Power save analysis of cellular networks with continuous connectivity

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1 Powe save analysis of cellula netwoks with continuous connectivity Vincenzo Mancuso Institute IMDEA Netwoks Madid, Spain Saa Alouf INRIA Sophia Antipolis Méditeanée Sophia Antipolis, Fance Abstact In this pape, we analyze the powe save and its impact on web taffic pefomance when customes adopt the continuous connectivity paadigm. To this aim, 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. The model is validated though packet-level simulations. Ou model shows that damatic enegy save can be achieved by both mobile uses and base stations, e.g., as much as 70% of the enegy cost due to packet tansmission at the base station. Keywods-powe saving; cellula netwok; analytical model; I. INTRODUCTION The total opeating cost fo a cellula netwok is of the ode of tens of millions of dollas fo a mediumsmall netwok with twenty thousand base stations []. A elevant potion of this cost is due to powe consumption, which can be damatically educed by using efficient powe save stategies. Powe save 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 save 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 case of continuous connectivity, a huge amount of enegy might be spent just to contol the high-speed connection, unless powe save is enfoced. Howeve, since powe save mode affects packet delay, some This wok was suppoted in pat by the WiNEM poject (funded by ANR RNRT 006), the ICT FLAVIA Poject (funded by the EU Famewok 7 Pogamme), and the MEDIANET Poject (gant S009/TIC-468) fom the Geneal Diectoate of Univesities and Reseach of the Regional Govenment of Madid. constaints have to be consideed when tuning to the powe save opeational mode. Powe save 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 save in the UMTS UE has been evaluated in [] and [3] by means of a semi-makov chain model. The authos of [4] poposed an embedded Makov chain to model the system vacations in IEEE 80.6e, whee the base station queue is seen as an M/GI//N system. In [5], the authos use an M/G/ queue with epeated vacations to model an 80.6elike sleep mode and to compute the sevice cost fo a single use download. 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 [6]. The authos of [7] povide an adaptive algoithm that minimizes enegy subject to QoS equiements fo delay. The existing wok does not tackles 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 [8]. In contast, we use a G/G/ queue with vacations to model the behavio of each UE, and we compose the behavio of multiple uses into a single G/G/PS queue that models the enb taffic. We analytically compute the cost eduction achievable thanks to powe save 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) [9]. The impotance of DRX has been addessed in [0], 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 [] by means of a simple cost model. In [], the authos use heuistics and simulation to show the impotance of DRX fo the UE. The contibution of this pape is theefold: (i) we ae the fist to povide a complete model fo the behavio of uses (UEs) and base stations (enbs) in continuous connectivity //$6.00 c 0 IEEE

2 and with non-poisson taffic, (ii) we povide a cost model that incopoates the diffeent causes of opeational costs, and (iii) we show how to use the model to minimize opeational costs unde QoS constaints. Ou model has been validated though packet-level simulations, and ou esults confim that a temendous cost eduction can be attained by coectly tuning the powe save paametes. In paticula, enb tansmission costs can be loweed by moe than 70%. The pape is oganized as follows: Section II pesents powe save opeations in continuous connectivity mode; Section III descibes a model fo cellula uses geneating web taffic. Section IV illustates a model fo downlink tansmissions, and Section V descibes how to evaluate flow pefomance and tansmission costs. In Section VI we validate the model though simulation, and show the achievable powe saving. Section VII concludes the pape. II. 