SpeedBalance: Speed-Scaling-Aware Optimal Load Balancing for Green Cellular Networks

Transcription

1 SpeedBalance: Speed-Scalng-Aware Optmal Load Balancng for Green Cellular Networks Kyuho Son and Bhaskar Krshnamachar Department of Electrcal Engneerng, Vterb School of Engneerng Unversty of Southern Calforna, Los Angeles, CA 989 Emal: kyuhoson and Abstract Ths paper consders a component-level deceleraton technque n BS operaton, called speed-scalng, that s more conservatve than entrely shuttng down BSs, yet can conserve dynamc power effectvely durng perods of low load whle ensurng full coverage at all tmes. By formulatng a total cost mnmzaton that allows for a flexble tradeoff between delay and energy, we frst study how to adaptvely vary the processng speed based on ncomng load. We then nvestgate how ths speedscalng affects the desgn of network protocol, specfcally, wth respect to user assocaton. Based on our nvestgaton, we propose and analyze a dstrbuted algorthm, called SpeedBalance, that can yeld sgnfcant energy savngs. I. INTRODUCTION Recently, potental harmful effects to the envronment caused by CO emssons and the depleton of non-renewable resources brng renewed focus on the need to develop more energy-effcent underlyng network nfrastructures. In partcular, the focus of ths paper s on reducng the power consumpton at base statons (BSs) as they are the key source of heavy energy usage n cellular networks, reported to amount to about 6-8%. From the perspectve of moble network operators, reducng energy consumpton s not only a matter of socal responsblty towards beng green and sustanable but also tghtly related to ther busness survvablty n comng years. They are spendng huge operatonal expendtures (OPEX) to pay electrcty blls. Moreover, t s expected to grow due to explosve growth n data demand and the possble ncrease of energy prce 3. Accordng to a study from ABI Research 4, the collectve cellular network OPEX wll reach $ bllon n 3. Thus, renng back the spralng OPEX s crucal to the contnung success of operators. There have been many studes on dynamc BS swtchng technques for energy conservaton, 5 8, whch allow the system to entrely shut down some underutlzed BSs and transfer the correspondng load to neghborng BSs durng low traffc perods such as nghttme. It has substantal potental to obtan energy savngs by even reducng statc (or standby) power. Nevertheless, the operators are reluctant to turn off ther BSs not only due to the techncal challenges of mplementng t n practce, but also due to concerns about possble serous degradaton n user experence: () users orgnally n the swtched-off cell need to communcate wth farther BSs (e.g., Ths research was supported n part by NSF NetSE grant 788. more moble power consumpton for fle uploadng), and () there s always a danger of creatng coverage holes. Thus, n ths paper, we consder to ncorporate a componentlevel deceleraton technque n BS operaton that s more conservatve than turnng off BSs, yet can conserve dynamc power effectvely. Ths technque, called dynamc voltage frequency scalng (DVFS, or smply speed-scalng) 9,, allows a central processng unt (CPU) to adapt ts speed for energy conservaton based on ncomng processng demand. Note that examples of n-bs processng are ncreasngly abundant from OFDM modulaton, codng, to even securty and multmeda converson. It s also worthwhle mentonng that DVFS lowers heat dsspaton as well. As a consequence, t can reduce the power consumpton n coolng equpment contrbutng to a consderable amount of total energy consumpton, where ths exertng nfluence s often lnear. In the meantme, measurements of real BSs over several days ndcate that the power consumpton vares only about % for a GSM BS and 3% for a UMTS BS over tme regardless of ts load level. Ths mples that typcal macro BSs deployed today do not adopt dynamc power savng features. More recently, however, Alcatel-Lucent has demonstrated the feasblty of exceptonal dynamc power savngs on BSs by software upgrades and t can be expected that such BSs wll become even more wdespread n the near future. Nevertheless, the applcatons of these features to BSs and ther mpacts on the desgn of network protocols n cellular networks have not been fully understood yet. Our objectve and contrbutons: The goal of ths paper s to () characterze an equlbrum resultng from the nteracton between speed-scalng and load balancng for green cellular networks and to () propose a dstrbuted teratve optmal speed control and user assocaton polcy. The man contrbutons of the paper are summarzed as follows: ) We develop a theoretcal framework for BS energy savng that jontly encompasses speed-scalng and user assocaton. To the best of our knowledge, ths work s the frst to consder speed-scalng as a tool addressng a flexble tradeoff between delay performance and energy consumpton n both networkng and processng components of BSs. ) We frst derve an optmal processng speed for two dfferent processors havng dfferent capabltes: statc speedscalng and gated-statc speed-scalng, and then present the optmal structure of speed-scalng-aware load balancng.

