sensitivity analysis of the optimal parameter settings of an lte packet scheduler

8/12/2019 Sensitivity Analysis of the Optimal Parameter Settings of an LTE Packet Scheduler

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Sensitivity Analysis of the Optimal ParameterSettings of an LTE Packet Scheduler

I. Fernandez Diaz,

R. Litjensand J.L. van den BergTNO ICT, The Netherlands

E-mail: {Irene.FernandezDiaz,Remco.Litjens and J.L.vandenBerg }@tno.nl

D.C. DimitrovaUniversity of Twente, The NetherlandsE-mail: [email protected]

K. SpaeyIBBT, Belgium

E-mail: [email protected]

Abstract Advanced packet scheduling schemes in 3G/3G+mobile networks provide one or more parameters to optimise thetrade-off between QoS and resource efciency. In this paper westudy the sensitivity of the optimal parameter setting for packetscheduling in LTE radio networks with respect to various trafcand environment aspects. For our investigations we consider

a reference packet scheduling algorithm containing elementsof proportional fairness and packet urgency to support mixesof real-time and non-real-time trafc. We present extensivesimulation results showing the impact of trafc characteristics(like le size distribution, trafc mix) and environment conditions(regarding e.g. multipath fading and shadowing) on the optimalparameter setting. Although, in some cases, efciency gains of about twenty percent can be achieved by proper tuning of thescheduling parameters, the overall view from our investigationsis that a single, robust setting of the parameters can be deter-mined which provides near optimal trade-offs under almost allpractically relevant conditions.

I. INTRODUCTION

One of the key radio resource management mechanisms in

3G+ mobile networks is the packet scheduler, which coor-dinates the access to shared channel resources. In OFDMA-based LTE systems, for example, this coordination generallyconsiders two distinct dimensions, viz. the time dimension(allocation of time frames) and the frequency dimension (allo-cation of subcarriers). The main challenge in designing packetschedulers is to optimise resource efciency (e.g. by exploitingmulti-user and frequency diversity), while satisfying the usersQuality of Service (QoS) requirements and achieving somedegree of spatial fairness. Many packet scheduling schemes formobile access networks have been proposed and implementedof which the so called Proportional Fair (PF) scheduler isprobably the most well known, see e.g. [1], [2]. It explicitlyaddresses the trade-off between efciency, QoS and fairness,which can be tuned by a single parameter , 0 1.

An important issue is how packet scheduling performancedepends on actual system and trafc characteristics regardinge.g. shadowing and fast fading, mobility, le size distribution,trafc mix, etc. A particular relevant question in this light ishow the optimal setting of the scheduling parameters hasto be adapted when one or more of these system or trafcconditions change over time. Somewhat surprisingly, studiessystematically investigating this issue are rare or completely

lacking. E.g., for the PF scheduler it is often stated that closeto zero (e.g. = 0 .01) is generally a good choice, see e.g.[2], but mostly without any support of results from extensiveexperiments and/or simulations.

The aim of the present paper is to get more insight into

the sensitivity of the optimal parameter setting for packetscheduling in LTE. For that purpose we analyse the optimalparameter settings of a particular reference (downlink) packetscheduling algorithm under different system and trafc con-ditions. The reference packet scheduler, containing elementsof proportional fairness and packet urgency, supports mixes of real-time and non real-time trafc. Besides the parameter of the PF-part of the scheduler it contains a second parameter( ) that can be used to tune the relative importance of the twoelements in the scheduling decision. To enable our analysiswe have developed a tool for dynamic LTE simulations.

Apart from the evident importance of studying the sensi-tivity of packet schedulers with respect to changes in system

and trafc conditions, the present study is also motivated byour investigations in the eld of self-optimisation of radioresource management in LTE, see [3]. Obviously, beforestarting to develop self-optimisation algorithms, its importantto get insight into these sensitivity issues and the potentialperformance/efciency gains that may be achieved.

A. Related work

Most of the downlink scheduling schemes for 3G+ wirelessnetworks adopt the well-known Proportional Fair (PF) algo-rithm. It primarily aims at an appropriate trade-off betweenthroughput efciency (through diversity gain) and fairness fornon-real-time data trafc, see e.g. [1], [4], [5], [6], [7], [8],[9]. Originally developed for purely time domain scheduling,as e.g. in HSDPA, the PF algorithm has been adapted inseveral ways for efcient and fair utilisation of both time andfrequency domain resources in OFDMA systems like LTE andWiMax, see e.g. [10], [11], [12] and the references therein.For scheduling multimedia trafc so-called deadline-basedschemes have been developed, explicitly taking care of packetdelays for real-time services, see e.g Necker [2] and Elsayedand Khattab [13], [14]. In particular, the work by Elsayed andKhattab (in the context of TDMA-based wireless networks)

978-1-4244-2519-8/10/$26.00 2010 IEEE


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describes an interesting and pragmatic scheduling principle,denoted the Channel-Aware Earliest Deadline Due scheme. Itincorporates both channel-awareness and due date aspects (byextending a PF scheduler with a delay dependent component)to allow for a mixture of real-time and non-real-time trafc.Our reference scheduler is based on the scheduler proposedby Elsayed and Khattab and extends it for deployment in theLTE context.