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 seconds 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 [3]. A highly efficient powe save 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 save 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 to a cycle. Thee ae actually two possible DTX cycles. The fist cycle is used when some data activity is pesent in the uplink (nomal opeation), and it is a shot cycle (one o vey few subfames). The second cycle is longe (up to tens of subfames), and is tiggeed afte an inactivity timeout in the uplink data channel expies (powe save mode opeation). The theshold M fo inactivity peiod is a powe of subfames. Since tansmissions on uplink data channel can only stat in paallel with DPCCH tansmissions, DTX also egulates data tansmissions. queue size Figue. T out powe save mode check waiting packets busy I ps fist aival T ln check fo T ln sec. T sub T sub nomal mode I nom I nom busy I nom fist aival T sub Downlink queue activity with powe save and nomal opeation. Discontinuous eception. DRX is an opeational mode defined by 3GPP elease 6 fo the UE to save enegy while monitoing the contol infomation tansmitted by the enb. It also affects data delivey, since no data can be dependably eceived without an associated contol fame. 3GPP specifications define a 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 0 subfames (i.e., using a ms subfame in HSPA yields a cycle of 8 to 40 ms). DRX is activated only upon a timeout expiy afte the last downlink tansmission, and like DTX, the timeout theshold specified in the standad is M subfames, with M being a powe of. III. POWER SAVE 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 [3]. Thus, uplink powe save 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 save is similaly enfoced by setting the DRX cycle and timeout. Theeby, powe save 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. In fact, the evaluation of the costs at the enb, can be seen as the collection of costs ove the contol and data channels towads the vaious UEs, plus a fixed pecell 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 save in downlink. As illustated in Figue, downlink powe save can be obtained by altenating between two possible DRX cycles: afte any downlink data activity thee is a shot cycle in which the UE continuously checks the contol channel at each subfame (nomal opeation t

3 mode); instead, upon the expiation of an inactivity timeout T out, consisting of M subfames, thee is a longe cycle in which the UE checks the contol channel peiodically, with peiodmsubfames (powe save mode). In powe save mode, the UE samples 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 save mode. To quantify the powe save that can be achieved at the UE, in Section IV we model the behavio of downlink tansmissions with DRX opeations enabled and uses geneating web taffic. Then, in Section V 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 [3]. 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 save cycle duation, though 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 save 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/PS queue with epeated fixed-length vacations of seconds. 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 3GPP in [4]: 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 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 save 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 subfames and the UE will not eceive any packet fo M subfames. queue size access delay fist aival busy access delay busy main object pasing embedded object(s) eading system cycle (web page) Figue. System cycle with web taffic as defined in [4]. 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. Figue epesents the UE s downlink queue size at the enb duing a geneic web page equest and download. Table I 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 distibution of the tuncated Paeto andom vaiable Y descibed ( in Table I: ψ 0 = P(y min Y < y min + ) = ymin α. y min+) 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 an 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 save mode can be tiggeed afte an object download begins, i.e., all powe save 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 can be decomposed in fou phases, as depicted in Figue : (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. IV. MODEL DERIVATION Hee we deive the time spent by the system in the vaious cycle phases. Fo ease of notation, we define β p = e λpt sub and β = e λt 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 in eading time, and β M p in pasing time. t