2 Motvated by the above, we propose SpeedBalance, an algorthm that can be mplemented n a totally dstrbuted manner. We further evaluate the performance of SpeedBalance through extensve smulatons under an acqured 3G cellular topology and traffc trace. II. SYSTEM MODEL AND PROBLEM FORMULATION A. Model and Notaton ) Network and traffc model: We consder a downlnk cellular wreless network wth a set of base statons (BSs) B, whch serve a regonl R. Let x L denote a locaton and B be the ndex of a typcal -th BS. Fle transfer requests are assumed to arrve followng a spatally nhomogeneous Posson pont process wth arrval rate per unt area λ(x) and fle szes whch are ndependently dstrbuted wth mean /µ(x) at locatonx L, so the traffc load demand s defned as γ(x) =. λ(x) µ(x) < bts/sec. Note that ths captures spatal traffc varablty such as a hot spot. ) Channel model: The average transmsson rate of a user located at x and served by BS s denoted by c (x) bts/sec. Note that c (x) s locaton-dependent but not necessarly determned by the dstance from the BS. Hence, t can capture shadowng effect, e.g., c (x) can be very small n a shadowed area where the channel gan s very low. 3) Processng model: Each BS s assumed to have a processng component such as CPU wth a scalable speed s cycles/sec n (,s,max. Flows may have dfferent processng demands. We represent ths noton by processng densty w(x), whch s defned as the average number of CPU cycles requred per bt for the flow at locaton x. The processng demand of the traffc load at locaton x s then w(x)γ(x). 4) System utlzaton and feasble regon: Fg. llustrates our system model, where a BS s decomposed nto two parts: one part wth processng components and the other part wth RF functonaltes. A routng functon p (x) specfes the probablty that a flow at locaton x s assocated wth BS. We wll see later that, however, the optmal p (x) wll turn out to be ether or,.e., determnstc routng s optmal. As there are processng and transmsson resources, we can defne two types of system utlzaton (.e., the fractons of tme the processor or network s busy) for BS as follows: Processng utlzaton: ρ. w(x)γ(x) = p (x)dx, () L s Network utlzaton: ρ. γ(x) = L c (x) p (x)dx. () We further denote the vectors contanng processng utlzatons and network utlzatons of all BSs by ρ = (ρ,,ρ B ) and ρ = (ρ,,ρ B ), respectvely. Defnton. (Feasblty): The set F of feasble system utlzaton ρ = (ρ,ρ ) s gven by F = ρ ρ, ρ ǫ, p (x), B p (x) =, (3) < s s,max, B, x L }, Servce request at locatonx γ(x) bts/sec, w(x) cycles/bt Fg.. Vrtual dstrbuted load balancer p (x) BS Processng component (e.g., CPU, cooler) BS BS B Scalable processor speeds Networkng component (e.g., antenna, amplfer) Transmsson ratec (x) Flow-level queueng model n the dual-resource envronment. where ǫ s an arbtrarly small postve constant. Hence, the feasble system utlzaton ρ has the assocated processng speed vector s = (s,,s B ) and routng probablty vector p(x) = (p (x),,p B (x)) for all x L. B. Problem Formulaton The objectve functon we consder s mn ρ F EN+ηEP, (4) where N s the expected number of flows n the system and P s the system power consumpton. Note that the parameter η, controls the tradeoff between delay and energy. When η s zero, we only focus on delay performance, however, as η grows, more emphass s gven to energy conservaton. () The cost functon of delay performance: We consder the M/GI/ mult-class processor sharng (PS) system 3. We focus on ths model not only because PS s a tractable model of current schedulng polces, but also because mult-class can reflect the fact that users see dfferent servce rates and fle szes based on ther locatons. Usng standard queueng theory, EN, the summaton of the expected number of flows n two seral queues for all BSs, s then gven by EN = B φ (ρ )+φ (ρ ) and φ (ρ, (5) where φ (ρ ) = ρ ρ ) = ρ ρ expected number of flows n each queue, respectvely. are the () The cost functon of energy consumpton: We consder a general cost functon of energy consumpton, whch conssts of two types of powers expended n the processng and networkng components, respectvely. ψ (ρ )+ψ (ρ ), (6) EP = B The networkng components are assumed to gradually consume more power as the actvty level ncreases. Thus, the energy cost for networkng s gven by ψ (ρ ) = b ρ, (7) From Lttle s law and energy-power relatonshp, the general problem (4) s equvalent to mnmzng ED+ηEE, where N s the expected number of flows n the system and P s the system power consumpton.

