LTE DRX

1. Abstract
The discontinuous reception (DRX) operation is included in
longtermevolution(LTE)toachievepowersavingandprolonged
battery life of the UE. An improvement in DRX power saving
usually leads to a potential increase in the packet delay. An
optimumDRXconfigurationdependsonthecurrentdatatraffic,
whichisnoteasytoestimateaccurately,especially,fornonreal-time
applications. In this paper, we propose a novel way to vary the
DRX cycle length avoiding continuous estimation of the data
traffic when only nonreal-time applications are running with no
real-time applications active. Since small delay in nonreal-time
traffic does not essentially impact the user’s experience adversely,
we allow limited amount of delay deliberately in our proposal to
attainsignificantimprovementinpowersaving.Ourproposalalso
improvesthedelayinserviceresumptionafteralonginactivity.We
use a stochastic analysis assuming M/G/1 queue to validate the
improvementoftheproposal.
Keywords:LTE,DRX,nonreal-timetraffic,powersaving.
ManuscriptreceivedOct.03,2015;revisedJan.23,2016;acceptedMar.02,2016.
MohammadTawhidKawser(correspondingauthor,mkawser@hotmail.com),MohammadRakibul
Islam(rakibultowhid@yahoo.com),ZiaulIslam(ziaiut@gmail.com),MohammadA.Islam
(m.atiqislam@gmail.com),MohammadHassan(mehadi.hassan347@gmail.com),ZobayerAhmed
(zbiutian@gmail.com),andRafidHasan(rafidhasan204@gmail.com)arewithDepartmentofElectricaland
ElectronicEngineering,IslamicUniversityofTechnology,Gazipur,Bangladesh..
I.Introduction
Long termevolution (LTE),based on 3GPP standards, is the latest step in
theevolutionofcellularservices.Theincrediblyhigherdataratesandbetter
quality of services have motivated the advent and use of many different
applicationsinLTE.Thiscausesthebatteryoftheuserequipment(UE)to
drain out quickly and the battery power saving has become a significant
concern.Thekeytechniquetosavepowerandprolongbatterylifeisto let
the UE switch off the receiver circuitry periodically. This is referred to as
discontinuousreception(DRX).TheperiodiccycleinDRXiscalledDRX
cycle.TheDRXcycleconsistsofanactiveperiodin thebeginning,called
on duration and then a period with the receiver circuitry off, called off
duration[1].Ifapacketarrivesduringtheoffduration,itcannotbescheduled
until the off duration is over. This enhances the packet delay, which is the
main drawback of DRX operation. A longer DRX cycle allows better
powersavingbutwithalongerpacketdelay.Thus,theDRXcyclelength
involvesatrade-offbetweenpowersavingandpacketdelay.TheeNodeB
configurestwotypesofDRXcyclesforuse,namely,shortandlongDRX
cycles and as their names suggest, their lengths are short and long,
respectively.
[2]-[5]investigatedtheimpactofDRXparametervaluesonpowersaving
and delay. Such investigation was also performed for the industrial DRX
modelproposedbyNokia[6].Itisshownthatagoodpowersavingcanbe
achievedatthecostofdelay.Consideringthisfact,[7]proposesanalgorithm
to find feasible ranges of DRX parameter values for maximizing power
saving while satisfying a specified delay constraint as well as minimizing
delay while satisfying a specified power saving. [8] proposes a scheme to
select DRX configuration by jointly formulating power saving and delay
and considering the operator’s preference of power saving over delay. [9]
proposesscalingthelengthofbothshortandlongDRXcyclestochoosea
desiredbalancebetweenpowersavinganddelay.[10]proposesvaryingon
durationinadditiontothelengthofshortandlongcycles.[10]alsoproposes
switching between short and long cyclesusingvariouspatterns for desired
performance. [11] proposes an algorithm to select appropriate DRX
configuration while keeping the delay below a threshold. While many
proposalsaremadetoreachanappropriateDRXconfiguration,thecurrent
datatrafficlargelydictateswhichconfigurationmaybeappropriateandso,
adaptation of DRX parameters based on the current traffic can be more
efficient.[3],[4],[11]showthatcontinuousadaptationofDRXparameters
canobtainbetterperformancecomparedtofixedDRXparameters.[12],[13]
Improvement in DRX Power Saving for
Nonreal-Time Traffic in LTE
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883
RP1510-0883e ⓒ 2016 ETRI 1
MohammadT.Kawser,MohammadR.Islam,ZiaulIslam,MohammadA.Islam, MohammadM.Hassan,
ZobayerAhmed,andRafidHasan1

2. also suggest adaptation based on the current traffic. For estimation of the
currenttraffic,[12]usesasinglebitfeedbackfromtheUEknownaspower
preference indication (PPI), which has been adopted in 3GPP Release 11.
[13]suggestsamethodofquickestimationofthetrafficusingthemaximum
likelihoodmethodandthepropertiesofGammadistribution.[14]proposes
adaptationbasedonthetrafficwherethetimeinstantstoreconfigureDRX
parametersalsodependonthetrafficandshowsanenhancementofpower
saving considering the delay constraint. [15] proposes the use of a fuzzy
logiccontroller(FLC)toadjustDRXcycleafterthetrafficisestimated.
