Dimensioning X2 backhaul link in LTE networksAlexandre Blogowski and Olivier Klopfenstein and Benjamin Renard

Orange Labs38 rue du general Leclerc, 92130 Issy-les-Moulineaux, France

e-mail: alexandre.blogowski@orange.com

Abstract—A central objective in designing Long Term Evolu-tion networks (LTE) is to provide a better quality of experiencefor the end user. One of the implemented enhancements is adirect connection between neighbouring base stations throughX2 interface. This interface enables mobility management andthe transfer of the user’s data in case of a handover. The aimof this paper is to study the impact of user mobility on capacityplanning and to provide an analytical model to dimension theX2 bandwidth under certain performance objectives.

I. INTRODUCTION

LTE networks are widely considered as one solution forfuture high-capacity mobile communications. A higher bitrate, a wider cell coverage, a lower latency, an enhanced andseamless mobility management... are some of new features ofLTE networks [2], [9], [11]. In LTE architecture, the space ispartitioned into cells, each cell being attached to a base station.Each base station (also called eNB) provides air interface to auser equipment (UE) and receives traffic from the core networkthrough a so called S1 interface. When a UE moves fromone cell to another (handover process), its data are transferredthrough a X2 interface that connects two neighbouring eNBs.As we will only consider the path between the eNB and thefirst intermediate node for S1, and the path between two eNBsfor X2, we will refer to S1 and X2 links (see Fig. 1). Fromthe operational point of view, LTE network planning wouldbe easier if a simple relation could be established between thecapacities needed on S1 and X2 links.

Fig. 1. S1 and X2 interfaces.

Main uses of the X2 interface include intra-LTE mobilitysupport (handover process), inter-cell interference coordina-tion and load management. While load management can beconsidered as requiring a constant and negligible bandwidth,handover support and interference coordination bandwidthdepend on the cell state. As interference coordination is not

likely to be used in homogeneous LTE networks, this paperonly investigates the bandwidth needed for handover support.

For this use, traffic on the X2 link can be generated bycontrol or user plane. However, it has been demonstrated in[14] that control plane traffic for X2 is negligible comparedto user plane traffic. We thus consider only user plane trafficin this paper. X2 traffic can also be divided between outgoingtraffic (UEs leaving the cell) and ingoing traffic (UEs enteringthe cell). As in an homogeneous network those traffics areequal, we only deal with outgoing traffic. Finally, since X2

and S1 links shares the same physical link (see Fig. 1), wehave to dimension a single X2 link per site.

Let us note that X2 dimensioning has already been inves-tigated in [14]. Using Erlang formula, the authors proposedimensioning rules for X2 link. However, although this so-phisticated approach may be closer to real-life network, it maybe unnecessarily accurate at the planning scale, where globalassumptions are made to draw future capacity investments. Wepropose here a simpler analytical model which can be usedeasily by network planners and in case a relation between S1

and X2 links can easily be found. Furthermore, the results weobtain appear to be close to those of [14].

The dimensioning of the X2 link is driven by a target qualityof service in case of handover. Hence, one of the criticalingredients for this analysis is a model for UE mobility. Thisaspect of mobile networks has been extensively studied in theliterature. A mapping of various mobility models, used forwireless systems, is given in [1]. To the best of our knowledge,most of the existing papers dealing with the handover problemonly involve a single UE. In this context, many preciseanalytical models are proposed, such as random waypoint [7],smooth random mobility [1] or one-moment model [3]; someother approaches are more geometric [13]. Several simulatorshave been proposed, see [5], [13]. Based on a fluid mobilitymodel, [14] is one of the rare papers dealing with a populationof UEs and its impact on network dimensioning. Here, wedescribe first a simple mobility model for a single UE, andextend it to a population of UEs. This approach is natural andsimplifies the X2 capacity analysis.

The paper is organized as follows. In Section II, a mobilitymodel and its impact for X2 dimensioning are described fora population of UEs. Section III investigates the multi serviceaspect and the effects of transport protocols on the proposedimprovements. In Section IV a comparison with an othermodel [14] is examined. Finally, numerical tests are providedin Section V where a numerical analysis of the X2/S1 ratio is

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performed. Section VI concludes this paper.

