Pervasive and Mobile Computing. Analysis of power saving and its impact on web traffic in cellular networks with continuous connectivity

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1 Pevasive and Mobile Computing ( ) Contents lists available at SciVese ScienceDiect Pevasive and Mobile Computing jounal homepage: Fast tack aticle Analysis of powe saving and its impact on web taffic in cellula netwoks with continuous connectivity Saa Alouf a, Vincenzo Mancuso b,, Nicaise Choungmo Fofack a,c a INRIA, Sophia Antipolis, Fance b Institute IMDEA Netwoks, Madid, Spain c Univesity of Nice Sophia Antipolis, Fance a t i c l e i n f o a b s t a c t Aticle histoy: Available online xxxx Keywods: Geen IT Continuous connectivity Powe saving Analysis Web taffic In this wok, we analyze the powe saving and its impact on web taffic pefomance when customes adopt the continuous connectivity paadigm. To this end, we povide a model fo packet tansmission and cost. We model each mobile use s taffic with a ealistic web taffic pofile, and study the aggegate behavio of the uses attached to a base station by means of a pocesso-shaed queueing system. In paticula, we evaluate use access delay, download time and expected economy of enegy in the cell. Ou study shows that damatic enegy saving can be achieved by mobile devices and base stations, e.g., as much as 70% 90% of the enegy cost in cells with ealistic taffic load and the consideed paamete settings Elsevie B.V. All ights eseved. 1. Intoduction The total opeating cost fo a cellula netwok is of the ode of tens of millions of dollas fo a medium small netwok with twenty thousand base stations [1]. A elevant potion of this cost is due to powe consumption, which can be damatically educed by using efficient powe saving stategies. Powe saving can be achieved in cellula netwoks opeating WiMAX, HSPA, o LTE potocols by optimizing the hadwae, the coveage and the distibution of the signal, o also by implementing enegy-awae adio esouce management mechanisms. In paticula, we focus on powe saving in wieless tansmissions, which would enable the deployment of compact (e.g., ai conditioning fee) and geen (e.g., sola powe opeated) base stations, thus equiing less opeational and management costs. An inteesting case study is offeed by the behavioal analysis of uses that emain online fo long peiods. These uses equest a continuous availability of a dedicated wideband data channel, in ode to shoten the delay to access the netwok as soon as new packets have to be exchanged. This continuous connectivity equies fequent exchange of contol packets, even when no data ae awaiting fo tansmission. Theefoe, in the case of continuous connectivity, a huge amount of enegy might be spent just to contol the high-speed connection, unless powe saving is enfoced. Howeve, since powe saving mode affects packet delay, some constaints have to be consideed when tuning to the powe saving opeational mode. Powe saving and sleep mode in cellula netwoks have been analytically and expeimentally investigated in the liteatue, mainly fom the use equipment (UE) viewpoint. E.g., powe saving in the UMTS UE has been evaluated in [2,3] by means of a semi-makov chain model. The authos of [4] popose an embedded Makov chain to model the system This manuscipt is an extended vesion of Mancuso and Alouf (2011) [16]. Coesponding autho. addesses: saa.alouf@inia.f (S. Alouf), vincenzo.mancuso@ieee.og, vincenzo.mancuso@imdea.og (V. Mancuso), nicaise.choungmo_fofack@inia.f (N.C. Fofack) /$ see font matte 2012 Elsevie B.V. All ights eseved. doi: /j.pmcj

2 2 S. Alouf et al. / Pevasive and Mobile Computing ( ) vacations in IEEE e, whee the base station queue is seen as an M/GI/1/N system. The authos of [5] use an M/G/1 queue with epeated vacations to model an e-like sleep mode and to compute the sevice cost fo a single use download. Using Laplace Stieltjes Tansfom and Pobability Geneating Functions, [6] deives closed fom expessions fo the aveage powe consumption (objective) and the aveage packet delay (constaint) fo an UE. The authos of [6] also design a sleep mode mechanism based on taffic estimation and a solution of the optimization poblem. Analytical models, suppoted by simulations, wee poposed by Xiao fo evaluating the pefomance of the UE in tems of enegy consumption and access delay in both downlink and uplink [7]. Almhana et al. povide an adaptive algoithm that minimizes enegy subject to QoS equiements fo delay [8]. The woks [9,10] closely elate to ou poposal and mainly focus on the analysis of the discontinuous eception mode in 3GPP LTE and IEEE m espectively. The authos conside both the uplink and downlink packets fo the UE and show that uplink packets incease the powe consumption and decease the delay. The existing wok does not tackle the base station (o evolved node B, namely enb) viewpoint no analytically captues the elation between cell load and sevice ate statistics. Futhemoe, fo sake of tactability, many of those studies assume that packet aivals follow a Poisson model. Instead, in eal netwoks, the use taffic can be vey busty and follow long tail distibutions [11]. In contast, we use a G/G/1 queue with vacations to model the behavio of each UE, and we compose the behavio of multiple uses into a single G/G/1 PS queue that models the enb taffic. We analytically compute the cost eduction achievable thanks to powe saving mode opeations, and show how to minimize the system cost unde QoS constaints. In paticula we efe to the mechanisms made available by 3GPP fo Continuous Packet Connectivity (CPC), i.e., the discontinuous tansmission (DTX) and discontinuous eception (DRX) [12]. The impotance of DRX has been addessed in [13], whee the authos model a pocedue fo adapting the DRX paametes based on the taffic demand, in LTE and UMTS, via a semi-makov model fo busty packet data taffic. A desciption of DRX advantages in LTE fom the use viewpoint is given in [14] by means of a simple cost model. In [15], the authos use heuistics and simulation to show the impotance of DRX fo the UE. The contibutions of ou wok ae as follows: (i) we ae the fist to povide a complete model fo the behavio of uses (UEs) and base stations (enbs) in continuous connectivity and with non-poisson taffic (namely web taffic), (ii) we povide a cost model that incopoates the diffeent causes of opeational costs, (iii) we validate ou model using packet-level simulations, (iv) we study the impotance of a vaiety of model paametes by means of a sensitivity analysis, and (v) we show how to use the model to minimize opeational costs unde QoS constaints. Ou esults confim that a temendous cost eduction can be attained by coectly tuning the powe saving paametes. In paticula, tansmission costs can be loweed by moe than 90% with ealistic taffic loads. This aticle extends ou wok published in the poceedings of IEEE WoWMoM 2011 [16]. Compaed with the confeence pape, we implemented the following modifications and additions: (i) We have done a eseach eview of ecent woks and have amended the elated wok section by adding thee new efeences. (ii) The pesentation of the