4 Table I PARAMETERS SUGGESTED BY 3GPP FOR THE EVALUATION OF WEB TRAFFIC Quantity Deivation Pobability distibution Paametes Main object size S mo = X ( ) πσ (ln x µ X ) σ X e X f X (x) = xmax (ln t µ X ) σ e X dt µ X = 8.35, σ X =.37, x min ( πσ X ) x [x min,x max] x min = 00 bytes, x max = 0 6 bytes Numbe of embedded objects N eo = Y y min f Y (y) = α yα min y α+, y [y min,y max[ y min =, y max = 55 Embedded object size S eo = Z f Z (z) = [ ( ) y α ] f Y (y max) = min y δ(y ymax) α =. max ( ) πσ (lnz µ Z ) σ Z e Z zmax z min ( πσ Z ) z [z min,z max] (lnt µ Z ) σ e Z dt µ Z = 6.7, σ Z =.36, z min = 50 bytes, z max = 0 6 bytes Reading time Λ f Λ (t) = λ e λt, t 0 λ = 0.03 Pasing time Λ p f Λp (t) = λ pe λpt, t 0 λ p = 7.69 Timeouts in a cycle. Each cycle always includes one eading time, while the pasing time is pesent with pobability ψ 0, i.e., only if thee ae embedded objects. Theefoe, the aveage numbe of timeouts in a system cycle is: E[N to ] = β M +( ψ 0 )β M p. () Hence each cycle includes, on aveage, E[N to ](M )T sub seconds due to timeout occuences. Idle time in powe save mode. The aveage time pe cycle duing which the system is in powe save mode, denoted as I 0, is computed by summing up the time spent in powe save mode (the intevals I ps as in Figue ) 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 save inteval that begins in the eading time lasts a multiple numbe of checking intevals, with the following distibution and aveage: P (I 0 = j eading timeout) =P(0 aivals in (j ) )[ P(0 aivals in )] = (β m ) j ( β m ), j ; E[I 0 eading] = β M β m ; () whee we also emoved the conditioning on the timeout occuence. Similaly, fo the pasing time: E[I 0 pasing] = β M p β m p. (3) Theefoe, the expected value of the time spent in powe save mode in a system cycle is given by the following aveage: E[I 0 ] = β M β m +( ψ 0 )β M p β m p. (4) Note that E[I 0 ] is a function of m and M, the web taffic paametes being fixed. It is easy to find that m E[I 0] > 0, and M E[I 0] < 0, hence the powe save 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 (), hee we only count the intevals I nom, whose sum ove a system cycle is denoted by I = 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 in eading time isi nom eading, the conditional distibution of I in eading time is as follows: P(I = jt sub eading) = P(I nom = jt sub exp. aivals with ate λ ) { β M j = 0; = β j ( β ) j M. Hence the conditional expected value of this inteval I is: Mβ M +(M )β M E[I eading] = T sub. (5) β Similaly, the expected value fo the time spent in nomal mode with no taffic to be seved duing pasing, without counting the timeout, is given by Mβp M +(M )βp M E[I pasing] = T sub. (6) β p Theefoe, on aveage, the time spent in nomal mode without seving any taffic duing a system cycle is given by the timeout intevals plus E[I eading], plus ψ 0 times E[I pasing]. So, the expected value of I inceases with the timeout duation, though M.

5 Cumulative idle time. The cumulative amount of idle time I in a cycle is the sum of timeouts, I 0, and I. Its expected value is then as follows: E[I] = β M β ( m +( ψ 0 ) β M +T sub β β M p β m p βp M +T sub β p ). (7) 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: λ + ψ 0 λ p <E[I]< λ + +( ψ 0 ) ( ) +. 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. The expected time spent to seve the packets of a web page, i.e., the busy time in a cycle, is given by the expected numbe of packets E[N p ] pe web page times the expected sevice time E[σ]. The numbe of packets depends on the distibution of the web page objects, and it is with the 3GPP taffic model epoted in Table I. 