WeproposeanovelbutsimplewaytovarytheDRXcyclelength,which
canbeappliedonlywhennonreal-time(NRT)applicationsarerunningwith
no real-time (RT) applications active. The examples of NRT applications
arebufferedstreamingvideo,webbrowsing,e-mail,chat,FTP,andP2Pfile
sharing,.Ontheotherhand,theexamplesofRTapplicationsarevoice,live
streaming video and online gaming. Unlike RT traffic, the NRT traffic
permits the delay requirement to slacken to some extent. In otherwords,a
limited amountofdelaycanbeallowed to NRTtrafficessentiallywithno
adverseimpactontheuser’sexperience.Therefore,weexploittheallowable
delayforNRTtraffictoimprovepowersavinginourproposal.
Theprocessingintheaccessstrata(AS)oftheprotocolstackdependsonthe
QoSclassidentifier(QCI)ofthedatatraffic.QCItakesonvariousattributes
for different types of applications. Thus, RT and NRT traffic are treated
differently and consequently, NRT traffic takes longer processing delay
comparedtoRTtraffic.Thislongerprocessingdelayconsumespartofthe
additionaldelay,permissibleforNRTtrafficincomparisonwithRTtraffic.
Nevertheless, after this consumption, it can be shown that some additional
delayisleftover.Ourproposalexploitsthisleftoverdelayandso,itincreases
thedelayofNRTtrafficwithinapermissiblelimitdeliberately.
Our proposal avoids the continuous estimation of traffic. In fact, the
estimation of current traffic, used in many proposals as mentioned earlier,
increases complicacy and burden. More importantly, the NRT traffic is
highlyirregularandunpredictable.So,thetrafficestimationforNRTtraffic
cannotbeveryaccurateandanadaptationofDRXconfigurationbasedon
thisestimationwillnotresultinaveryoptimumoutcomeinpractice.
[16] proposes an algorithm to adjust DRX parameters when the delay
crosses predefined high and low threshold values. [16] also proposes a
second algorithm, which additionally considers the recently used
Modulation and Coding Scheme (MCS) to cross predefined threshold
values. However, all these threshold values need to be adaptive for an
optimumperformanceinpracticeandproperselectionoradaptationofthe
threshold values may not be easy. [17] proposes that the UE sends an
indication to the eNodeB when the application is delay tolerant. Then the
eNodeB can use DRX MAC control element to command the UE to
switchtolongDRXcyclesfromshortDRXcycles.However,nosidesmay
befullyawareofthepotentialdelayinpacketarrivalandso,thedecisionfor
switching to long cycle may not be very optimal. Our proposal also
functions for delay tolerant applications but avoiding the overhead of the
messagesandadmittingtheuncertaintyinpacketarrivals.
Our proposal additionally reduces the delay in service resumption when
therehasbeenalonginactivitywithoutterminatinganNRTsession.Such
long inactivity may result from various reasons. For example, the server
application may get busy and may not respond for a while. Also, the user
maytakeabreaktotaketea,coffeeorlunch,todiscusswithco-workers,to
usetherestroom,etc.Insuchcases,theDRXrunsforalongperiodoverthe
inactivity. In the existing scheme, the data transfer takes quite a while to
resumeaftertheinactivityandthiscanbeanuisance.
The remainder of this paper is organized as follows. Section II shows
different states associated with DRX. Section III describes what causes a
difference in delay between RT and NRT services and establishes a
relationship between the delays. Section IV explains the proposed DRX
scheme. Section V develops analytical models for the performance
evaluation of the proposed and existing schemes. Section VI shows the
expected performance of the proposed scheme and compares it with the
existingscheme.Finally,thewholepaperisconcludedinSectionVII.
II.StatesAssociatedwithDRX
InRRC_CONNECTEDstate,theUEinitiatesDRXwithshortcyclesbut
it transitions to long cycles after a maximum number of short cycles. The
eNodeBspecifiesthemaximumnumberofshortcycles,thelengthofshort
andlongcyclesandthelengthofonduration.IftheUEdetectsanypacket
schedulingduringanondurationofDRXcycle,itstopsDRXandbegins
continuous data transfer. When the data transfer stops, the UE starts an
inactivity timer. If new packets arrive, they can be scheduled while the
inactivitytimerisrunningandso,theUEkeepsmonitoring.Ifnoscheduling
is detected until the expiry of the timer, the UE initiates DRX cycles
immediately. On the other hand, if any scheduling occurs while the
inactivity timer is running, data transfer resumes and the inactivity timer
restarts after this data transfer finishes. Thus, the inactivity timer can restart
again and again. It is uncertain how many times the inactivity timer may
restartassuchandhowlongitwouldrunbeforegettingreset.