analytical model has been impoved as some equations/deivations have been explicitly witten. The cost model has also been efined impacting all the numeical esults which ely on it. (iii) We have pefomed simulations in which each use has p paallel bowsing sessions; the aim is to evaluate whethe ou study can be used when each use s taffic consists of supeposed aival pocesses. (iv) A sensitivity analysis has been pefomed. We povide both fist ode and total sensitivity indices and comment on the implications and the intepetations of these indices. (v) The numeical analysis has been evisited and expanded with new numeical esults. (vi) A lessons leaned section has been added, summaizing ou ecommendations and suggesting a setup which achieves a good tadeoff between enegy savings and QoS pefomance. The est of the manuscipt is oganized as follows: Section 2 pesents powe saving opeations in continuous connectivity mode. Section 3 descibes a model fo cellula uses geneating web taffic. Section 4 illustates a model fo downlink tansmissions, and Section 5 descibes how to evaluate flow pefomance and tansmission costs. In Section 6 we validate the model though simulation. A sensitivity analysis is pefomed in Section 7, and a pefomance analysis and optimization is done in Section 8 showing the achievable powe saving. Section 9 concludes the aticle. 2. Continuous connectivity Cellula packet netwoks, in which the base station schedules the use activity, equie the online UEs to check a contol channel continuously, namely fo T ln s pe system slot (i.e., pe subfame T sub ). Fo instance, CPC has been defined by 3GPP fo the next geneation of high-speed mobile uses, in which uses egiste to the data packet sevice of thei wieless opeato and then emain online even when they do not tansmit o eceive any data fo long peiods [17]. A highly efficient powe saving mode opeation is then stongly equied, which would allow disabling both tansmission and eception of fames duing the idle peiods. The UE, howeve, has to tansmit and eceive contol fames at egula hythm, evey few tens of milliseconds, so that synchonization with the base station and powe contol loop can be maintained. Theefoe, idle peiods ae limited by the mandatoy contol activity that involves the UE. To save enegy, when thee is no taffic fo the use, the UE can ente a powe saving mode in which it checks and epots on the contol channels accoding to a fixed patten, i.e., only once evey m time slots. Relevant enegy economy can be achieved. In change, the queued packets have to wait fo the mth subfame befoe being seved. Discontinuous tansmission. DTX has been fist defined by 3GPP elease 7. It is a UE opeational mode fo discontinuous uplink tansmission ove the Dedicated Physical Contol Channel (DPCCH). With DTX, UEs tansmit contol infomation accoding

3 S. Alouf et al. / Pevasive and Mobile Computing ( ) 3 Fig. 1. Downlink queue activity with powe saving and nomal opeation. to a cycle. Thee ae actually two possible DTX cycles. The fist cycle is shot (few subfames) and is used when some data activity is pesent in the uplink (nomal opeation). The second cycle is longe (up to tens of subfames) and is activated when an inactivity time in the uplink data channel expies (powe saving mode opeation). The theshold M fo inactivity peiod is a powe of 2 subfames (specified values ae in {2 1, 2 2,..., 2 9 }). Discontinuous eception. DRX is an opeational mode defined by 3GPP elease 6. It allows the UE to save enegy while monitoing the contol infomation tansmitted by the enb. DRX affects data delivey, since no data can be dependably eceived without an associated contol fame. 3GPP specifications define a DRX cycle, that is the total numbe of subfames in a listening/sleeping window out of which only one subfame is used fo contol eception. Valid values fo this cycle ae 4 to 20 subfames (i.e., using a 2 ms subfame in HSPA yields cycles of 8 to 40 ms). DRX is activated only upon a timeout afte the last downlink tansmission, and like DTX, the timeout theshold M specified in the standad is a powe of 2 subfames. 3. Powe saving model We focus on the powe consumption due to wieless activity on the ai inteface of mobile uses (UEs) and base station (enb). On the one hand, we assume that uplink contol tansmission follows the DTX patten. On the othe hand, the UE has to decode the downlink contol channel accoding to the DRX patten, and eceive packets accodingly [17]. Thus, uplink powe saving can be enabled by means of a long DTX cycle, with a timeout whose duation can be of the same ode of the subfame size. Downlink powe saving is similaly enfoced by setting the DRX cycle and timeout. Theeby, powe saving issues in uplink and downlink can be modeled in a simila way, and thee is little diffeence between the cost computation of a single UE and the one of a base station. Indeed, the oveall cost at the enb can be seen as the collection of costs ove the contol and data channels towads the vaious UEs, plus a fixed pe-cell opeational cost that the enb has to pay to notify its pesence and maintain the uses synchonized. Theefoe, hee we focus on the downlink only, and begin ou analysis with the behavio of a UE eceiving a data steam. Powe saving in downlink. As illustated in Fig. 1, downlink powe saving can be obtained by altenating between two possible DRX cycles: afte any downlink data activity thee is a shot cycle in which the UE checks the contol channel at each subfame (nomal opeation mode); instead, upon the expiation of T out (inactivity time consisting of M subfames), thee is a longe cycle in which the UE checks the contol channel peiodically, with peiod m subfames (powe saving mode). 1 In powe saving mode, the UE monitos the downlink contol channel evey m subfames, and etuns to nomal mode as soon as the channel sampling detects a contol message indicating that the downlink queue is no longe empty. Note that UEs do not eceive any sevice duing: (i) I nom, i.e., idle intevals in nomal opeation, (ii) timeout intevals, and (iii) I ps, i.e., idle intevals in powe saving mode. To quantify the powe saving that can be achieved at the UE, in Section 4 we model the behavio of downlink tansmissions with DRX opeations enabled and uses geneating web taffic. Then, in Section 5 we discuss the tadeoff between pe-packet pefomance and pe-ue cost. Ou model can be used fo systems using slotted opeations, and in paticula LTE and HSPA [17]. The model can be applied to both uplink and downlink. Howeve, fo sake of claity, we explicitly deal with the downlink case. Achievable cost saving and pefomance metics will be expessed as a function of the subfame length T sub and the DRX paametes, namely the timeout duation, though the paamete M, and the DRX powe saving cycle duation, though 1 The actual system timeout is M-subfame long. Howeve, since the UE checks fo new taffic at the beginning of a subfame, the UE switches to powe saving mode if it does not eceive any taffic alet at the beginning of the Mth idle subfame. Theefoe, it is enough to have no aivals fo M 1 subfames and the UE will not eceive any packet fo M subfames.