The remainder of this paper is organised as follows. First,in Section II, we specify the scheduling algorithm that willbe used as a reference algorithm in our study, and we explainthe set-up of the sensitivity analysis of the optimal parametersettings for the reference scheduler. Section III describes themain modelling assumptions in the LTE simulation tool andgives the simulation parameters used in the reference scenario.In Section IV we present and discuss the simulation results.The conclusions and some topics for further research arepresented in Section V.

I I . R EFERENCE PACKET SCHEDULER

We have developed a reference packet scheduler for usein LTEs OFDMA downlink, inspired by algorithms encoun-tered in the literature, in particular those in [13], [14]. Thescheduling principles proposed in these papers have beenextended from a pure time-domain focus to cover both time-and frequency-domain scheduling, as is relevant when appliedin the LTE context. The scheduler supports both real-time andnon real-time services, and in that light contains elementsof proportional fairness (aiming at resource efciency andfairness) and packet urgency (for adequate support of delay-sensitive services). The reference packet scheduler assigns ineach TTI (time domain: 1 ms granularity) a priority level forevery subchannel (frequency domain: 180 kHz granularity) tothe head of line (HoL) packet of every non-empty user buffer,taking into account the potential bit rate at which the usercan be served on the different subchannels (based on channelquality feedback from the user), as well as the experiencedand maximum tolerable delay of the packet.

The scheduler comprises two steps. In the rst step, pri-ority levels are calculated for each combination of user andsubchannel. In the second step these priority levels are appliedin the actual assignment of subchannels to users.

At time t , the priority level P i,c (t) assigned to user i s HoLpacket associated with subchannel c is calculated according tothe formula

P i,c (t) = serviceR i,c,potential (t )

R i (t)1 +

W i (t)T i W i (t )

(1)The notation is explained in Table I. In the above formula, therst component is the so-called channel adaptivity factor andreects a proportional fairness scheduling principle. Regardingthis component, at TTI t , R i (t ) is updated for each user iaccording to the formula

R i (t) = (1 )R i (t 1) + R i (t 1), (2)

TABLE INOTATION

R i,c,potential (t ) The potential bit rate at which user i can beserved on subchannel c at TTI t. These ratesare based on a discretisation of the SINR-to-rate mapping presented in [15].

R i (t ) The exponentially smoothed average bit rateat which user i has been served, aggre-gated over the subchannels that have beenassigned to user i , at TTI t

R i (t ) The bit rate at which user i is served,aggregated over all subchannels assigned touser i , at TTI t

Exponential smoothing parameter, used forthe smoothing of R i (t )

T i Maximum allowed delay for packet associ-ated with user i (T i = if user i is a nonreal-time user)

W i (t ) Delay experienced by HoL packet of useri at TTI t , i.e. the present time minusthe packets arrival time in the buffer. If W i ( t ) > T i the packet is dropped (real-time sessions only).

Scheduling parameter that affects the rela-tive importance of the channel adaptivityand packet urgency components of the

priority level function service Service-specic requested bit rate, i.e. theminimum throughput target for non real-time sessions or the xed bit rate for real-time sessions. The purpose of this correc-tion factor is to prevent the scheduler fromgiving undesiredly high preference to real-time sessions, which may typically experi-ence lower throughputs due to their limitedsource rate, rather than due to any unfairnessin the scheduling scheme.

where R i (t ) is initialised at the aggregate bit rate at whichuser i can potentially be served at the time of call creation,assuming all subchannels are available. The second componentof P i,c (t) is the packet urgency factor. The parameter 0allows setting the relative importance of the channel adaptivity(i.e. efciency) and the packet urgency components.

We have developed a heuristic procedure for the assignmentof subchannels, based on these priority levels. Due to a lack of space we reproduce here only the main principles, i.e. (i) theassignment of a given subchannel to the user with the highestpriority on that subchannel; and (ii) in order to comply withthe uniformity restriction that multiple subchannels assignedto a given user must use the same MCS (modulation andcoding scheme), all subchannels assigned to a given user are jointly considered and a common MCS is selected which

maximises the aggregate bit rate for that user; subchannelsthat are potentially released in this step can be reassigned toother users.