3 where b > s the maxmum networkng power of BS, when fully utlzed,.e., ρ =, whch ncludes the power consumptons of Tx antenna, power amplfer and so on. The remanng s to defne the form of the energy cost for processng ψ ( ), whch also depends on the capablty of the processor for provsonng ts speed. We deal wth two dfferent types of processors ntroduced n : statc speedscalng (SS) and gated-statc speed-scalng (GS). We do not know at ths moment the explct form of ψ ( ) although we wll derve t n Secton III-A later, whch s one of our contrbutons. For now, we try to express the energy cost wth a processng speed s. Let g(s) denote the power consumpton when the processor s runnng at speed s. In the doman of processor desgn, t has been typcally assumed to be polynomal,.e., g(s) = as β. Thus, ψ ( ) s gven by a s β ψ (ρ, when SS, (8a) ) = a ρ s β, when GS, (8b) where a > and β > are some constants. Note that, for the case of GS, the energy cost s only ncurred durng the fracton of tme the processor s busy,.e., ρ. III. SPEED-SCALING-AWARE OPTIMAL LOAD BALANCING In ths paper, we consder not only delay and energy consumpton n BS s networkng components but also consder delay and energy consumpton n BS s processng components. We rewrte our orgnal problem n (4) as follows. Speed-scalng-Aware Load Balancng SA-LB: mn Ω(ρ) = φ (ρ )+φ (ρ ) ρ F } } B delay performance +η ( ψ (ρ )+ψ (ρ ) ) } } energy consumpton A. Speed-scalng Gven Processng Demand We shall start by consderng a gven processng demand. In ths case, we prove that the delay performance and energy consumpton of the networkng component can be gnored n the orgnal problem n (4) and the problem can be further decomposed nto ntra-cell speed-scalng subproblems. Theorem 3.: For any fxed routng probablty p(x), the problem n (4) s reduced to B ndependent subproblems that fnd an optmal speed s for each BS. mn s Γ s Γ + ηa s β, when SS, (9a) ηa Γ s β, when GS, (9b) where Γ. = L w(x)γ(x)p (x)dx. We call ths problem ntracell optmal speed-scalng. Proof: Due to the space lmtatons, the proof s provded n our techncal report 4. When the problem n (9) s feasble, dfferentatng and solvng gves the followng optmal condtons: for GS, z ss (s ) =. s β (s Γ ) = Γ ηa β, () z gs (s ). = s β (s Γ ) = ηa (β ). () Snce the functon z ss (s ) (resp. z gs (s )) s equal to zero at s = Γ and monotoncally ncreases for s > Γ, t Γ wll eventually cross the postve constant value ηa (resp. β ηa ) just once. Let s (β ),ss ands,gs denote the unque pont that satsfes () and () for s > Γ, respectvely. Ths can be explctly solved for some β, e.g., s,gs = Γ + ηa when ( ) β = and s,ss = Γ + Γ +4 Γ 3ηa when β = 3. Substtutng Γ = ρ s nto () and () and after some smplfcaton, we frst obtan the followng closed form expresson for the optmal speed s as a functon of ρ s (ρ ) = β β ρ ηa β( ρ : ), () ηa (β )( ρ ), for GS. We have expressed the energy cost for processng wth a processng speed s n (8). Now we can wrte t n a more explct form as a functon of the processng utlzaton ρ ψ (ρ ) = ρ ηβ( ρ. ), (3) ρ η(β )( ρ ), for GS. B. Optmal Structure of Speed-scalng-aware Load Balancng Based on the speed-scalng derved n the prevous secton, we now nvestgate the optmal structure of speed-scalngaware load balancng. Theorem 3.: Suppose that the problem SA-LB s feasble. Let us denote the optmal system utlzaton ρ = (ρ,ρ ),.e., soluton to SA-LB. Then, the followng user assocaton rule for the MT at locaton x s optmal: (x) = argmn j B M j w(x) + M j, x L, (4) c j (x) where M j = ( ρ ) j + ηψ j (ρ j )/s (ρ j ) and M j = ( ρ ) j +ηbj are metrcs that can be computed at the j-th BS sde. Proof: The proof s a generalzaton of that of 5, wth the addtonal energy cost. The problem SA-LB s a convex optmzaton because ts feasble set F has been proved to be convex and the objectve functon s the sum of convex functons. Hence, t s suffcent to show that, for all ρ F, Ω(ρ ), ρ, where ρ = ρ ρ. (5) Let p(x) and p (x) be the assocated routng probablty vectors for ρ and ρ, respectvely. Then, (4) generates the determnstc cell coverage,.e., p (x) = = argmnm j (x) j B }, (6) Ths assocaton rule can be nterpreted as sayng that each MT selfshly tres to mnmze the sum of two types of cost: () processng cost per unt CPU speed and () networkng cost per unt Tx capacty.