4 4 S. Alouf et al. / Pevasive and Mobile Computing ( ) Fig. 2. System cycle with web taffic as defined in [18]. Table 1 Paametes suggested by 3GPP2 fo the evaluation of web taffic. Quantity Pobability distibution Paametes Main object size S mo = X f X (x) = 1 (ln x µ X )2 2πσ 2 2 2σ 2 X e X xmax x 2πσ 2 min X 1 2 e (ln t µ X )2 2σ 2 X α yα min y, y [y min, y Numbe of embedded objects N eo = Y y min f Y (y) = α+1 max [ α ymin 1, y = y max Embedded object size S eo = Z f Z (z) = y max 1 (ln z µ Z )2 2πσ 2 2 2σ 2 Z e Z zmax z 2πσ 2 min Z 1 2 e (ln t µ Z )2 2σ 2 Z dt dt, x [x min, x max ] µ X = 8.35 σ X = 1.37 x min = 100 bytes x max = bytes y min = 2 y max = 55 α = 1.1, z [z min, z max ] µ Z = 6.17 σ Z = 2.36 z min = 50 bytes z max = bytes Reading time Λ f Λ (t) = λ e λ t, t 0 λ = 0.03 s Pasing time Λ p f Λp (t) = λ p e λpt, t 0 λ p = 7.69 s the paamete m. We assume fixed-length packets, and the seve capacity is exactly one packet pe subfame. Howeve, no packet is seved fo UEs in powe saving mode, and the seve capacity is shaed, in each subfame, between the UEs opeating in nomal mode. Theefoe, we model a system which behaves as a G/G/1 PS queue with epeated fixed-length vacations of s. Befoe poceeding with the model deivation, we intoduce the taffic model adopted in this study. Taffic model. We assume that downlink taffic is the composition of uses web bowsing sessions. Taffic pofile is the same fo all uses and is as follows. The size of each web equest is modeled as suggested by 3GPP2 in [18]: a web page consists of one main object, whose size is a andom vaiable with tuncated lognomal distibution, and zeo o moe embedded objects, each with andom, tuncated lognomal distibuted size. The numbe of embedded objects is a andom vaiable deived fom a tuncated Paeto distibution. Each web page equest tigges the download of the packets caying the main object only. Then a pasing time is needed fo the use application to pase the main object and equest the embedded objects, if any. The pasing time distibution is exponential with ate λ p. Afte having eceived the last packet of the last object, the custome eads the web page fo an exponentially distibuted eading time, whose ate is λ. If no object is embedded, the eading time includes the pasing time. Finally he/she equests anothe web page. Fig. 2 epesents the UE s downlink queue size at the enb duing a geneic web page equest and download. Table 1 summaizes the paametes used fo the geneation of web bowsing sessions. Note that the pobability ψ 0 to have no embedded objects in a web page can be computed though the α y distibution of the tuncated Paeto andom vaiable Y descibed in Table 1: ψ 0 = P(y min Y < y min +1) = 1 min. y min +1 Note also that the downlink of the web page expeiences a small access delay due to the completion of the cuent DRX cycle befoe the fist packet of the new bust could be seved. In ou model, we assume that the time to equest a web object with a http GET command is negligible in compaison with the time needed to pase the main object, and theefoe also in compaison with the time needed fo a custome to ead the web page. Hence we incopoate this equest delay in the pasing time and in the eading time. In this way, we clealy focus ou study on the sole impact of the wieless technology on the system pefomance and costs. Futhemoe, packet aivals ae supposed to be busty afte each GET equest, so that no powe saving mode can be tiggeed afte an object download begins, i.e., all powe saving intevals ae contained in eithe pasing o eading times. With these assumptions, we study the system pefomance though the analysis of a geneic web page download and its fuition. Moe pecisely, we study the system cycle defined as the time in between two consecutive web page equests. Theefoe, the system cycle

5 S. Alouf et al. / Pevasive and Mobile Computing ( ) 5 can be decomposed in fou phases, as depicted in Fig. 2: (i) download of the main object of the web page, (ii) pasing of the main object, (iii) download of embedded objects, and (iv) web page eading. The fist thee phases epesent the web page download time, fom the fist packet aival in the enb queue to the last packet delivey to the UE. Access delay and download time chaacteize the sevice expeienced by the custome. 4. Model deivation Hee we deive the time spent by the system in the vaious cycle phases. Fo ease of notation, we define β p = e λ pt sub and β = e λ T sub as the pobabilities that, espectively, the exponentially distibuted pasing time and eading time ae longe than one subfame. Hence the timeout pobability is β M 1 in eading time, and β M 1 p in pasing time. Timeouts in a cycle. Cycles always include one eading time, but the pasing time is pesent only if thee ae embedded objects (i.e., with pobability 1 ψ 0 ). The aveage numbe of timeouts in a cycle is then: E[N to ] = β M 1 + (1 ψ 0 ) β M 1 p. Hence each cycle includes, on aveage, E[N to ](M 1)T sub s due to timeout occuences. Idle time in powe saving mode. The aveage time pe cycle duing which the system is in powe saving mode, denoted as I 0, is computed by summing up the time spent in powe saving mode (the intevals I ps as in Fig. 1) occuing in the eading time and in the pasing time, if any is pesent in the cycle: I 0 = I ps eading + I ps pasing. Thanks to the memoyless popety of exponential aivals, the inteval between the timeout expiation and the aival of the next data packet is exponential too, and has the same exponential ate. In paticula, the powe saving inteval that begins in the eading time lasts a multiple numbe of checking intevals, with the following distibution and aveage: eading, I 0 = j timeout P = P 0 aivals in (j 1) 1 P 0 aivals in = β m j 1 1 β m, j 1; E[I 0 eading] = β M 1 1 β m ; whee we also emoved the conditioning on the timeout occuence. Similaly, fo the pasing time: E[I 0 pasing] = β M 1 p. 1 βp m Theefoe, the expected value of the time spent in powe saving mode in a system cycle is given by the following aveage: E[I 0 ] = β M 1 1 β m + (1 ψ 0 ) β M 1 p. (2) 1 βp m Note that E[I 0 ] is a function