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 duation of a cycle is given by: E[T c ] = E[N to ](M )T sub +E[I 0 ]+E[I ]+E[N p ]E[σ] = E[I]+E[N p ]E[σ]. (8) 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 numben 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] <. (9) E[N p ]E[σ]+E[I] 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<. We use 500-byte packets and conside each object as an intege numbe of packets. Hence, afte having computed the numbe of bytes N b in an object, we conside that object as consisting of N b 500 packets. 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 the active and backlogged 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 = + ν, with ν being a andom vaiable exhibiting a binomial distibution between 0 andn u with success pobability ρ. Theeby, the aveage sevice time is: E[σ] = T sub E[+ν] = T sub [+(N u )ρ]. (0) 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 E[σ] is the unique positive solution of the following quadatic equation: E[N p ]E [σ]+(e[i] E[N p ]N u T sub )E[σ] E[I]T sub = 0. Poof: the equation is obtained by combining (9) and (0). 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. Coollay : The expected packet sevice is E[σ] = (E[N p]n ut sub E[I])+ (E[I] E[N p]n ut sub ) +4E[I]E[N p]t sub E[N p]. As we stessed befoe, the teme[i] inceases withmand 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 cumulative taffic geneated and seved E[N pe subfame is N p] u E[N p]e[σ]+e[i] T sub. Thus, as the system appoaches satuation, E[σ] tends to N u T sub, since in satuation the N u uses ae always active and eceive a faction /N u of the seve capacity. The asymptotic distibution of the system cycle duation is constant and

6 equal to Tc up = E[N p ]N u T sub +E[I], which scales linealy with the numbe of uses and loosely depends on the powe save paametes m and M. Tc up is an uppe bound fo the evaluation of the system cycle, and can be used to limit the maximum numbe of customes, thus guaanteeing a maximum web page pocessing time to any custome. V. PERFORMANCE AND COST METRICS The impact of powe save 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 save can be ealistically obtained. Then we deive the paametic expessions fo cost and powe save at both UE and enb. A. Pefomance metics and powe save 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 ] λ. () 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. We name D the total access delay expeienced within a web page download, thus accounting fo the delay accumulated in both eading and pasing times. E[D] can be easily computed by subtacting the pasing time, the eading time and the busy time fom the expected system cycle duation (see Figue ), i.e.: E[D] = E[I] ( λ + ψ 0 λ p ). () The expected access delay is a function of the powe save paametes used in the DRX configuation, plus the taffic pofile paametes, thoughλ, λ p, E[N p ], andψ 0. Howeve, using the uppe bound fo E[I], one can conclude that the access delay is uppe bounded to ( ψ 0 ). Powe save 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 save 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, but fo the intevals in which the UE has to check the contol channel, i.e., exactly T ln seconds out of m subfames. The powe save time atio is then defined as follows: R. = ( T ln ) E[I0 ] E[T c ]. (3) Consideing that E[T c ] is almost insensible to m andm, but inceases with N u, and ecalling that E[I 0 ] inceases with m and deceases with M, we conclude that R is an inceasing function of m, and it deceases with M and N u. B. Cost analysis Cost at the UE. Wheneve the UE eceive is active, its consumption ate is c on, and c ps < c on othewise. Decoding a packet has an additional consumption ate c x, while listening to the contol channel has an additional consumption ate c ln. The aveage consumption is a combination of these fou consumption tems. Using definitions (9) and (3), ecalling that contol channel listening is pefomed in each subfame in nomal mode, but only in one out of m subfames in powe save mode, and taking the aveage ove a system cycle, we obtain the following cost pe UE: C UE (m,m,n u ) = ( R)c on +Rc ps +ρc ( x + m ) E[I 0 ] Tln c ln. (4) m E[T c ] T sub Consideing a fixed web taffic pofile, the cost is a function of the powe save 