar energy generaed during he day ime o power iself a nigh, when here is no solar energy generaion. As menioned in Secion II, he number of UE enering he nework a each ime slo follows a Poisson disribuion wih rae parameer λ r. Each UE is enering he nework wih predeermined ravel roues and speed. The ravel roues decision, speed and λ r are se in a manner ha he average raffic volume of each road segmens and cross srees S R will saisfy he hisorical daa in [23]. Furhermore, he ransmission channel model is specified by he Vehicular o Evolved Node B (enb) ype RSU channel model in [25] wih pah loss model lised in Table 1 and he ransmied power of SBS and UE are specified as a ypical small cell nework [26]. Figure 7. Iniial power consumpion for wo SRSUs and afer MPCA To model he offloading of he vehicle asks and he uplink/downlink daa, we assume ha each UE will upload a 1080p 30fps H.264 encoded video file o is associaed SRSU a each ime slo, which requires approximaely 10 Million insrucions per second (MIPS) for video processing including decoding and objec deecion by he MEC [27] [28]. We se he uploaded daa size o be uniformly disribued beween 11 o 13.5 MB. Since he delay sensiive downlink daa size depends on he informaion in he uplink daa, we assume he daa size is uniformly disribued beween 0.1 o 0.3 MB. In he meanime, half of he vehicles will reques o download a 720p or 1080p 30fps H.264 encoded video wih duraion τ, each wih 0.5 probabiliy and delay consrain equals τ. In he nex subsecion, we firs presen he effecs of MPCA, TEBA and SEBA by showing he change of individual SRSU s power consumpion and user associaion. Then, we compare he performance of QLM in erms of is weighed QoS loss of he offloaded ask processing by using wo Greedy SRSU Energy Managemen (GEM) sraegies for emporal solar power allocaion. The firs GEM, he Ordinary GEM (OGEM), allows each SRSU o uilize any available solar and baery energy o saisfy is power demand a ime slo and sore he remaining solar power o he baery. Consequenly, OGEM will make each SRSU s AUPR equal o 1 a every ime slo, which resrains UE from being re-associaed beween differen SRSUs since SRSUs have no redundan energy o serve exra workload. The second GEM sraegy ses he allocaed solar energy a each ime slo o he value ha is 1.2 imes higher han is esimaed power consumpion when he baery level is higher han a hreshold 50 Whr. We denoe his sraegy as he Reserved GEM Figure 8. Solar generaion, power consumpion and vehicle associaions for wo SRSUs. (a) lef, solar generaion profile; (b) middle, iniial power consumpion and afer QLM algorihm; (c) righ, iniial vehicle associaion and afer QLM. To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

9 Figure 9. (a) lef, overall QoS loss of hree algorihms for each ime slo; (b) righ, power consumpion of a SRSU for hree algorihms: QLM, OGEM and RGEM. (RGEM). If he baery level is less han 50 Whr, RGEM operaes in he same way as OGEM. We assume RGEM performs he same UE associaion sraegy as SEBA since RGEM allows SRSU s AUPR be greaer han 1. B. Simulaion Resul We firs observe he effec of MPCA by comparing is resul wih SRSU s power consumpion wihou MPCA. We assume ha wihou MPCA, SRSU communicaion and compuing resources are allocaed by he following rules: w bi,u and w bi,dt are allocaed by (24); u bi and w bi,ds are calculaed so ha boh of he compuaion delay and downlink ransmission delay are equal o 0.5 d i. The resuls in Fig. 7 shows ha he power consumpion of SRSU1 and SRSU2 decreases afer MCPA under he same offloaded ask profiles. Fig, 8 shows he effecs of TEBA and SEBA. Fig 8 (a) depics he solar power generaion profiles of wo SRSUs during he 24-hour simulaion period. Fig. 8 (b) shows he iniial power consumpion and final power consumpion of SRSU 1 and SRSU 2 afer applying QLM algorihm. As menioned in Secion III, a ime slo, UEs in he nework will iniially connec o SRSU which provides