of m and M, the web taffic paametes being fixed. It is easy to find that E[I m 0] > 0, and E[I M 0] < 0, hence the powe saving inteval I 0 monotonically gows with the duation of the DRX cycle, and deceases with the duation of the timeout. Idle time in nomal mode. The amount of time spent in nomal mode without seving any taffic is the sum of the nomal mode idle intevals due to pasing and eading times. Since we counted apat the time spent in timeouts by means of (1), hee we only count the intevals I nom, whose sum ove a system cycle is denoted by I 1 = I nom eading +I nom pasing. Consideing that I nom is always a multiple of T sub but smalle than a timeout, and since the component of I 1 in eading time is I nom eading, the conditional distibution of I 1 in eading time and its expectation ae as follows: P I 1 = jt sub eading = P I nom = jt sub exp. aivals with ate λ β M 1, j = 0; = β j 1 (1 β ), 1 j M 1; 1 Mβ M 1 + (M 1)β M E[I 1 eading] = T sub. (3) 1 β Similaly, the expected value of the time spent in nomal mode with no taffic to be seved duing pasing, not counting the timeout, is given by 1 Mβ M 1 p + (M 1)β M p E[I 1 pasing] = T sub. (4) 1 β p (1)

6 6 S. Alouf et al. / Pevasive and Mobile Computing ( ) Theefoe, the aveage duation of I 1, attained by using (3) and (4), is an inceasing function of the timeout duation, as expessed by the following fomula: 1 Mβ M 1 + (M 1)β M E[I 1 ] = T sub + (1 ψ 0 ) 1 MβM 1 p + (M 1)β M p. (5) 1 β 1 β p Cumulative idle time. The cumulative amount of idle time I in a cycle is the sum of timeouts, I 0, and I 1. Its expected value is then as follows: β M 1 p E[I] = βm 1 1 β m 1 β M 1 + T sub + (1 ψ 0 ) 1 β 1 β m p 1 β M 1 p + T sub. (6) 1 β p E[I] is a deceasing function of M, and inceases with m. Howeve, with ou model assumptions, E[I] is slightly lage than the sum of eading and pasing times. Moe pecisely, its value is bounded as follows: ψ 0 < E[I] < (1 ψ 0 ) +. (7) λ λ p λ λ p Given that m can be as high as few tens, and T sub is only few milliseconds, the poduct is negligible in compaison with the aveage pasing and eading times. Hence, fo all ealistic values of m, the pe-cycle idle time can be consideed constant and equal to its lowe bound. Busy time in a cycle. It is the time spent to seve the packets of a web page. Its expectation is the expected numbe of packets pe web page, E[N p ], times the expected sevice time E[σ ]. The numbe of packets depends on the distibution of the web page objects. Assuming the 3GPP2 taffic model epoted in Table 1 and 1500 byte long packets, we can compute: Smo Seo E[N p ] = E + E[N eo ] E = The sevice time depends on the numbe of active UEs and on the seve capacity, as we show late in this section. System cycle duation. Putting togethe the esults fo the time spent in timeouts, idle intevals, and busy peiods, the expected cycle duation is: E[T c ] = E[I] + E[N p ]E[σ ]. The elation between E[T c ] and E[σ ] is linea with a coefficient that is detemined by the web page object distibution. Since E[σ ] too will be shown to gow with m and decease with M (see next paagaph), the entie expected system cycle inceases with m and deceases with M. Futhemoe, as the expected sevice time inceases with the numbe N u of UEs attached to the enb, the system cycle behaves likewise. Howeve, both E[I] and E[σ ] ae baely affected by m and M, theeby E[T c ] is mainly affected by N u only. Sevice time. We assume that thee ae N u homogeneous UEs in the cell. The activity facto of each UE is: ρ = E[N p]e[σ ] E[T c ] = E[N p ]E[σ ] < 1. (9) E[I] + E[N p ]E[σ ] Equivalently, we can intepet ρ as the pobability that a UE is unde sevice. Note that E[σ ], E[N p ], and E[I] assume always positive values, and thus E[T c ] > 0 and 0 < ρ < 1. Fom the point of view of a geneic queue, the sevice time in the lth subfame only depends on the numbe N a (l) of queues which tansmit in that specific subfame. In fact, the downlink bandwidth is shaed between all backlogged active queues, the total seving capacity being fixed to one packet pe subfame. Thus, given that the ith queue has a packet unde sevice in the lth system subfame, the sevice time fo the ith queue is T sub N a (l). Since we ae inteested in the sevice time fo the ith queue, we condition the obsevation of the sevice time to the tansmission of a packet queued in the ith queue. Hence, consideing all queues as i.i.d., the numbe of active queues is a andom vaiable N a = 1 + ν, with ν being a andom vaiable exhibiting a binomial distibution between 0 and N u 1 with success pobability ρ. Theeby, the aveage sevice time is: E[σ ] = T sub E[1 + ν] = T sub [1 + (N u 1)ρ]. (10) Hence, consideing the expession (9) of ρ as a function of E[σ ], we have a system of two equations in two vaiables, fom which we can compute E[σ ]. Poposition. The expected packet sevice time E[σ ] is the unique positive solution of the following quadatic equation: E[N p ] E 2 [σ ] + E[I] E[N p ] N u T sub E[σ ] E[I]Tsub = 0. Poof. The equation is obtained by combining (9) and (10). Since E[N p ] and E[I] ae positive numbes, the quadatic coefficient in the equation is always positive, whilst the constant tem is negative: this is necessay and sufficient to have one positive solution and one negative solution. Howeve, the negative solution has no physical meaning. Thus, the positive solution is the only acceptable solution candidate. (8)