II. DIMENSIONING THE X2 LINK

A. The case of a single UEA UE can move from one cell to another during the same

communication. Its probability of leaving a cell depends oncell size, communication duration and mobility parameters(speed, direction...). Each network handover process requiressome network resources on the X2 link to route the commu-nication to the target eNB.

We consider first the case of a single UE in a given radiocell based on the same assumptions as in [3], [5], [6], [7],[10], to establish an analytical mobility model. The cell isassumed circular with radius R. Within the latter, the UEkeeps the same constant velocity v and the same direction(moving in a straight line). Let ∆ be the constant duration ofa communication. The case where speed and direction of theUE are not constant within the cell, is treated in [1], [5], [6],[7]. During its communication, the UE travels a distance v·∆.If v·∆ > 2R, it leaves the cell with probability 1. If v·∆ ≤ 2R,the probability of exit depends on its starting position in thecell and its direction. Under the assumption that this startingpoint is uniformly distributed on the cell, the dotted disk inFigure 2 represents the horizontally translated initial cell bydistance v·∆. Furthermore, as the circle is invariant underrotation, the selection of the direction (in straight line) has noinfluence in our further analysis. Hence, the probability thatthe UE stays in the cell is the ratio between the intersectionof the two disks in Figure 2 (the shaded area S) and the areaof a disk, that is:

Pstay =Area(S)

πR2(1)

Fig. 2. The shaded area represents remaining UEs in the cell.

A simple calculation shows that, for v·∆2R ≤ 1:

Pstay =1

π

2 arccos

(v ·∆2R

)− v ·∆

R

√1−

(v ·∆2R

)2(2)

Note again that if v·∆ = 2R, then Pstay = 0, and if v·∆ = 0,then Pstay = 1. In the remaining, let Pexit = 1 − Pstay . Forsmall v∆/2R, Taylor expansion of Pexit is:

Pexit =2v∆

πR+ o

(v∆

2R

)(3)

Parameters Description UnityR Radius of the cell mv UE velocity m/s∆ Duration of a communication sβ Period during which data are stored in the buffer msQ Buffer size and data in transit Mbδ Delay constraint ms

DX2X2 link capacity for a single UE Mb/s

d UE’s throughput Mb/sN Number of UEss A time slotk Simultaneous outputs

P(k,N) Probability of k outputs among N %CX2 X2 link capacity Mb/sCS1 S1 link traffic Mb/sBS1

Bandwidth used on the S1 link Mb/sk∗ mink ∈ N|Pexit ·

∑N−1j=k P(j,N−1) ≤ p

p Percentage of congestion %γ Size of the reordering buffer of RTP msC Number of classes of servicek Handover distribution

Pr(k, n) Probability of having a handover distribution k %

Pc(i, k)Probability that a class-i user

experiences congestion %

TABLE INOTATION TABLE

Therefore, under the above assumption, Pexit depends linearlyon v and ∆. Replacing v and ∆ with their average values,the above approximation is exactly the value of the meannumber of handover during a communication, as given in [12]for the Random WayPoint mobility model. This is perfectlyunderstandable as if a UE is not likely to do more than onehandover, the mean number of handover is the probability ofleaving the current cell.

We already know that a UE can move from one cell toanother during the same communication with probability Pexitgiven by equation (2). This causes, for a time δ, an interruptionof the radio link between the transmitting eNB and the UE.During this interruption, the source eNB should transfer tothe target eNB an amount Q of data over the X2 link. Thisamount is composed of data buffered at the source eNB andongoing data which continue to arrive via the S1 link. Q isproportional to the UE’s throughput d on S1 link and we noteβ = Q/d. Consequently, to ensure transparency for the UEduring the handover process, we need to transfer, on the X2

link, an amount Q of data in less than δ seconds. Hence, forevery UE leaving the cell, we need a capacity of:

DX2=βd

δ(4)

B. Dimensioning X2 for a population

We assume that all UEs have the same mobility and trafficcharacteristics (e.g same v, maximum bit rate...) and the samecommunication duration ∆. We also assume constant theexpected maximum number N of UEs in the cell and considerit as the number of active UEs within the cell at any time. Thisassumption is considered as providing conservative results.