Fig.1.StatesassociatedwithDRX
The various states associated with DRX are shown in Fig. 1. State A
indicates ordinary data transfer and represents its duration. State B
indicates running inactivity timer at the end of ordinary data transfer and
represents itsduration.In state B, theinactivity timer isresetbefore it
expiresbecauseofthearrivalofapacket.StateCindicatesdatatransferafter
state B and represents the duration of state C. After every state C, the
inactivitytimerrestarts. representshowmanytimestheinactivitytimer
restarts.StateDindicatesrunninginactivitytimerwhenthetimercanrunup
toitsexpirywithnopacketarrivals. representsthewholedurationofthe
inactivitytimer.StateEindicatesrunningDRXcyclesaftertheexpiryofthe
inactivitytimer.TheshortcycleswouldrunfirstandtherecanbeNnumber
ofshortcyclesatthemaximum.AfterNnumberofshortcycles,longcycles
startrunning. and representthelengthofshortandlongDRXcycles,
respectively. represents the duration of state E. DRX operation is
terminated if new packets arrive and then ordinary data transfer starts. So,
stateAappearsafterstateE.Thenotationsandstates,showninthissection,
willbeusedinSectionV.
RP1510-0883e ⓒ 2016 ETRI 2
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

3. III.DifferenceinDelaybetweenRTandNRTServices
Each of the EPS bearers is associated with a particular QCI. Each QCI
correspondstoapriority,apacketerrorlossrate(PELR)andapacketdelay
budget (PDB). Here, the PDB indicates an upper limit for packet delay
betweentheUEandthepolicyandchargingenforcementfunction(PCEF)
inthecorenetwork.ThedelayshouldnotexceedPDBinthecaseof98%of
the packets that have not been dropped due to congestion. The quality-of-
service(QoS)requirementsarequitedifferentbetweenRTandNRTtraffic
and so, they assume different QCI. RT traffic has a stringent delay
requirement, while some level of packet loss rate can be acceptable.
Conversely,NRTtrafficiserror-sensitivebutthetransmissiondelaycanbe
larger. The PELR is typically 103
and 106
for RT and NRT traffic,
respectively. The PDB is typically 100 ms and 300 ms for RT and NRT
traffic,respectively[18].TheprocessinginASdependsonQCIoftheEPS
bearer and consequently, RT and NRT services differ in their processing
delays.TheschedulingofradioresourcesattheMAClayerusesalgorithms,
which treat RT and NRT traffic differently [19]. Similarly, the RLC layer
usesdifferentmodesforRTandNRTtraffic.TheRTbearerstypicallyuse
unacknowledged mode (UM) of RLC since they are error-tolerant.
Conversely,NRTapplicationstypicallyuseacknowledgedmode(AM)of
RLC,whichperformretransmissionsinordertolimittheerrors.
The major factor that can be attributed to the difference in the processing
delay between RT and NRT traffic is the use of RLC modes. This is
becausetheretransmissionsinRLCAMincursomedelay.TheRLCcan
receiveoutofsequencePDUs.IfthereceivingRLCentityfindsagapinthe
sequenceof the PDUs, it starts a reordering timer.When thetimer expires
without the arrival of the missing PDU, the receiving entity infers that the
PDUhasbeenlost.Atthisjuncture,RLCUMdoesnotattempttorecover
thelostPDUsbutRLCAMdoes.ThereceivingRLCAMentitysendsa
status report that includes positive acknowledgement for the correctly
received PDUs and negative acknowledgement for the fully and partially
missing PDUs. Then the transmitting RLC AM entity retransmits the
missingdata[1].Theoveralldelayinthecorrectionofdatacanbeestimated
as the summation of the reordering timer value and the round trip time
(RTT). The RTT includes round trip propagation delay and processing
delayatbothends.ThereorderingtimervalueisconfiguredbytheeNodeB.
Letusassumethat and representtheexpecteddelayfor
RTandNRTtraffic,respectively. representstheexpecteddelay
forRLCAMretransmissions,whichoccursonlyinthecaseofNRTtraffic.
IgnoringallminorcausesofdifferencesinthedelaysbetweenRTandNRT
traffic,incrudeterms,werelatethesedelaysas
+ . (1)
ThePDBforNRTtrafficismuchlargerthanthatofRTtrafficbecauseof
the delay tolerance of NRT applications. Thus,
, where and denote the PDB
forNRTandRTtraffic,respectively.So,weobtain
̅ (2)
where ̅canbeexpressedusing(1)as
̅ . (3)
IV.ProposedDRXScheme
WeproposeanovelwaytovarytheDRXcyclelengthsuchthatitimproves
the power saving while increasing the delay of NRT traffic within a
permissible limit. The proposed scheme is based on the fact that
can be permissible in
the system. Therefore, according to (2), can be allowed to be
increasedtoanewvalue givenby
∆ (4)
where∆ ̅. (5)
Here,(5)setsaconstraint.Inourproposal, isincreasedpurposely
to achieve improvement in power saving while satisfying the constraint in
(5).To accomplishitin asimplemethod,weproposethattheDRXcycle
length starts increasing linearly with time. A simple method can invoke
small changes in the associated protocols and help easy and quick
implementation. In our proposal, instead of allowing a few short cycles in
the beginning, the DRX cycle length keeps increasing from TS by a fixed
step size Tst until it reaches TL. Let us assume that n number of cycles are
takentoreachTL.OncenDRXcycleshavebeenexecutedwithnopacket
arrivals, we consider that there has been already a long inactivity in the
session. Our proposal attempts to limit delay in service resumption after a
long inactivity. Since a smaller DRX cycle length reduces this delay, we
propose that after n DRX cycles, the DRX cycle length starts decreasing
fromTLtoTSbythesamefixedstepsizeTst.Aftercompletionofthisdecline
uptoTS,assumingthattheservicemaynotresumesoon,ariseintheDRX
cyclelengthwithpreviouspatternisagainused.Therisewillbefollowedby
a fall like before for the same reason. These alternate repetitions continue
leading to a triangular fashion of variation in the DRX cycle length as
illustratedinFig.2.ThesmoothgradualvariationintheDRXcyclelength
canbeexpectedtomatchachangeinthedatatraffictosomeextentandthus,
the estimation of data traffic is avoided. We propose that the eNodeB
configuresTS,TL andTst usingalayer3messagewhenasession issetup
and for this configuration, the eNodeB considers theoperator’s choiceand
an overall estimate of the potential traffic. The period of the triangular
variation is 2 1 . The numerical examples in
SectionVIshowthattheproposedschemecansatisfytheconstraintin(5).