7 S. Alouf et al. / Pevasive and Mobile Computing ( ) 7 Coollay. The expected packet sevice time is E[σ ] = (E[N p]n u T sub E[I]) + (E[I] E[N p ] N u T sub ) 2 + 4E[I] E[N p ] T sub. 2E[N p ] As we stessed befoe, the tem E[I] inceases with m and deceases with M, but its vaiations ae quite limited. So, thanks to the Coollay, we can conclude that E[σ ] behaves as E[I], i.e., it is baely affected by m and M. Futhemoe, E[σ ] gows with N u, i.e., with the numbe of UEs in the cell. Notably, the impact of N u on E[σ ] is amplified by a facto equal to the aveage page size E[N p ]. Since a new web page is equested only afte the eading time of the pevious equest, the numbe of customes has no theoetical uppe bound. In fact, sevice time and system cycle just keep gowing with the numbe of UEs, and the aveage E[N cumulative taffic geneated and seved pe subfame is N p ] u E[N p ] E[σ ]+E[I] 1. Thus, as the system appoaches satuation, T sub E[σ ] tends to N u T sub, since in satuation the N u uses ae always active and eceive a faction 1/N u of the seve capacity. The asymptotic distibution of the system cycle duation is constant and equal to T up c = E[N p ] N u T sub + E[I], which scales linealy with the numbe of uses and loosely depends on the powe saving paametes m and M. T up c is an uppe bound on E[T c ], and can be used to limit the maximum numbe of customes, thus guaanteeing a maximum web page pocessing time to any custome. 5. Pefomance and cost metics The impact of powe saving mode on web taffic can be evaluated in tems of access delay and page download time, assuming that all the taffic is seved. Costs due to wieless tansmission and eception of packets ae to be taded off with such indicatos. Theefoe, we fist deive an expession fo pefomance metics and show how to compute the faction of time duing which powe saving can be ealistically obtained. Then we deive the paametic expessions fo cost and powe saving at both UE and enb Pefomance metics and powe saving oppotunities Page download time. The time W needed to download a web page includes the time to download each and evey page s packet, the time to pase the main object of the page, and the access delay. Hence, we can deive E[W] as the diffeence between E[T c ] and the expected eading time: E[W] = E[T c ] 1 λ. (11) Consideing (7) and (8), a tight lowe bound on the expected page download time is E[N p ]E[σ ] + (1 ψ 0 )/λ p. Access delay. The access delay is the delay expeienced afte any download equest. In ou model we conside only that pat of the access delay which is due to the wieless access potocol. In paticula, we have two epochs within each cycle at which a equest can expeience access delay: at the end of the eading time, coesponding to a new page equest, and at the end of the pasing time, coesponding to the equest fo the embedded objects. Let D be the total access delay expeienced within a web page download, accounting fo the delay accumulated in both eading and pasing times. E[D] can be easily computed by subtacting pasing, eading, and busy times fom the expected system cycle duation (see Fig. 2), i.e.: E[D] = E[I] 1 λ + 1 ψ 0 λ p. The expected access delay is a function of the powe saving paametes used in the DRX configuation, plus the taffic pofile paametes, though λ, λ p, E[N p ], and ψ 0. Howeve, using the uppe bound fo E[I], one can conclude that the access delay is uppe bounded to (2 ψ 0 ). Powe saving time atio. Economy of enegy can be achieved by educing the adio activity, including the possibility to tun off the adio tansceive, accoding to the DTX/DRX patten. Theefoe, powe saving oppotunities can be measued though the faction of cycle duing which the tansceive can be deactivated. In pactice, UE and enb can save powe duing I 0, which is a multiple of duing which no tansmissions occu. Howeve, in the inteval I 0, the UE has to peiodically be active to listen to the contol channel fo exactly T ln T sub s out of m subfames. The powe saving time atio is then defined as follows: R 1 T ln E[I0 ] E[T c ]. Recall that E[T c ] is almost insensible to m and M, but inceases with N u, and that E[I 0 ] inceases with m and deceases with M. Theefoe, R is an inceasing function of m, and it deceases with M and N u. (12) (13)

8 8 S. Alouf et al. / Pevasive and Mobile Computing ( ) 5.2. Cost analysis Cost at the UE. The basic consumption ate of the UE eceive is c on if active and c ps < c on othewise. Receiving a packet inceases the basic consumption ate by c x, while listening to the contol channel inceases it by c ln. The aveage consumption is a combination of these fou consumption tems. Fo sake of geneality we assume that listening to the contol channel can last diffeently, depending on whethe data ae associated to the contol message o not. Fo instance, in HSPA systems, the use can switch fom contol to data channel afte having decoded the initial pat (one thid) of the contol fame indicating the aival of a new data fame [17]. We denote by T ln the listening time when no data ae tansmitted, and by T ln the listening time when data follow the contol message. Theefoe, using definitions (9) and (13), and ecalling that contol channel listening is pefomed in each subfame in nomal mode, but only in one out of m subfames in powe saving mode, we can compute the cost pe UE by taking the aveage ove a system cycle while keeping sepaated the listening occuences with and without associated data tansmissions. Namely, 1 ρ m 1 m C UE (m, M, N u ) = (1 R)c on + Rc ps + ρc x + T sub E[I 0 ] E[T c ] T ln + ρt ln T sub cln. (14) Consideing a fixed web taffic pofile, the cost is a function of the powe saving paametes m and M affecting R, ρ, E[I 0 ], and E[T c ], and of the numbe of uses N u which appeas in E[T c ] and hence in R. The cost with no powe saving mode is computed by plugging E[I 0 ] = 0, which is equivalent to setting m = 1 and M, in (14): C UE (1,, N u ) = c on + ρ c x + (1 ρ) T ln + ρ T ln T sub T sub Finally, the elative powe saving gain that can be attained is: G UE (m, M, N u ) C UE(1,, N u ) C UE (m, M, N u ) C UE (1,, N u ) c ln. (15) = γ (m)e[i 0]/E[T c ] C UE (1,, N u ), (16) whee the quantity γ (m) is a cost eduction facto which inceases with the DRX powe saving cycle length m, namely: γ (m) 1 T ln con c ps Tln c ln. (17) m T sub Note that T ln does not affect the cost eduction (numeato of (16)). Summaizing, the elative gain is a function that inceases with the duation of the DRX powe saving cycle (i.e., with m), and deceases with the timeout (i.e., with M) and with the numbe N u of uses in the cell. Cost at the enb. The powe consumption ate at the enb is the sum of a fixed component, c f, that does not depend on the tansceive activity, and a vaiable component that depends on the activity of UEs in the cell. Namely, the powe consumption ate at the enb is C BS (m, M, N u ) = c f + N u C UE (m, M, N u). whee C UE (m, M, N u) is the cost pe time unit to tansmit to a single UE. It can be witten as follows: C UE (m, M, N u) = C UE (1,, N u) γ (m) E[I 0] with C UE (1,, N u) = c on + ρ c tx + T ln γ (m) = 1 T ln (18) E[T c ], (19) c sg ; (20) T sub con c ps T ln c sg. (21) m T sub Hee, c tx is a tansmission cost ate and c sg is a signaling cost. Last, the elative powe saving gain is: γ (m) G BS (m, M, N u ) = C (1,, E[I 0] UE N u) + c f E[T c ]. (22) N u Note that with few uses the main enb cost is epesented by the fixed cost c f. Hence, the gain inceases with the numbe of uses until the pe-use cost becomes the pedominant tem in the denominato of (22). 