When a UE leaves the cell, a capacity of DX2must be

reserved on the X2 link. We focus on the probability that theUE goes out from the cell at a given moment. To do this,

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we discretize the duration of the communication ∆ in ∆/δsegments of size δ (time slots). For v∆/2R small enough,the distribution of exit time τ of a UE has almost a lineardistribution function, i.e.

Pexit(τ ≤ t) ≈2vt

πR, t ≤ ∆ (5)

We can therefore consider that this distribution is uniform overthe interval [1,∆] and that the probability of exit during a timeslot s with duration δ is:

Pexit(s) =2vδ

πR(6)

The probability that a UE goes out on a given slot s isPexit(s) = 2v∆/πR · δ/∆ = Pexit · δ/∆, and the probabilitythat there are exactly k outputs on this slot s is thus given by:

P(k,N) = CkN ·(Pexit

δ

∆

)k·(

1− Pexitδ

∆

)N−k(7)

If Pexit = 1, we truncate the duration of the communicationto the maximum time spent inside the cell, or ∆max = 2R

v .

Note that the above discrete model can be approximatedby a Poisson distribution with parameter λ. Indeed, eqn. (7)follows a binomial law with parameters N and Pexit · δ/∆,but for N large enough and Pexit ·δ/∆ small enough, we have

λ = NPexit · δ/∆ (8)

From the network point of view, having exactly k outputsat the same time (i.e. on the same time slot) corresponds to athroughput of k · DX2 = k · Q/δ which must be transferredon the X2 link. We denote P (network)

c (k) the probability thatthe X2 link needs a capacity of less than k ·Q/δ. We have:

P (network)c (k) =

k∑i=0

CiN ·(Pexit

δ

∆

)i·(

1− Pexitδ

∆

)N−i(9)

Now, we wish to determine the dimensioning of the X2 linkin order to guarantee a certain target quality of service (QoS)for all users. It is during the communication time ∆ that theuser can perceive the network congestion (overall slowdownof the network). In our model, we consider that, in case ofcongestion on a slot s, flows are blocked and discarded at theend of the slot. Excess data are thus lost.

If the network has been dimensioned for k simultaneousoutputs, the user will experience congestion if he leaves thecell on the same time slot as k (or more) other users. Wedenote Pc(k) the probability that at least k+1 UEs (includingthe reference UE) leave the cell on the same time slot. Wehave, for k ≤ N − 1:

Pc(k) =

∆∑s=1

(Pexit δ∆

)·N−1∑j=k

P(j,N−1)

(10)

= Pexit ·N−1∑j=k

P(j,N−1) (11)

We have thus characterized the quality perceived by a user(probability of congestion) for a given dimensioning of theX2 link. Conversely, we can deduce the capacity of the X2

link corresponding to a given target QoS.

We are now focusing on the viewpoint of the user and ona target quality of service. We will denote by p the maximumcongestion probability on the X2 link, i.e. the user experiencesthe congestion due to its mobility with a probability no greaterthan p. The capacity CX2 of the X2 link is then

CX2= k∗DX2

= k∗βd

δ(12)

where

k∗ = min

k ∈ N∣∣∣Pexit · N−1∑

j=k

P(j,N−1) ≤ p

(13)

III. MULTI-SERVICE MODEL

A. Extending the single service modelThe previous model considers only one type of flows. How-

ever, in IP networks, various type of flows can be found, withdifferent traffic characteristics (data rate, mean communicationduration...) and needs in term of QoS. Assume now that wehave C classes of service. Each class i has a data rate di, amean communication duration ∆i, an amount of data Qi totransfer in case of handover and pi will denote the maximumcongestion probability. We still consider a fixed number Nof active UEs and we also consider a fixed number of activeUEs in each class. We denote by n = (n1, . . . , nC) the staticdistribution of UEs among classes.