4 Power amplfer 35W (%) Antenna 44W (3%) Etc. 3W (%) Sgnal processng 348W (33%) Coolng 34W (%) (a) Macro BS: 64W n total Power amplfer 8W (8%) Antenna W (5%) Etc. 4.3W (%) Sgnal processng 8.8W (67%) (b) Mcro BS : 43.W n total Fg.. Maxmum power consumpton breakdown of LTE BSs based on data obtaned from. Total power consumpton kw η = 4 Conventonal SpeedBalance η = 3 λ(x)=x 4 λ(x)=3x 4 λ(x)=5x 4 η = η = η = where M j (x) = M j j c j(x). Then, the nner product Ω(ρ ), ρ can be calculated such as φ w(x) + M = (ρ )+ψ (ρ } (ρ ) B + φ (ρ )+ψ (ρ } (ρ ) = Lγ(x) M (x) (p (x) p (x)) dx. B ρ ) ρ ) (7) From (6), as p (x) s an ndcator for the mnmzer of M (x), we have the followng nequalty: BM (x) p (x) B M (x) p (x) (8) Substtutng (8) nto (7) yelds the condton n (5), whch completes the optmalty proof. C. Dstrbuted Iteratve Algorthm To determne the assocaton n (4), MTs need to know ρ a pror. However, ths wll be relaxed n our proposed dstrbuted algorthm, called SpeedBalance, whch can acheve the global optmum n an teratve manner. The dstrbuted algorthm nvolves two parts. At the k-th teraton perod, Moble termnal: MTs estmate the transmsson rate c (x) and receve the system utlzaton ρ k, e.g., through broadcast control messages from BSs. Then, a new flow request for a MT smply selects the BS k (x) based on the determnstc rule n (4), but usng the current system utlzaton ρ k nstead of the optmal one ρ. Base staton: Each BS adapts ts processng speed s accordng to (). It measures the system utlzaton ρ k+, calculates the metrcs ( M,M ), and then broadcasts them to MTs for the next teraton. IV. NUMERICAL RESULTS We frst nvestgate the component-level power consumpton breakdown of LTE BSs n Fg.. Ths reveals that () sgnal processng contrbutes to a consderable porton of total power consumpton, and () coolng and power amplfer are also major components than Tx antenna does. Note that mcro BSs typcally do not have coolng components. Etc. (e.g., power supply and battery backup) amounts to about % Per flow delay sec Fg. 3. Energy-delay tradeoff by SpeedBalance w/ SS. As η ncreases, energy savngs can be obtaned at the cost of delay ncrease. Based on these data n Fg., we choose parameters for our energy cost functon. We consder the power amplfer and antenna as networkng components, and consder the sgnal processng and coolng as processng components. To capture the statc power of these components, 5% of ther total power consumptons s consdered as statc power. Thus, we set a for macro and mcro BSs to be 6.6 and 5.3 so that ther maxmum dynamc power consumptons at the maxmum speed s =.6 Gcps are equal to 75% of (348+34)W and 8.8W. We set lkewse b for macro and mcro BSs to be 84.3 and 7.5. The macro and mcro BSs have the transmsson powers of 43.8dBm and 33dBm, respectvely. Each MT s request has exactly one fle that s log-normally dstrbuted wth mean /µ(x) = Kbyte and the processng densty w(x) over space s consdered to be unform. Other smulaton parameters are gven n 4. A. Performance Under A Mxed Macro/Mcro BS Topology We frst verfy the energy-delay tradeoff of SpeedBalance and also compare ts performance wth a conventonal scheme usng the sgnal strength-based user assocaton and do not adopt the speed-scalng. Fg. 3 shows tradeoff curves by varyng the energy-delay tradeoff parameter η from 4 to for the dfferent values of arrval rate λ(x). The results are consstent wth our expectatons: the hgher η s, the more possble energy savngs are possble at the cost of delay. In order to examne where and how the energy savngs come from, we frst plot Fgs. 4 (a) and (b) that show the convergence of processng speeds, networkng and processng utlzatons for the cases of low η = 3 and hgh η =. As can be seen, BSs slow down ther processng speeds when η s hgh (.e., gvng more emphass on energy conservaton) compared to the case of low η. Ths s one of the man reasons for reducton n power consumpton. There s another reason beyond the speed-scalng. Fg. 5 llustrates the snapshots of cell coverage by SpeedBalance for both cases. By comparng two fgures, we can clearly see that mcro BSs have large