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 save mode is computed by plugging E[I 0 ] = 0, which is equivalent to setting m = and M, in (4): C UE (,,N u ) = c on +ρc x + T ln T sub c ln. (5) Finally, the elative powe save gain that can be attained is: G UE (m,m,n u ). = C UE(,,N u ) C UE (m,m,n u ) C UE (,,N u ) γ(m) E[I 0 ] = C UE (,,N u ) E[T c ], (6) whee the quantity γ(m) is a cost eduction facto which inceases with the DRX powe save cycle length, that is: γ(m) =. ( T ) ( ln (c on c ps )+ ) Tln c ln. (7) m T sub We can conclude that the elative gain is a function that inceases with the duation of the DRX powe save 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 discontinuous eception and tansmission is defined on a pe-ue basis, and hence the enb powe save can be expessed as the sum of powe save ove all uses. Howeve, the enb expeiences some additional

7 cost fo cell management (synchonization, pilots, etc.). Hence, the enb cost pe associated UE, namely C UE is expessed similaly to the UE cost computed ealie in this section, whee the eception cost ate c x is eplaced by a tansmission cost ate c tx, and the listening cost c ln is eplaced by the signaling cost c sg. The additional pe-enb fixed cost c f does not depend on the tansceive activity and it is nomally huge. Recent woks show that it can be as high as 0 times the aveage cost fo tansmitting data ove the ai inteface [5]. In sum, the total base station cost ate with homogeneous uses is: C BS (m,m,n u ) = N u C UE (m,m,n u)+c f. (8) The elative powe save gain is then as follows: γ (m) G BS (m,m,n u ) = C UE (,,N u)+ c E[I 0] f N u E[T c ], (9) whee γ is obtained fom (7) by eplacing c ln with c sg. Note that with few uses the main enb cost is epesented by the fixed cost c f, theeby the gain inceases with the numbe of uses until the pe-use cost becomes the pedominant tem in the denominato of (9). VI. EVALUATION In this section we fist evaluate the model using a packetlevel simulato that epoduces the behavio of downlink tansmissions. Second, we use the model to pefom the optimization of powe save paametes m and M in ode to minimize the tansmission/eception cost, subject to an uppe bound fo access delay E[D] and download time E[W]. A. Simulating the G/G/PS queue with web taffic We developed a C++ event-diven simulato that epoduces the behavio of a time slotted G/G/ P S queue with N u homogeneous classes. In the simulato, each class can be in two diffeent opeational modes, namely nomal mode and powe save 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 3GPP evaluation methodology discussed in Section III. Futhemoe, all simulated packets have the same size, i.e., 500 bytes, and the pocesso capacity is 500 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. Howeve, if a class has not enough backlog to use all its pocesso shae, unused esouces ae edistibuted amongst the emaining classes. The sevice pocess can last one o moe time slots pe packet, and 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 (though M), and duation of DRX powe save cycle (though m). Each simulation consists of a wam-up peiod lasting 0,000 seconds (5,000,000 slots), followed by 00 uns, each lasting 0,000 seconds. Statistics ae sepaately collected in each un. At the end of a simulation, all statistics ae aveaged ove the 00 uns and 99% confidence intevals ae computed fo each aveage esult. Simulations have to be un 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 hous of a 3 GHz Intel Coe TM 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 seconds 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]. Howeve, the compaison between model and simulation shows that the model appoximates the system pefomance with a good accuacy. In paticula, hee we compae thee pefomance indicatos: system cycle duation E[T c ], powe save time atio R, and sevice time E[σ]. E[W] could be easily computed fom E[T c ]. 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 the paametes m, M, and N u. Figue 3 compaes the estimates of E[T c ] obtained with the model (lines with maks) and with the simulato (maked points) fo two vey diffeent values of m (4, which is the minimum in the 3GPP ecommendations, and 00). The lowe pat of the 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 %, and it is below % with N u = 400. Howeve, 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. In fact, by obseving Figue 4, it is clea that the model slightly oveestimates the sevice time fo high values ofn 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