III . S IMULATION MODEL AND SCENARIOS

A dynamic system-level simulator has been developed forstudying the packet scheduler in the LTE OFDMA downlink.This are the main characteristics of the simulator:

We consider a hexagonal layout of twelve sectorised sites,comprising three sectors each, with an inter-site distance


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of 2.23 km. A bandwidth of 5 MHz is assumed. The applied propagation model comprises three parts:

distance dependent path loss (COST 231-Hata), shadow-ing and multipath fading. Shadowing is modelled with astandard deviation of (default setting = 9 .4 dB), anintra-site correlation of 1 and an inter-site correlation of 0.5. The default multipath environment is a PedestrianAmodel with a fading velocity of 3 km/h.

The trafc model considers call level dynamics. Arrivalsof non-persistent (nite) sessions of two distinct services(le transfer and video telephony) are governed by Pois-son arrivals. Data trafc is mainly characterised by thearrival rate, the le size (lognormally distributed) andits elastic nature. The default average le size is 500kbit and the coefcient of variation is 1. The referencescenario is a data-only scenario. Video telephony sessionsare characterised by the session arrival rate, a xed bitrate of 110 kbit/s, an exponentially distributed durationwith a mean of 10 s and packet delay budget of 150 ms.

Packets that cannot be delivered within this delay budgetare dropped by the base station and hence contribute tothe experienced packet loss.

Upon generation of a new session, the location of thecorresponding user is sampled. This location is eithersampled from a uniform distribution (default setting) orfrom hot spots situated half-way between the sites andthe cell edges.

We have carried out a thorough sensitivity analysis toassess to what extent the optimal settings of the schedulingparameters, and , depend on the following aspects:

Data trafc characteristics - The average le size and thecoefcient of variation of the le size distribution arevaried;

Multipath fading environment - We compare scenarioswithout multipath fading, a PedestrianA channel modelwith a fading velocity of 3 km/h and a VehicularA modelwith a fading velocity of 30 km/h;

Variability of the average signal strengths among calls -This variability depends on the considered spatial userdistribution (see above) and the assumed shadowing pa-rameter, for which values of equal to 0, 9.4 and 14 dBwill be considered;

Service mix - We consider two types of trafc: letransfer and video telephony. The relative fraction of the

offered trafc load (in kbit/s) for the video and dataservices is varied.

IV. N UMERICAL RESULTS

A. Reference scenario

The reference scenario is a data-only scenario. Hence thepacket urgency component of the scheduler equals 1 becausethe packet delay budget T i is innite for packets of non real-time services. Therefore we will only study the sensitivity of the parameter .

In Figure 1(a) the 10th percentile of the call throughputversus cell load is shown for the reference scheduler and three values. As reference, the results for a maximum SINR and around robin scheduler is also plotted. For relatively high loads,the reference scheduler performs better than the maximumSINR scheduler. This scheduler is the most efcient in termsof spectrum use, but it is not fair. The round robin schedulergives the worst results. The reason is that scheduler is notchannel aware and hence, not very efcient.

In the remainder of this section we consider an operatorpolicy which tries to guarantee a minimum performance forthe worst calls, measured in terms of the 10th percentile of thecall throughput at the cell edge, equal to 500 kbit/s. We willconcentrate on the maximum supportable cell load for whichthis performance target can still be guaranteed. Figure 1(b)illustrates the maximum supportable load for the referencescenario for three different values and the maximum SINRand the round robin scheduler. equals 0.01 gives the bestresults.

B. Impact of the data trafc characteristics

We now study the sensitivity of the optimal parametersettings of the scheduler with respect to various trafc aspects.Figure 2(a) shows the maximum supportable cell load fordifferent values, for three average le sizes (500 kbitcorresponds to the reference scenario, 50 and 5000 kbit). Forsmall le sizes (50 kbit), = 0 .1 is the optimal setting.However the results are not shown because the performancetarget of 500 kbit/s is not reached, even for very low loads. Forlarge le sizes, = 0 .001 is the optimal setting. The largerthe le size, the smaller the optimal value. The explanationis that a small means a larger window size in the averageexponential smoothing (more weight is given to the history).

Hence, for large le sizes, where more history can be takeninto account to achieve fairness, a lower value than in thereference scenario is optimal.