WealsoproposeanewfactortoestimatethepowersavinginDRXanalysis.
Variousfactorshavebeenusedsofar.[20]usespercentagepowersavingas
100
wherethepowerconsumptionduringdatatransferandduringtheperiodof
DRX cycles are denoted as and , respectively. The expected
durations of these two states are denoted as and ,
respectively. representsthemeanwholedurationincludingdata
RP1510-0883e ⓒ 2016 ETRI 3
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

4. transferandDRX.[4]usespowersavingfactoras
where and representtheexpectedshortand
long DRX periods, respectively, excluding the on durations. [21], [22] use
power saving factor as without incorporating any power levels.
However, there is a significant difference among the power consumptions
during effective data transfer, during the period while the inactivity timer
runslookingfordataandduringDRX.So,wesuggesttheincorporationof
powerlevelsinpowersavingestimationbutintroducingathirdpowerlevel
denoted as the power consumption while the inactivity timer runs.
Secondly,thepowerconsumptionbecomesextremelylowforDRXcycles
of any length [23]-[25]. In fact, the impact of differences in power
consumption for DRX cycles of different lengths and for on durations of
different lengths istrivial and so,we ignoresuchdifferencesfor simplicity.
Wedefinetheaveragepowerconsumptionas
. . .
(6)
where denotes the expected duration of running the inactivity
timerand
. (7)
To better indicate the practicalpower saving inDRX,wepropose that the
percentagepowerconsumptionisdefinedas
100.
(8)
Fig.2.ExistingandproposedschemesforDRXcycles
V.AnalyticalModel
In order to evaluate the proposed and existing schemes, in this section, we
present analytical models using the approach presented in [21], [26]. We
assumeM/G/1systemqueue.So,thepacketarrivalfollowsPoissonprocess
andtheinter-arrivaltimesaredistributedexponentially.Weassumethatthe
packetarrivalrateisλandtheserviceortransmissionrateofthepacketsisμ.
The mean transmission time of a packet is 1/μ. The traffic
intensity can be expressed as /μ. We assume that the system is
stable with μ > λ. The probability of packet arrival in t1 duration is
е 1 е .Thus,theprobabilityofnopacketarrivalin
t1durationis1 е е .
To estimate power saving, we compute percentage power consumption
using (8) and for this purpose, , and are
evaluatedbelowfortheproposedandexistingschemes.Since,thePoisson
trafficmodelisshortrangedependent,theearlyeventswillbeprominentin
ouranalysis.
1.MeanDurationofDRXOperation
The expected duration of continuous DRX operation in the proposed
scheme canbegivenby
(9)
where and represent the mean duration of DRX operation
intherisepartsandthefallpartsofthetriangularperiods,respectively.The
probabilitythatnopacketarrivesinjnumberoftriangularperiodsand(k1)
numberofDRXcyclesoftherisepartof(j+1)numberedtriangularperiod
andthereafterpacketarrivesinthenextDRXcycle(thatis,thekth
cycleof
therisepart),canbeexpressedas
, . (10)
RP1510-0883e ⓒ 2016 ETRI 4
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

5. Here, isgivenby
, 1 (11)
where , isgivenby
, 2 ∙∙∙∙∙∙∙ 1
1 . (12)
ThewholedurationofDRXassociatedwith , isgivenby
, 2 ∙∙∙∙∙
. (13)
canbeexpressedas
, . ,
1
2
∑ 1 ∑
. (14)
Similarly, the probability that no packet arrives in j number of triangular
periodsandinthe /2 longrisepartand(k1)numberofDRXcyclesof
thefallpartof(j+1)numberedtriangularperiodandthereafterpacketarrives
inthenextDRXcycle(thatis,thekth
cycleofthefallpart),canbeexpressed
as
,
/
. (15)
Here, isgivenby
, 1 (16)
where , isgivenby
, 1 ⋯ 1
1
. (17)
ThewholedurationofDRXassociatedwith , isgivenby
, 1 . . ]
. (18)
canbeexpressedas
, . ,
/
2
1
2
∑ 1 ∑
. (19)
cannowbedeterminedusing(9),(14)and(19).Themean
durationofDRXintheexistingscheme isgivenby
(20)
where and represent the mean duration of short and long
cycles,respectively.Theprobabilitythat(i1)numberofshortcyclesoccur
with no packet arrival and thereafterpacket arrives in ith
shortcycle,canbe
expressedas
1 . (21)
Themeannumberofshortcycles isgivenby
. 1
. (22)
isgivenby
. (23)
TheprobabilitythatnopacketarrivesinNnumberofshortcyclesand(j1)
numberoflongcyclesandthereafter,packetarrivesinjth
longcycle,canbe
expressedas
1 . (24)
So,themeannumberoflongcycles isgivenby
1
. (25)
isgivenby
RP1510-0883e ⓒ 2016 ETRI 5
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

6. . (26)
cannowbedeterminedusing(20),(23)and(26).