8 E[T c ] [s] model: N u =, m=4 model: N u =, m=00 model: N u =400, m=4 model: N u =400, m=4 3 M 8 5 sim: N u =, m=4 sim: N u =, m=00 sim: N u =400, m=4 sim: N u =400, m=00 Figue 3. System cycle duation is affected by the numbe of uses. It slightly gows with m and is almost insensitive to M. E[σ] [s] model: M=, m=4 model: M=, m=00 model: M=5, m=00 sim: M=, m=4 sim: M=, m=00 sim: M=5, m= N u Figue 4. The sevice time gows with the numbe of uses and is almost not affected by the timeout and the DRX powe save cycle duations. R model: N u =, m=4 model: N u =, m=00 model: N u =400, m=4 model: n=400, m=00 sim: N u =, m=4 sim: N u =, m=00 sim: N u =400, m=4 sim: N u =400, m= Figue 5. The powe save time atio computed fo T ln = T sub /3. E[σ]. Figue 5 illustates the powe save time atio R. Model s and simulation s esults ae vey close in all cases, and confidence intevals ae vey small, so we omitted them in the figue. 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 save with good accuacy. M 8 B. Model-based paamete optimization Hee we want to compute the optimal values of m and M that yield the highest gain while keeping low the access delay and the download time. We conside the enb cost only, but the esults can be easily extended to the UE. Reasonably, the cost fo tansmitting a data packet is lage than the cost fo tansmitting a contol packet, which usually takes less bandwidth. Both tansmitting and signaling costs ae much highe than the cost to stay on, which, in tun, is at least one ode of magnitude geate than the cost to stay in powe save mode. As an example, we use E[D] [s] m Figue G BS N u =00 N u =0 N u = M Access delay (independent on the numbe of uses) M m Figue 7. Relevant powe save gain can be obtained with small timeouts, even fo powe save intevals lasting few subfames. the following values: c tx = 00, c sg = 50, c on = 0, and c ps =. Additionally, as suggested by expeimental measuements [5], we conside a base station cost one ode of magnitude highe than the tansmission cost: c f = 000. We assume that contol packets have a duation T ln = T sub 3, e.g., the UE has to listen to the contol channel only duing the fist of the thee slots composing an HSPA subfame. The access delay expeienced in the netwok is epoted in Figue 6.E[D] is sensitive tom, especially with low timeout values. Howeve, easonable values of m, e.g., below 0, yield access delay times not highe than 40 ms. With the chosen cost paametes, the functionγ (m) not depicted hee fo lack of space gows vey fast fo small m, but it quickly satuates. In pactice, values of m lage than 0 do not give substantial gain advantages with espect to m = 0, that is the maximum value suggested by 3GPP fo CPC. The elative gain at the enb is epoted in Figue 7 fo a few values of N u. One can notice that low to medium values of the timeout, jointly with modeately high values of m, allow to obtain a elevant gain as soon as the numbe of uses eaches 0. In fact, when few uses ae attached to the enb, the main cost figue becomes c f, which is fixed. Howeve, as shown in Figue 8, if the numbe of uses gows above 350, the gain ecedes. In fact, with too many uses, the system satuates and the powe save oppotunities diminish. Last, Figue 9 shows some paticula cases of system optimization. In the figue,d x andw x denote the maximum allowable access delay and download time, espectively. Each optimization is pefomed ove m and M, given a fixed numbe of uses N u. Each optimized value of the gain 0