6. Validation though simulations In this section we evaluate the obustness of the model by compaing the analytical esults to simulations. The main assumption used in the model states that queues elated to diffeent active UEs ae i.i.d.; howeve, queues ae coelated in pactice as they shae the same pocesso. This assumption is not met in the simulations.

9 S. Alouf et al. / Pevasive and Mobile Computing ( ) 9 Fig. 3. E[σ ] gows with N u and is almost not affected by the timeout and the DRX powe saving cycle duations. (a) Expected system cycle duation E[T c ]. (b) Powe saving time atio R. Fig. 4. Compaison of analytic and simulation esults: (a) E[T c ], and (b) R. We developed a C++ packet-level event-diven simulato that epoduces the behavio of a time slotted G/G/1 PS queue with N u homogeneous classes. In the simulato, each class can be in two diffeent opeational modes, namely nomal mode and powe saving mode. The shaed pocesso esouces ae allocated equally to all classes in nomal mode at the beginning of each time slot of duation T sub. The taffic is homogeneously geneated, in accodance to the 3GPP2 suggested web taffic model of Table 1. Futhemoe, all simulated packets have the same size, i.e., 1500 bytes, and the pocesso capacity is 1500 bytes pe slot. Hence, if only one class is unde sevice, a packet is seved completely in one slot. Othewise, since the pocesso is shaed, all classes in nomal mode have a faction of packet seved in that slot. The fai pe-class shae is computed as one ove the numbe of classes in nomal mode. If a class has not enough backlog to use all its pocesso shae, unused esouces ae edistibuted among the emaining classes. Packet sevice is consideed complete at the end of its last sevice slot. Simulations ae pefomed fo diffeent numbes of classes N u, duation of the timeout M, and length of DRX powe saving cycle m. Heeafte, we will use λ = 1/30 s, λ p = 1/0.13, ψ 0 = 1 (2/3) 1.1, and T sub = 2 ms. Each simulation consists of a wam-up peiod lasting 10,000 s (5,000,000 slots), followed by 100 uns, each lasting 10,000 s. Statistics ae sepaately collected in each un. At the end of a simulation, all statistics ae aveaged ove the 100 uns and 99% confidence intevals ae computed fo each aveage esult. We need to un simulations fo such a long time to have statistics with elatively small confidence intevals. In fact, due to heavy tailed distibutions involved in the geneation of web taffic, the numbe of packets pe cycle has a huge vaiance. Futhemoe, simulations with a high numbe of uses equie vey long CPU time (in ou specific case, a single simulation point equies up to 12 h of a 3 GHz Intel Coe TM 2 Duo E6850 CPU), which makes it pohibitive to exploe in detail all possible values of the input paametes. As a efeence, ou model can be un with the Maple softwae in as few as 30 s on the same machine used fo simulations. The model, howeve, neglects the coelation between the activity of diffeent uses, e.g., in the computation of E[σ ]. Nevetheless, the compaison between model and simulation shows that the model appoximates the system pefomance with a good accuacy. Numeical esults fo E[σ ], obtained fom both the model and the simulations, ae epoted in Fig. 3. It is clea fom the figue that the model slightly oveestimates the sevice time fo high values of N u, i.e., when the coelation between multiple uses, in tems of pobability to shae the same tansmission slot, becomes elevant. As pedicted, m and M do not significantly affect E[σ ]. We now compae two pefomance metics: the system cycle duation E[T c ] and the powe saving time atio R. E[W] can be easily computed fom E[T c ]; cf. (11). Fo claity of pesentation, we show only a subset of the esults obtained. In paticula we selected some exteme cases that well depict the vaiability of pefomance with m, M, and N u. Fig. 4(a) compaes the estimates of E[T c ] obtained with the model (lines) and with the simulato (maked points) fo two vey diffeent values of m (4, which is the minimum in the 3GPP ecommendations, and 100). The lowe pat of the

10 10 S. Alouf et al. / Pevasive and Mobile Computing ( ) (a) High saving configuation. (b) Low saving configuation. (c) Recommended setup. Fig. 5. Impact of the numbe p of paallel use s bowsing sessions on R, fo T ln = T sub 3. figue contains the esults obtained with one use, and the uppe pat epots the esults with N u = 400 uses. The esults of the simulation ae highly vaiable due to the heavy tailed distibution in web page size statistics, hence 99%-confidence intevals appea lage ove the zoomed y-scale used in the figue. Though the aveage values show some small diffeence, both simulations and model behave similaly. The maximum elative diffeence between model and simulation with one use is within 1%, and it is below 2% with N u = 400. Noticeably, model estimates ae within the 99%-confidence intevals of simulation estimates. The main cause of the diffeence between the esults of the model and the ones obtained via simulation is in the estimation of the sevice time, which linealy affects the cycle duation. Simila diffeences can be obseved fo the powe saving time atio R with N u = 400 in Fig. 4(b). Analytic and simulation esults emain howeve vey close. The esults ae sensitive to m and N u, while the effect of M is almost negligible