2.MeanDurationofRunningInactivityTimer
Theprobability thattheinactivitytimerrestartsxtimesbecauseofpacket
arrivalsandthereafter,theinactivitytimerexpirersoncecompleting ,can
beexpressedas
1 . (27)
So,themeannumberofrestartoftheinactivitytimer isgivenby
∑ 1 1. (28)
Astheinactivitytimerruns,theoccurrencesinthescenarioarelimitedtothe
expiry of the timer, which means that the occurrences lie only within the
rangeaslongasthetimerruns.Thus,thetruncatedexponentialdistribution
can be used for the packet arrivals to estimate . The truncated
exponentialdistributioncanbeexpressedas
1
, 0
0. (29)
canbeexpressedas
1
– . (30)
The mean duration of running inactivity timer is the summation of the
averageperiodinstateBandstateD.SincetheaverageperiodinstateBis
and the period in state D is , for both the
existingandtheproposedmethodscanbeexpressedas
. (31)
3.MeanDurationofDataTransfer
Themeandurationofdatatransferisthesummationoftheaverageperiodin
state A and state C. Since is the mean number of restart of the
inactivity timer, the mean duration of data transfer for both the
existingandtheproposedmethodscanbegivenby
. (32)
Whenasinglepacketistransmitted,itsmeantransmissiontimeisE[S]=1/µ.
The probability of m number of packet arrivals in this 1/µ duration is
givenby
!
∙
!
. (33)
So,themeannumberofpacketarrivalsin1/µdurationcanbeshownas
∑ ∑
∙
!
. (34)
If one packet arrives while the inactivity timer is running, then within its
transmission period, additional  number of packets arrive on average.
These additional packets require additional μ transmission period in
which further μ number of packets arrive on average. This
ideallygrowsupandthetotalexpectedtransmissionperiodisgivenby
1
∙∙∙∙∙∙∙∙
∑ . (35)
canbedeterminedsimilarly.DuringtheDRXperiod ,
number of packets arrive. These packets require
μ transmission period. In this period,
additional numberofpacketsarrive,whichrequireadditional
μ transmission period. Thus, is
givenby
∙∙∙∙∙∙∙∙∙∙
∑ . (36)
Usingequations(28),(32),(35)and(36), canbeexpressedas
1
1
1
μ 1
1
1
(37)
and canbeevaluatedfortheexistingand
the proposed methods, respectively, using (9), (20), (31) and (37).
Similarly, and can be evaluated for the
existingandtheproposedmethods,respectively,using(7).
4.DelayPerformance
The delay analysis will be different between the cases when the UE is
running DRX and when the UE is not running. Let us assume that
representsthenumberofpacketsinthequeuebutexcludingthoseforwhom
transmission is ongoing and represents the waiting time of a packet
fromthemomentitarrivesuntilitstransmissioncommences.ThenLittle’s
formulagivestherelationship
. (38)
RP1510-0883e ⓒ 2016 ETRI 6
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

7. The mean residual service time represents the mean service or
transmissiontimeofpacketscurrentlyintransmissionwhenapacketarrives.
Since represents the service time of all packets ahead in the queue
waiting for service, according to Pollaczek Khintchine formula, the mean
waittimeinthequeueisgivenby
. (39)
UsingLittle’sformula,weobtain
. (40)
Whenthetransmissionrateisveryhighcomparedtothepacketarrivalrate,
makingμ>>λ,thepacketsaheadinthequeuecanbequicklytransmitted
resultingin . hastherelationship[27]
. (41)
Using(40),weobtain
. (42)
WhiletheUEisnotinDRX(instatesA,B,CorD),thepacketdelaycanbe
givenby
_ . (43)
On the other hand, while the UE is running DRX (in state E), the packet
mayarriveanytimewithintheDRXcycle.Thentherewillbeanadditional
delay because the packets are not processed until the particular
DRXcycleisover.Theoverallmeandelay canbegivenby
. (44)
ThePoissonprocess hastime-homogeneity. Thus, thepacketcan arriveat
anytimeduringtheDRXcyclewithequalprobabilityandithastowaitfor
therestoftheDRXcycleforanyprocesstobegin.Themeanwaittimecan
be computed as the half of the average length of the DRX cycle and it is
independentofthepacketarrivalrate.Thismeanwaittimeisequivalentto
and foreithertherisetimeorthefalltimeoftheproposed
methodcanbeexpressedas
1
2
2
2
. .