9 G BS M=5, m=00 M=, m=4 M=5, m=4 M=, m= N u Figue 8. A lage gain can be obtained ove a wide spectum of numbe of uses as soon as m gows to few tens. Optimal enb gain D x =0.0 s, W x =.0 s D x =0.50 s, W x =.0 s D x =0.0 s, W x =5.0 s D x =0.30 s, W x =5.0 s (56,9) (,54) (,58) (,60) (56,9) (,54) (,58) (,60) 0 (56,9) (,54) (,58) (,60) 00 N u (56,9) (,54) (,58) (,60) 300 (56,9) (,4) (,58) (,60) Figue 9. Relative gain fo diffeent numbe of uses, optimized ove bounded download time and access delay. is labeled with the pai (M,m) which coesponds to the optimum. The figue shows that the gain can exceed 70% while keeping the access delay bounded to less than half second, and the total web page download time below one second. Howeve, with 400 uses, the minimum download time gows above one second and the system cannot be optimized unless W x was aised to a few seconds. Note also that the optimization with vey small values of the access delay can only be obtained by setting a long timeout and shot powe save intevals (e.g., M = 56 and m = 9 with 00 uses yields a 60% gain with no moe than 0 ms of access delay). With highe access delay bounds, e.g., as high as 00 ms, the optimal timeout is the shotest possible, i.e., M =. Almost in all cases, the optimization suggests to use vey lage values fo m. Howeve, obseving Figue 7, it is clea that nea-optimal gain can be obtained with values of m as low as 0. VII. CONCLUSIONS The pape shows how to model and simulate a G/G/PS system epesenting the download tansmission queues of cellula uses adopting the continuous connectivity model. The model, which has been validated though simulation, is based on two basic assumptions: (i) uses can eceive taffic accoding to the DRX paadigm, and (ii) the use geneated taffic is a ealistic sequence of web page equests. We model the pe-use activity and evaluate the sevice shae that the base station pocesso can gant to each use. Futhemoe, we popose a cost model and show how to optimize the powe save paametes to minimize the cost unde bounded 350 (-,-) (-,-) (,58) (,60) 400 access delay and page download time. Remakably, we show that up to 70% o moe of the downlink tansmission cost can be saved while peseving the quality of packet flows. REFERENCES [] Nujia Ltd., State of the at RF powe technology fo defense systems, white pape, Feb. 009, uploads/whitepapes/state of the At RF Powe Technology fo Defence Systems EU.pdf. [] S. Yang and Y. Lin, Modeling UMTS discontinuous eception mechanism, IEEE Tansactions on Wieless Communications, vol. 4, no., pp. 3 39, Jan [3] K. Han and S. Choi, Pefomance analysis of sleep mode opeation in IEEE 80.6e mobile boadband wieless access systems, in Poc. of IEEE VTC 006-Sping, vol. 3, Melboune, Austalia, May 006, pp [4] J. Seo, S. Lee, N. Pak, H. Lee, and C. Cho, Pefomance analysis of sleep mode opeation in IEEE 80.6e, in Poc. of IEEE VTC 004-Fall, vol., Los Angeles, Califonia, USA, Sep. 004, pp [5] S. Alouf, E. Altman, and A.P. Azad, M/G/ queue with epeated inhomogeneous vacations applied to IEEE 80.6e powe saving, in Poc. of ACM Sigmetics, Annapolis, Mayland, Jun [6] Y. Xiao, Pefomance analysis of an enegy saving mechanism in the IEEE 80.6e wieless MAN, in Poc. of IEEE CCNC, vol., Jan. 006, pp [7] J. Almhana, Z. Liu, C. Li, and R. McGoman, Taffic estimation and powe saving mechanism optimization of IEEE 80.6e netwoks, in Poc. of IEEE ICC 008, vol. 9-3, Beijin, China, May 008, pp [8] H. Choi and J. Limb, A behavioal model of web taffic, in ICNP 99, Washington, DC, USA, Oct [9] 3GPP TS 5.4, Physical laye pocedues (FDD), el. 8. [0] L. Zhou, H. Xu, H. Tian, Y. Gao, L. Du, and L. Chen, Pefomance analysis of powe saving mechanism with adjustable DRX cycles in 3GPP LTE, in IEEE VTC 008-Fall, Calgay, Albeta, Cananda, Sep. 008, pp. 5. [] C. Bontu and E. Illidge, DRX mechanism fo powe saving in LTE, IEEE Communications Magazine, vol. 47, no. 6, pp , Jun [] T. Kolding, J. Wigad, and L. Dalsgaad, Balancing powe saving and single use expeience with discontinuous eception in LTE, in Poc. of IEEE ISWCS, 008, pp [3] E. Dahlman, S. Pakvall, J. Skold, and P. Beming, 3G Evolution: HSPA and LTE fo Mobile Boadband, Second ed. Oxfod, UK: Academic Pess, 008. [4] 3GPP C.R00-B v.0, CDMA000 evaluation methodology - Revision B, Dec [5] F. Coêa Alegia and F.A. Matins Tavassos, Implementation details of an automatic monitoing system used on a Vodafone adiocommunication base station, IAENG Engineeing Lettes, vol. 6, no. 4, Nov. 008.