he highes RSSI. Based on he communicaion and compuing consrains, SRSU hen finds is feasible associaion se ζ (b), which leads o he iniial esimaion of SRSU power consumpion a ime slo. The effec of TEBA can be observed from final SRSU power consumpion resul shown in Fig. 8(b), as he solar generaion profiles in Fig. 8(a) are arranged by TEMA o mach he iniial power consumpion esimaion. Since solar generaed by SRSU 1 is no sufficien o serve all he workload from UEs in he iniial feasible associaion se ζ (1), during SEBA, SRSU 1 will associae some of he UEs in ζ (1) o SRSU 2, reducing is power consumpion and prevening hese UEs from experiencing QoS loss. Consequenly, he number of associaed UEs decreases in SRSU 1 while SRSU 2 shows he opposie rend, as shown in Fig. 8(c). Table II shows he performance comparison of OGEM, RGEM and QLM, where Drop and Handover in Table II represens he QoS loss of offloaded UE applicaion from UE drop and UE handover inroduced by (15) (16) divided by he number of UEs in he nework respecively. On he oher hands, Overall in Table II represens he overall average QoS loss inroduced in (17). QLM can reduce he weighed QoS loss by 31% compared o OGEM and 52% compared o RGEM. As menioned in previous subsecion, OGEM canno balance he offloaded ask profile among differen SRSUs. If a SRSU is running ou of solar energy and is baery is fully discharged, i will drop he served UEs insead of rying o offload hem, leading o higher drop rae compared o QLM. In comparison, alhough RGEM allows UEs o be re-associaed beween SRSUs, is power consumpion unaware baery charging sraegy makes SRSUs eiher have surplus allocaed solar power or suffer power deficiency simulaneously mos of he ime. Table II. QoS Loss Performance QoS Loss a Algorihms QLM OGEM RGEM Drop Handover Overall a Uni: % Therefore, RGEM fails o ake he advanage of UE reassociaion o reduce he QoS loss. Fig. 9(a) elaboraes he QoS loss performance of OGEM, RGEM and QLM a each ime slos. Before 5 AM, all of he algorihms have similar performance. This is because he energy sored in he baery is enough o saisfy he SRSU s iniial power consumpion esimaion during his period. Afer 5 PM, he overall average QoS loss of OGEM and RGEM escalaes due o insufficien solar generaion and fully discharged baery. The same phenomenon can be observed in Fig. 9(b), where he SRSU is forced o shu down during 5 o 9 AM by RGEM and 7 o 9 AM by OGEM under he absence of solar power and an empy baery. On he conrary, QLM keeps he QoS loss average during he whole simulaion period low by opimally allocaing he solar energy o each ime slos hrough scheduled charging and discharging of he baery and balance he offloaded ask among SRSUs. The resul indicaes ha our algorihm no only can balance he mismach of SRSU solar energy generaion and power consumpion over differen ime slos bu can also opimally compensae he power deficiency of a single SRSU by uilizing resources from is neighboring SRSUs. VI. CONCLUSION In his paper, we show he feasibiliy of a green road infrasrucure of solar-powered RSUs, consising of small cell bases saion and edge compuing, o suppor he compuing and communicaions needs of vehicles. We propose he QLM algorihm, which is a join solar power conservaion and user associaion algorihm which minimizes he average QoS loss due o service ouage and handover loss possible when a SRSU runs ou of solar or baery power. We break down he problem ino hree sub-problems and propose algorihms for each subproblem including combinaions of SRSU s communicaion and compuing resource allocaion, solar power conservaion and UE associaion echniques. Our simulaion resuls shows ha QLM significanly reduces he average QoS loss caused by power deficiency compared o greedy algorihms. To appear in Proc. of IEEE Inernaional Conference on Compuer Communicaions and Neworks (ICCCN 18)

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