5 5 5 5 Number of teratons Number of teratons.5 Processng speed: s Network utlzaton: ρ Processng utlzaton: ρ Number of teratons (a) Low η = Number of teratons Number of teratons.5 Processng speed: s Network utlzaton: ρ Processng utlzaton: ρ Number of teratons (b) Hgh η = Fg. 4. Convergence of SpeedBalance w/ SS. (λ(x) = 5 4 ). The dfferent curve corresponds to each of BSs. Dstance km.5.5 Macro mcro 9 Macro mcro 6 Macro 3 Macro 5 mcro mcro 7 Macro 4 mcro Dstance km (a) Low η = 3 Dstance km.5.5 Macro Macro mcro 9 mcro 6 Macro 5 Macro 3 mcro mcro 7 Macro 4 mcro Dstance km (b) Hgh η = Fg. 5. Snapshots of cell coverage by SpeedBalance w/ SS. (λ(x) = 5 4 ). Asη ncreases, the mcro BSs ndexed by 6 to have larger coverage. coverages for hgh η. In other words, more MTs are assocated wth and served by the energy-effcent mcro BSs. On the other hand, per-flow delay wll grow as η ncreases. Ths s because reducng the processng speed and concentratng the traffc load n the mcro BSs wll result n the ncrease of the processng and networkng utlzatons as shown n Fg. 4. However, n Fg. 3, t s noteworthy that the most of energy savngs can be obtaned at η = 3 whle not penalzng the delay performance, compared to the conventonal scheme. Thus, we wll choose η = 3 throughout the rest of our smulaton study. B. Performance Under A Real 3G BS Deployment Topology In order to obtan more realstc amount of energy savngs, we further consder the real map of BS layout consstng of heterogeneous envronments (urban, suburban and rural areas) and normalzed traffc trace for our smulaton. 3 TA- BLE I summarzes the average energy use durng one day. As expected, compared to the conventonal scheme, sgnfcant amounts of energy savngs can be acheved by SpeedBalance, e.g., 3.8% and 36.4% for SS and GS n weekdays, 4.7% 3 Due to the space lmtatons, the BS layout from 6, traffc trace, and other nterestng results are provded n our techncal report 4. TABLE I AVERAGE ENERGY USE DURING ONE DAY Conventonal SpeedBalance SpeedBalance scheme w/ SS w/ GS Weekday 67.3kWh 4.3kWh 39.5kWh Weekend 578.3kWh 336.9kWh 39.kWh and 44.8% for SS and GS n weekends. More energy savngs are expected durng weekends than weekdays. Ths s because the traffc load durng weekends s relatvely lower than that durng weekdays. Also note that GS can provde % more savngs than SS due to ts superor characterstc. V. CONCLUDING REMARKS Ths paper consdered speed-scalng to address the tradeoff between delay and energy n both networkng and processng components of BSs. By nvestgatng the optmal speed for processors wth SS and GS and the optmal structure of speedscalng-aware load balancng, we proposed a dstrbuted teratve algorthm, SpeedBalance. Extensve smulatons showed that compared to the conventonal scheme, SpeedBalance can yeld sgnfcant energy savngs about 3-45%. REFERENCES E. Oh, B. Krshnamachar, X. Lu, and Z. Nu, Towards dynamc energy-effcent operaton of cellular network nfrastructure, IEEE Commun. Mag., vol. 49, no. 6, pp. 56 6, Jun.. M. A. Marsan, L. Charavglo, D. Cullo, and M. Meo, Optmal energy savngs n cellular access networks, n Proc. GreenComm., Jun G. Fettwes and E. Zmmermann, ICT energy consumpton trends and challenges, n Proc. IEEE WPMC, Lapland, Fnland, Sep Moble network energy OPEX to rse dramatcally to $ bllon n 3, ABI Research, Jul K. Son, E. Oh, and B. Krshnamachar, Energy-aware herarchcal cell confguraton: from deployment to operaton, n Proc. IEEE INFOCOM - GCN Workshop, Shangha, Chna, Apr., pp Z. Nu, Y. Wu, J. Gong, and Z. 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