fo shot timeouts. In conclusion, simulations suggest that we can safely use the model to estimate the system pefomance and evaluate its potentialities fo powe saving with good accuacy Impact of paallel use s bowsing sessions In eal life, a use can activate moe than one bowsing window and switch fom window to window while a page is being loaded. Thus, in pactice it is not uncommon to have moe than one bowsing session active on the same device. Theefoe, in that case, the aival pocess at the use s download queue will esult fom the supeposition of vaious pe-bowsing session aival pocesses. Hee we simulate the occuence of multiple active http bowsing sessions fo each use, and we compae the pefomance with the case of single bowsing session. Ou model does not captue the effect of paallel http sessions, hence the expeiments poposed in this subsection ae aimed at evaluating whethe ou study can be used to appoximate the netwok behavio in moe geneic and ealistic taffic scenaios. Specifically, we focus on one paticula metic, namely the powe saving time atio, since it is epesentative of the system s powe saving pefomance. In Fig. 5, we plot the powe saving time atio R fo thee scenaios: a configuation fo the DRX paametes (M, m) yielding high powe saving (Fig. 5(a)), a configuation yielding the minimum powe saving fo ealistic values of (M, m) (Fig. 5(b)), and the configuation that we ecommend in light of ou optimization analysis epoted in Section 8, i.e., (M, m) = (256, 4) (Fig. 5(c)). The ecommended configuation, yields a good tadeoff between powe saving and seving delay incued by the packets due to DRX opeations. Note that, since a use geneates a taffic volume which depends on the numbe p of paallel http bowsing sessions, in Fig. 5 we plot R as a function of the offeed load, expessed in tems of packet aivals pe second. Fo each epesented cuve, we change the load by changing the numbe of uses N u, and epot the coesponding aival ate in the x-axis, and the powe saving time atio R in the y-axis. As efeence, we include in each figue the esults obtained with the model by inceasing N u fom 1 to 1000, then computing E[σ ] by solving the system consisting of Eqs. (9) and (10), o with the fomula given in the Coollay in Section 4, fo each given value of N u, and eventually computing the load facto as N u E[N p ]T sub /E[T c ]. The latte fomula epesents the faction of time spent in a cycle to seve the aveage aggegate volume of downlink packets N u E[N p ] geneated in that cycle, when the volume of data coesponding to one packet is seved in exactly one subfame T sub. 2 In the model, the load in packet aivals pe second is computed by scaling the load facto by 1 T sub, which is the maximum numbe of packets that can be seved in a second, and is 500 in ou case, coesponding to the capacity of a HSPA downlink with 2-ms subfames. Clealy, a given aival ate coesponds to a diffeent numbe of uses N u when p changes, and the elation between the packet aival ate, the numbe of bowsing sessions p, and the numbe of uses N u cannot be pedicted with ou model. Theefoe, fo p > 1 we only show simulation esults. 2 Equivalently, the load facto can be computed as the sum of Nu activity factos expessed as in Eq. (9), multiplied by a coefficient T sub /E[σ ] which epesents the faction of esouces allotted to a use when shaing the pocesso with othe uses.

11 S. Alouf et al. / Pevasive and Mobile Computing ( ) 11 Obseving Fig. 5, one can notice that (i) the model accuately pedicts the simulation fo p = 1, and (ii) values of p as lage as 10 can have a emakable impact on the powe saving time atio R. Howeve the impact of p is impotant only fo high loads and fo lage values of the DRX timeout M, causing up to a 25% dop in powe saving oppotunities. Howeve, fo easonable values of p, e.g., 2 to 5, R emains always vey high, and within a few pecent fom the value achieved with p = 1. In light of this esult, we ague that using ou model can suitably appoximate the computation of the powe saving oppotunities of a system with uses bowsing a few (up to 5) web pages in paallel. We will now pefom a sensitivity analysis on ou model to evaluate which paametes mostly affect the pefomance metics. 7. Sensitivity analysis In the pevious sections, we gave the expessions of the pefomance and cost metics that enables us, by a patial deivation, to outline a peliminay behavio of ou metics accoding to the input paametes, namely M, m and N u. Ou objective now is to chaacteize qualitatively and quantitatively the impact of ou input paametes on the vaiability of ou metics. We will futhe analyze the sensitivity of the metics when the expected web page size E[N p ], the expected eading ate λ, and the expected pasing ate λ ae uncetain, in addition to the thee input paametes. Pefoming a sensitivity analysis is evaluating how vaiability in the output of a model can be appotioned to diffeent input paametes. Vaiance-based techniques define sensitivity indices (i) to measue the main effect of a given input on the output, (ii) to measue the elative impotance of any combination of input in the output vaiability, and (iii) to measue the total effect of a given input on the output. Moe pecisely, assuming the inputs to be andom vaiables X 1,..., X n, and the model output to be a andom vaiable Y = f (X 1,..., X n ), the fist ode and total sensitivity indices fo andom vaiable X i ae defined as follows: Va E[Y X i ] E Va(Y X i ) S i =, S T i =, (23) Va(Y) Va(Y) whee X i denotes all input andom vaiables except X i. S i is a quantitative measue of the main effect of X i on output Y (though its vaiance) and S T i is a quantitative measue of the total effect of X i, including the inteactions with othe input andom vaiables. The diffeence S T i S i measues the impotance of inteactions in the total effect of X i. When thee ae n no inteactions between the input andom vaiables, the sum i=1 S i = 1; othewise, this sum is less than 1. If S T i is small, then this means that the value of X i is not essential, and it can be consideed as deteministic, taking any value