2
. (45)
Using(40)and(45), canbeexpressedas
. (46)
The mean delay in the case of rise time and fall time
canbeexpressedusing(42),(44)and(46)as
. (47)
Denoting the probability of packet arrival during the rise time and the fall
time of the proposed method as and , respectively, they can be
expressedas
(48)
and
. (49)
So, the overall packet delay for the proposed method can
beexpressedas
1 _
. (50)
Similarly, can be estimated for the existing method as
_ and _ for short and long DRX cycles,
respectivelyandtheycanbeexpressedas
_ (51)
and
_ . (52)
Denotingtheprobabilityofpacketarrivalduringshortcycleandlongcycle
oftheexistingmethodas and ,respectively,theycanbeexpressedas
(53)
and
. (54)
The overall packet delay for the existing method can be
expressedas
1
2 1
2 1
. (55)
The mean delay in service resumption after a long inactivity, without
terminating the session, can be estimated as . So, it will be
and _ for the proposed and existing methods,
given by (46) and (52), respectively. When μ >> λ,
and _ and then will not vary
significantlywiththepacketarrivalrate.
RP1510-0883e ⓒ 2016 ETRI 7
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

8. VI.NumericalResults
The performance was evaluated for the proposed and existing methods
numerically using the analytical models. [18] gives the typical values of
PDBas 100 and 300 .Asshownin
SectionIII,theoveralldelayduetoRLCretransmissionscanbeestimatedas
the summation of the reordering timer value and RTT. The RTT is
commonly estimated as 8 ms [1]. The reordering timer value can take on
valuesbetween0msand100mswith5msgapsorvaluesbetween100ms
and200mswith10msgaps[28].Assumingallreorderingtimervaluesin
the specification equally likely to occur, we set the mean reordering timer
value as 85 ms. So, the mean overall delay due to RLC retransmissions
issetto93ms.Using(3), ̅canbeestimatedas107ms.So,the
constraint in (5) is∆ 107 . The performance evaluation was
performedforthreedifferentcasesforwhichtheassumptionsareshownin
Table1.μ>>λisused,whichisusuallythecase.ThevaluesofTI,TSandTL
inTable1complywiththepermissiblevaluesin[28].Thevaluesof ,
and in Table 1 follow the UE power consumption model
usedin[23]-[25].
Table1.Simulationassumptions.
Parameter Case1 Case2 Case3
TS 20ms 10ms 10ms
TL 320ms 640ms 40ms
Tst 20ms 30ms 10ms
n 15 21 3
TI 10ms
N 1,2,3,4,5,8,12and16
500mW
255mW
11mW
Packetarrivalrate(λ) 0.05to0.5packets/ms
Servicerate(μ) 100packets/ms
Figure 3 shows that the percentage power consumption, in case 1, has
significantly improved in the proposed method compared to the existing
method for almost all values of packet arrival rate λ. Figure 4 shows the
relativeDRXperiod indicatingthattheproposedmethodexhibits
much longer DRX period in most cases. However, the existing method
withN=1hasbetterpowersavingforasignificantrangeofλ.Thepower
savingisalsolittlebetterforN=2butforaverylimitedrangeofλ.Evidently,
asthepacketarrivalrateincreases,thedurationfordatatransferandinactivity
timer increases while terminating the DRX operation quicker and
consequently, the power saving declines in all cases. [8] shows that short
DRXcyclesareveryeffectiveinreducinglatency.Thisisalsodemonstrated
byFig.5inwhichthedelaytakesonthebestvaluesintheexistingmethod
with very high number of short DRX cycles. We use this delay
performance as the benchmark to evaluate ∆ for other cases.
Compared to this benchmark, the proposed method has roughly 60 ms
longerdelayforλ=0.05packets/msandso,weassume∆ 60 .
This increase in delay can be tolerable because ∆ 107 .
Conversely, the existing method with N = 1, has almost 120 ms longer
delay for λ = 0.05 packets/ms and this increased delay may not be
acceptable because ∆ 107 . Thus, repudiating the existing
methodwithN=1,theproposedmethodremainsthebestinperformance.
Thedelayisfoundtodropalmostlinearlywiththepacketarrivalrateinthe
proposed case. This is partly because the DRX cycle length linearly
decreasesinreversetimescaleandahigherpacketarrivalrateincreasesthe
likelihoodofterminatingDRXoperationinanearlierDRXcycle.
Fig.3.Percentagepowerconsumptionvs.packetarrivalrate(case1)
Fig.4.RelativeDRXperiod vs.packetarrivalrate(case1)
Fig.5.Overallpacketdelayvs.packetarrivalrate(case1)
RP1510-0883e ⓒ 2016 ETRI 8
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

9. Figure6showsthatthepercentagepowerconsumption,incase2,becomes
much better in the proposed method for a significant range of λ, except
when the existing method has N = 1, 2 and 3. The power saving is little
betterintheexistingmethodswithN=4and5,butforaverylimitedrange
ofλ.AsshowninFig.7,comparedtothebenchmark,theproposedmethod
has an increase in delay∆ 100 for λ = 0.05 packets/ms. This
increased delay can be tolerablebecause∆ 107 . Conversely,
thedelayintheexistingmethod,evenwithN=4,isalmost200mslonger
than the benchmark for λ = 0.05 packets/ms. Thus, the existing method is
notacceptableforsmallvaluesofNas∆ 107 .Consequently,
theproposedmethodcanberegardedasthebestoption.