In Figure 2(b) the impact of variations in the coefcient of variation of the le size is shown. When the coefcient of variation equals 0, 1 (reference scenario) and 2 the optimalvalue of is = 0 .01. For coefcient of variation 4 theoptimal value is 0.1. This can be explained as follows. Whenthe coefcient of variation equals 4, most les will be smallles and there will be few large les. For the exponentiallysmoothed average, a large window size ( close to zero) triesto achieve fairness over a period of time which is much largerthan the le download time. Therefore a smaller window size( value close to 1 instead to close to 0) is needed to achievethe required fairness in the case with many small les (i.e.large coefcient of variation). Simulation results show that forcoefcient of variation 4 the optimal value is 0.2. We donot reproduce these results due to a lack of space.

C. Impact of the multipath fading environment

Figure 3(a) illustrates the sensitivity of with respect tovariations in the multipath model. For both the referencescenario (PedestrianA, 3 km/h) and no multipath = 0 .01 is


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the optimal setting. A remarkable result in the scenario with aVehicularA channel model and a fading velocity of 30 km/h,is that the maximum supportable load is much higher than inthe reference scenario. This can be explained as follows. Ahigher velocity may affect the throughput results in two ways:one positive and one negative. The positive effect is that thereis more variability of the channel conditions per time unit.This allows calls to experience good channel conditions moreoften. For small to medium-sized ows this may result in lowerdownload times. The negative effect is due to estimation errorson the SINR; the higher the velocity, the more signicant isthe error. However, as the simulation model does not take intoaccount this estimation error, only the positive effect remains.As a consequence, the supportable cell load is higher than inthe reference scenario.

D. Impact of the differences in the average signal strengthamong calls

Figure 3(b) shows the sensitivity with respect to differencesin the average signal strength. Few differences corresponds to

the case with users situated around a hot spot centered half way between the site and the cell edge and no shadowing.Medium differences refers to the reference scenario. The labelmany differences is used in the case with uniform distributedusers and shadowing with = 14 dB. When there are fewdifferences in average signal strength among calls, those arepurely due to the multipath fading. In this case, there are nocalls which structurally experience worse channel conditionsthan the others. Therefore, in that case fairness is not reallyan issue and the maximum SINR scheduler gives the bestresults. When considering the reference scheduler, = 0 .001is optimal. When there is much difference in average signalstrength between users, = 0 .1 performs slightly better than

other values. High variability of the signal strength resultsin high variability in download times. In this case the optimal is a value close to one (i.e. fairness achieved at a small timescale).

So far we have considered unilateral variations with respectto the reference scenario. Simulation results show that bycombining several variations with respect to the referencescenario the performance in terms of maximum suported loadis a little more sensitive to the choice of . For example,the scenario with large le sizes (5000 kbit), coefcient of variation of the le size 0, VehicularA with a fading velocityof 30 km/h, and users placed around hot spots half-way thesites and the cell edges, the optimal value is 0.001. But evenin this extreme scenario, the maximum supportable load withthe optimal value is just 2 % higher than with = 0 .01. Wecan conclude that in data only scenarios = 0 .01 is overall agood choice and that this setting is fairly robust to the studiedvariations.

E. Impact of the service mix

In this set of simulations we consider both non real-timeand real-time services: le download and video telephony,respectively. In these scenarios both scheduler parameters:

and are relevant. In order to limit the number of scenarios,we will consider a xed equal to 0.01, based on the ndingsfor the data-only scenario, and concentrate on the sensitivityof the parameter . The performance of video telephony callsis measured in terms of the 90th percentile of the packetloss for cell edge calls. The performance target for thesecalls is 5 %. For data calls the same performance target isused as in the previous sections. We varied the percentage of video telephony load: 25 %, 50%, 75% and 100 %. Figures 4(a)and 4(b) illustrate the maximum supportable load for datadownloads and video telephony for service mixes of 25 % and75% respectively. The maximum supported cell load show onthe vertical axis is noted to be the maximum aggregate (videoplus data) load than can be supported, from the perspectiveof satisfying either the video or data services quality target(two distinct sets of bars). For relatively low video telephonyloads (25 and 50 %), the video performance improves as increases, while there is little performance degradation fordata calls. For relatively high video loads (75 and 100 %),the optimal is a value between 0.25 and 1. This can be

explained as follows. Higher values increase the relativeimportance of the packet urgency component of the scheduler.If this becomes too dominant, fewer scheduling decisions areactually channel-adaptive, which in turn makes the systemless efcient. This explains that for relatively high loads themaximum supportable load for video decreases as increases.