within its ange, without any significant impact on the model output. Note that an exhaustive sensitivity analysis equies to compute 2 n 1 sensitivity indices, including those accounting fo inteactions between any combination of input andom vaiables. The sum of these 2 n 1 indices amounts to 1. One method fo estimating S i and S T i fo non-coelated vaiables is the Extended Fouie Amplitude Sensitivity Test (EFAST), intoduced by Saltelli et al. in 1999 [19]. The EFAST method does not equie any knowledge on the function f ( ), which can be seen as a black box. The advantages of EFAST ae its obustness, especially at small sample size, and its computational efficiency. EFAST expands the output of the model by using the Fouie Seies, then assigns an intege fequency to each input paamete, to finally compute the vaiance of output as well as the contibution of each input to this vaiance. Using a bute-foce appoach, computing S i and S T i equies to evaluate a multidimensional vaiance integal. The main advantage of EFAST is to educe the computation of this complex integal to a monodimensional integal ove a cuve exploing the n-dimensional space. Fo a detailed desciption of the method we efe to [19,20]. We will now show the esults of the sensitivity analysis (SA) fo the five pefomance and cost metics intoduced in Sections 4 and 5. We have checked ou esults with two diffeent softwaes that implement SA SA esults with thee input paametes: M, m and N u We fist apply the EFAST method to ou model with the web taffic configuation specified by 3GPP2 (see Table 1). We conside the following anges fo the thee input paametes: M {2, 2 2,..., 2 15 }; m {1,..., 50} and N u {1,..., 600}. All othe paametes ae constant in this analysis. We compute the fist ode (S i ) and the total (S T i ) sensitivity indices of each of the paametes M, m and N u fo the five pefomance and cost metics defined in Section 5. The esults ae displayed in Fig. 6. It is clea that paametes with small impact on some metic may well be essential fo othe metics. We can make the following obsevations: The download time E[W] is affected only by the numbe of cell uses N u ; the DRX paametes M and m may take any value within thei ange without impacting E[W]. The cycle length m is essential fo the access delay E[D] and has a mino effect on the enb s elative gain G BS. Noticeably, about two thids of the total effect of m on G BS comes fom inteactions with othe vaiables. The timeout theshold M is the most elevant paamete as concens the powe saving time atio R and the gains G UE and G BS. The second input paamete affecting mostly these metics is N u. Last, inteactions between multiple vaiables ae mostly elevant fo the gain G BS.

12 12 S. Alouf et al. / Pevasive and Mobile Computing ( ) (a) Fist ode sensitivity indices S i. (b) Total ode sensitivity indices S T i. Fig. 6. Sensitivity indices of M, m and N u fo the defined metics. (a) Fist ode sensitivity indices S i. (b) Total ode sensitivity indices S T i. Fig. 7. Sensitivity indices of M, m, N u, λ, λ p and E[N p ] fo the defined metics SA esults with six input paametes: M, m, N u, λ, λ p and E[N p ] As the Intenet (and so the web) is evolving vey fast, it is easy to pedict that the taffic paametes suggested by 3GPP2 (see Table 1) will have to be modified. Theefoe, powe saving pefomance will change accodingly, and netwok optimization will equie a diffeent setup. In paticula, the actual tend fo mobile devices is to incease memoy and data pocessing speed; meanwhile, the web page sizes tend to incease because of the embedded objects, some of which ae lage images/videos o heavy scipts. Futhemoe, some websites offe light vesions of web pages specifically fo mobile clients. To give an insight on the elevance of these changes, we now pesent the esults of ou sensitivity analysis extended to the model paametes that chaacteize the use taffic behavio, namely the eading and pasing time, though λ and λ p, and the web page aveage size E[N p ]. In ou sensitivity analysis, we conside the following anges of vaiability fo the thee additional paametes: E[N p ] {20,..., 100}, λ [0.02, 0.1], and λ p [1, 50]. The selected anges include the oiginal 3GPP2 paametes, and account fo easonable paamete modifications. Fo the esulting 6-paamete SA of ou model, Fig. 7 shows the fist ode and total sensitivity indices fo cost and pefomance metics. The following is obseved. The pasing ate λ p is definitely unessential (this is mainly due to the negligible value of the aveage pasing time compaed to the othe duations) and can be fixed to any value within its ange. The obsevation on E[D] emains unchanged: it is only impacted by the DRX paametes M and m (including thei inteactions). Inteactions between multiple vaiables play a moe impotant ole than in the SA with thee input paametes. E[N p ] and λ ae equally elevant as concens G BS, G UE and R as they have almost the same total sensitivity index. The download time E[W] is still mostly affected by N u, but it is also impacted by the web page size E[N p ] and to a lesse extent by the eading ate λ. Ou analysis eveals that λ and E[N p ] ae essential fo ou model. It is ecommended to accuately estimate λ and E[N p ] befoe using the model to optimize the powe saving configuation in the netwok. 8. Pefomance analysis and optimization The section focuses on the analysis of the pefomance and on its optimization, using the model developed in Section 4 and validated in Section 6. Whee not specified, we use the taffic paametes epoted in Table 1. Access delay. The access delay is the pefomance metic mostly impacted by the tunable paametes M (timeout theshold) and m (DRX cycle length), as confimed by the sensitivity analysis. The access delay expeienced in the netwok is epoted in Fig. 8 fo the paamete set given in Table 1. E[D] is sensitive to m, especially with low timeout values. Howeve, easonable values of m, e.g., below 20, yield access delay times not highe than 40 ms. As fo the timeout theshold, an inteesting value is M = 256 (see shape of E[D] aound M = 256 in Fig. 8).