Fig.6.Percentagepowerconsumptionvs.packetarrivalrate(case2)
Fig.7.Overallpacketdelayvs.packetarrivalrate(case2)
Incase3,asmallvalueofTLisused.Inthiscase,asFig.8shows,thepower
saving becomes better in the proposed method compared to the existing
method with anyvalue ofN. Figure9 shows thatall the casesheresatisfy
∆ 107 .
Table2.Themeandelayinserviceresumptionafteralonginactivity
Method Case1 Case2 Case3
ExistingMethod 160.08ms 320.16ms 20.01ms
ProposedMethod 90.05ms 170.09ms 15.01ms
The mean delay in service resumption after a long inactivity for all three
cases are shown in Table 2 for the proposed and existing methods with
λ=0.05 packtes/ms. Since we have used μ >> λ, this delay will not vary
significantlywiththepacketarrivalrateandso,itisshownforasinglevalue
ofλ.Thisdelayisevidentlymuchbetterintheproposedmethod.
Fig.8.Percentagepowerconsumptionvs.packetarrivalrate(case3)
Fig.9.Overallpacketdelayvs.packetarrivalrate(case3)
Inthissection,thenumericalexamplesdemonstratethatasignificantlybetter
powersavingisachievedintheproposedmethodwithpermissibleincrease
inpacketdelay.Theexistingmethodmayoftenattainanevenbetterpower
savingsettingverysmallvaluesofNbutitsassociateddelaymightexceed
thetolerablelimitthen.Thedelayinserviceresumptionafteralonginactivity
isalwaysbetterintheproposedmethod.
VII.Conclusion
In this paper, we present the tradeoff between power saving and delay for
DRX operation in LTE. Since NRT applications are delay tolerant, to
improve power saving, we propose a new DRX method to be applied
when only NRT applications are running with no RT applications active.
The proposed method avoids the estimation of current traffic. It keeps
varying the DRX cycle length in a simple fashion. We present analytical
models to evaluate both the proposed and the existing methods. The
numerical examples exhibit a conspicuous success in power saving in the
proposedmethod.Wedefineanewfactorforamorepracticalestimationof
RP1510-0883e ⓒ 2016 ETRI 9
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883

10. powersaving.Theproposedmethodalsoattainslessmeandelayinservice
resumptionprovidedthattherehasbeenalonginactivity.
References
[1] MohammadT.Kawser,“LTEAirInterfaceProtocols”,ArtechHouse,ISBN:
978-1-60807-201-9,2011.
[2] Zhou, Lei, Haibo Xu, Hui Tian, Youjun Gao, Lei Du, and Lan Chen.
"PerformanceanalysisofpowersavingmechanismwithadjustableDRXcycles
in3GPPLTE."InVehicularTechnologyConference,(VTC2008-Fall),IEEE
68th,pp.1-5,2008.
[3] Mihov, Yakim Y., Kiril M. Kassev, and Boris P. Tsankov. "Analysis and
performanceevaluationoftheDRXmechanismforpowersavinginLTE."In
IEEE26thConventionofElectricalandElectronicsEngineersinIsrael(IEEEI),
pp.000520-000524,2010.
[4] Fowler, Scott, Ranjeet S. Bhamber, and Abdelhamid Mellouk. "Analysis of
adjustable and fixed drx mechanism for power saving in lte/lte-advanced." In
IEEE International Conference on Communications (ICC), pp. 1964-1969,
2012.
[5] Wang, Hwang-Cheng, Chih-Cheng Tseng, Guan-Yun Chen, Fang-Chang
Kuo,andKuo-ChangTing."PowersavingbyLTEDRXmechanismusinga
mixtureofshortandlongcycles."InTENCONIEEERegion10Conference,pp.
1-6,2013.
[6] Fowler, Scott, George Baravdish, and Di Yuan. "Numerical analysis of an
industrialpowersavingmechanisminLTE."InIEEEInternationalConference
onCommunications(ICC),pp.1748-1753,2014.
[7] Jha,Satish Chandra,AliTaha Koc,and RathVannithamby."Optimizationof
discontinuousreception (DRX) formobileInternet applications overLTE." In
VehicularTechnologyConference(VTCFall),pp.1-5,IEEE,2012.
[8] Koc, Ali T., Satish Chandra Jha, Rath Vannithamby, and Murat Torlak.
"OptimizingDRXconfigurationtoimprovebatterypowersavingandlatencyof
activemobileapplicationsoverLTE-Anetwork."InWirelessCommunications
andNetworkingConference(WCNC),pp.568-573.IEEE,2013.