Considering the two services, the maximum supportableload for the service mix is determined by the most restrictiveservice, which in our case is mostly le download. The optimal is a value between 0.25 and 1. In the studied case, it can besaid that the optimal setting is little sensitive to the servicemix. However it should be remarked that other simulationresults show that the sensitivity of is dependent on the

considered performance targets for both data and video. Forexample, if the performance target for video telephony is morestrict (for instance 1 % instead of 5 %), then the video telephonyperformance may become the limiting factor. In that case, theoptimal value of is more sensitive to the trafc mix: 3, 3, 2and 1.5 for respectively 25, 50, 75 and 100 % video telephonyload. We do not present these results due to a lack of space.

F. Potential gain of self-optimisation

From Figures 1(b) to 3(b) it can be concluded that = 0 .01is the best setting if the parameter settings of the schedulerwere xed. We want to compare this case with the case inwhich the scheduler is self-optimised. Our assumption is thatthe self-optimised algorithm is able to use the optimal settingin every situation. The potential gain of self-optimisation indata only scenarios is limited: on average 3.3 %, the maximumvalue is 16.6 % which corresponds to the scenario with fewdifferences in average signal strengh among users.

Based on the simulation results, we have obtained theoptimal value of zeta for different video telephony loadpercentages and for different performance targets for videoand data. If the parameter settings of the scheduler werexed, = 0 .75 (and = 0 .01) would be the best choice.


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This choice is fairly robust to the studied variations. Like inthe data only scenarios, we compare this case with the casein which the scheduler is self-optimised. The gain in termsof maximum supportable cell load of self-optimisation withrespect to the xed setting was quantied for six combinationsof performance targets, considering targets that apply eitherfor calls in the whole cell or at the cell edge and four videotelephony load percentages. Due to space limitations we donot show the resuls here, but it can be said that the potentialgain of self-optimisation in mixed trafc scenarios is limited:on average it is 4.6 % and the maximum gain is 20 %. Thismaximum value corresponds to the case with 25 % video and1% packet loss and 250 kbit/s throughput as performancetarget for respectively video and data for calls in the wholecell. If we consider that a practical implementation of the self-optimised scheduling algorithm would not be able to apply theoptimal parameter settings in every situation, the gain wouldbe lower.

V. C ONCLUSIONS

We have developed a packet scheduler which supports bothreal-time and non real-time services. We have performeda thorough sentivity analysis which shows that the optimalparameter settings of the scheduler are not very sensitive tochanges in the data trafc characteristics, the multipath fadingenvironment, the differences in average signal strength amongcalls and the service mix. Rather, we see that a single, robustsetting of the scheduling parameters exist, which providenear optimal trade-offs under almost all practically relevantconditions. As a consequence, we nd that the observedpotential gains of applying self-optimisation to the packetscheduling mechanism do not justify the development of self-optimisation algorithms for the packet scheduler. Needless to

say, this conclusion is based on the selected (proposed) refer-ence packet scheduler, which features some inherent degree of adaptiveness. Noting that packet scheduling schemes are notstandardised, but rather are vendour-specic, for different, e.g.less adaptive packet schedulers, self-optimisation may showmore potential.

In our further research we intend to consider other referenceschedulers and develop self-optimisation solutions if applica-ble. Furthermore, we are interested in the interaction between(potentially self-optimised) packet scheduling and inter-cellinterference coordination. Note that inter-cell interference co-ordination is in some sense also a scheduling mechanism, butwith an inter- rather than intra-cellular scope.

ACKNOWLEDGEMENT

The presented work was carried out within the FP7SOCRATES project [3], which is partially funded by theEuropean Union.

R EFERENCES

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(a) 10th percentile of the call throughput at the cell edge

(b) Maximum supportable cell load

Fig. 1. Performance metrics for the reference scenario: (a) the 10th percentileof the cell throughput at the cell edge, and (b) the maximum supportable cellload calculated therefrom.

(a) Impact of average le size

(b) Impact of coefcient of variation of the le size

Fig. 2. Impact of (a) the average le size and (b) the coefcient of variationof the le size on the maximum supportable load.


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(a) Impact of the multipath fading model

(b) Impact of the differences in the average signal strength

Fig. 3. Dependency of the maximum supportable load on: (a) the appliedmultipath fading model and on (b) the differences on the average signalstrength.

(a) Maximum supportable load-25 % video telephony

(b) Maximum supportable load-75 % video telephony

Fig. 4. Impact of the service mix on the maximum supportable load forincreasing video telephony load: (a) 25 % and (b) 75 %.

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sensitivity analysis of the optimal parameter settings of an lte packet scheduler

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