[9] Liu, Yu, Minh Huynh, Anurag Mangla, and Dipak Ghosal. "Performance
analysis of adjustable discontinuous reception (DRX) mechanism in LTE
network."InWirelessandOpticalCommunicationConference(WOCC),pp.1-
6.IEEE,2014.
[10] Rajesh, A., and R. Nakkeeran. "Performance analysis of enhanced DRX
mechanism in LTE networks." In International Conference on Computer
CommunicationandInformatics(ICCCI),pp.1-5.IEEE,2014.
[11] Karthik,R.M.,andArvindChakrapani."Practicalalgorithmforpowerefficient
drx configuration in next generation mobiles." InINFOCOM, pp. 1106-1114.
IEEE,2013.
[12] Koc, Ali T., Satish C. Jha, Rath Vannithamby, and Murat Torlak. "Device
power saving and latency optimization in LTE-A networks through DRX
configuration." In IEEE Transactions on Wireless Communications, Vol. 13,
Issueno.5,pp.2614-2625.2014.
[13] Wang,Kangping,XinLi,HongJi,andXinDu."ModelingandOptimizingthe
LTE Discontinuous Reception Mechanism under Self-Similar Traffic.", In
IEEETransactionsonVehicularTechnology,Vol.PP,Issueno.99,pp.1-1,2013.
[14] Y.-P.YuandK.-T.Feng,“Traffic-BasedDRXCyclesAdjustmentSchemefor
3GPP LTE Systems,” In IEEE Vehicular Technology Conference (VTC
Spring),pp.1–5,May2012.
[15] Yu, Gwo-Jong. "A fuzzy adaptive DRXpower saving mechanism for LTE-
Advanced networks." In The Fourth International Conference on Network of
theFuture(NOF),pp.1-5,IEEE,2013.
[16] Syama Varma R, Krishna M. Sivalingam, Li-Ping Tung2 and Ying-Dar
Lin,“DynamicDRXAlgorithmsforReducedEnergyConsumptionandDelay
in LTE Networks” In IEEE Conference on Wireless Days (WD), pp. 1 – 8,
2014.
[17] Zhang,Ziqi,ZhuyanZhao,HaoGuan,LeiDu,andZhenhuiTan."Performance
analysis of an adaptive DRX mechanism with flexible short/long cycle
switchinginLTEnetwork."InIEEEInternationalSymposiumonMicrowave,
Antenna, Propagation and EMC Technologies for Wireless Communications
(MAPE),pp.27-32,2013.
[18] 3GPPTS23.203,“Policyandchargingcontrolarchitecture.”Rel.12,v.12.9.0,
2014.
[19] MoustafaM.NasrallaandMariaG.Martini,“ADownlinkSchedulingApproac
hforBalancingQoSinLTEWirelessNetworks”InPersonalIndoorandMobil
eRadioCommunications(PIMRC), pp.1571-1575,2013.
[20] Bontu,ChandraS.,andEdIllidge."DRXmechanismforpowersavinginLTE.
"InCommunicationsMagazine,IEEE,Vol.47,Issueno.6,pp.48-55,2009.
[21] Jin,Sunggeun,andDajiQiao."Numericalanalysisofthepowersavingin3GPP
LTE advanced wireless networks.", IEEE Transactions onVehicular
Technology,Vol.61,Issueno.4,pp.1779-1785.IEEE,2012.
[22] Gupta, Pragya Kirti, R. V. Rajakumar, C. Senthil Kumar, and Goutam Das.
"Analyticalevaluationofsignallingcostonpowersavingmechanisminmobile
networks."InTENCONSpringConference,pp.376-380,IEEE,2013.
[23] Varma, Syama, Krishna M. Sivalingam, Li-Ping Tung, and Ying-Dar Lin.
"Analytical model for power savings in LTE networks using DRX
mechanism." In 2015 Twenty First National Conference on Communications
(NCC),pp.1-6,IEEE,2015.
[24] Fowler,Scott."StudyonpowersavingbasedonradioframeinLTEwireless
communication system using DRX." In GLOBECOM Workshops (GC
Workshops), pp.1062-1066.IEEE,2011.
[25] Wigard,Jeroen,TroelsKolding,LarsDalsgaard,andClaudioColetti."Onthe
user performance of LTE UE power savings schemes with discontinuous
reception in LTE." In IEEE International Conference on Communications
Workshops,2009.ICCWorkshops2009,pp.1-5.IEEE,2009.
[26] S.-R. Yang and Y.-B. Lin, “Modeling UMTS discontinuous reception
mechanism,”IEEETrans.WirelessCommun.,vol.4,no.1,pp.312–319,Jan.
2005.
[27] Zukerman,Moshe.“IntroductiontoQueuingTheoryandStochasticTeletraffic
Models”,http://www.eecityu.edu.hk/Zukerman/classnotepdf(2000-2015).
[28] 3GPPTS36.331,“RadioResourceControl(RRC)”,Rel.12,v.12.3.0,2014.
RP1510-0883e ⓒ 2016 ETRI 10
The article has been accepted for inclusion in a future issure of ETRI journal, but has not been fully edited. Content may change prior to final publication.
http://dx.doi.org/10.4218/etrij.16.0115.0883