Let P istay be the probability that a class-i UE will stay inits cell during the communication. We have the same equationthan eqn. (2) with ∆i instead of ∆. We also have P iexit =1 − P istay . Denote by Pr(k,n) the probability of having ahandover distribution k = (k1, . . . , kC):

Pr(k,n) =

C∏i=1

Pi(ki,ni)(14)

where Pi(ki,ni)is deduced from eqn. (7). Note that∑

k∈HnPr(k,n) = 1 where Hn = k|∀i, ki ≤ ni denotes

the possible handover distributions.

As in the single service model, we consider the point ofview of a user. If the X2 link has been dimensioned with acapacity CX2 , the user will experience congestion if he leavesthe cell on a slot such that the data rate needed by handoverUEs will be higher than CX2

. We will denote by Pc(i,k) theprobability that a class-i user experiences congestion if the X2

link has been dimensioned to allow a simultaneous handoverdistribution k:

Pc(i,k) = P iexit · P

total traffic on X2 >

C∑j=1

kjβjdjδ

= P iexit ·

∑l∈Λi

k

Pr(l,n− ei) (15)

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where ei is the ith unitary vector of NC and where

Λik =

l ∈ Hn−ei

∣∣∣ C∑j=1

ljβjdj + βidi >

C∑j=1

kjβjdj

We define k∗ as the distribution that minimizes the capacity

needed on the X2 link (and thus minimizes∑i kiβidi/δ)

while satisfying the conditions ∀i, Pc(i,k) ≤ pi. The neededcapacity on X2 is then

CX2 =

C∑i=1

diβiδk∗i (16)

B. Lowering the data rate on the X2 linkWhen a congestion occurs, the following slot is likely to

be empty or less used. If we postpone some data from thecongested slot to the following slot (by reducing the UE’sdata rate on the X2 link), it will be possible to avoid thiscongestion. Until now, all the UE’s data was transferred to thetarget eNB before the recovery of the radio link in the targetcell. However, it is highly likely that the UE will have the samedata rate on both radio links (as in both cases the UE is on celledge). The UE’s data will thus be entirely buffered at the targeteNB and then send to the UE with the same data rate di on theradio link than via the previous eNB. However, if both actions(transfer on X2 and radio links) are done simultaneously, theuser won’t experience additional congestion.

As a consequence, if the first packets transferred on the X2

link arrive before the recovery of the radio link and if thedata rate on the X2 is equal or higher than di, the user won’tsuffer from congestion. The first condition is fulfilled as theend-to-end delay on the X2 interface is between 10 and 20ms while the handover duration ranges from 25 to 50 ms.The second condition implies that we can lower the neededUE’s data rate on the X2 link from βidi/δ to di. The neededcapacity becomes

CX2=

C∑i=1

dik∗i . (17)

More details and improvements will be given in Section V.Nonetheless with our numerical inputs (∀i, βi = 100 ms andδ = 25 ms), this enhancement divides the needed X2 capacityby 4.

C. Impact of transport protocolsThe preceding enhancement has however some drawbacks.

If we consider that the target eNB starts receiving packetsfrom its S1 link as soon as the radio link is recovered, thisflow will collide with the X2 flow if the latter is still active(which couldn’t happen with the original model). The UE willthus receive packets in the wrong order and we are going to seethe impact of two transport protocols on this medley. A simplesolution would be to reorder packets at the target eNB, but thiswould need additional network features. We will thus study theimpact of transport protocols when there is no reordering atthe eNB level.

1) TCP: Transmission Control Protocol (TCP) is the maintransport protocol over the internet and is used for elastic flows(http, ftp...). As supposed in paragraph III-B, the data rateon X2 is higher or equal to the data rate on S1 and thusthere won’t be more than one packet from S1 between twoX2 packets, as shown on the following table:

Seq. number 0 1 2 10 3 11 4 ...Link X2 X2 X2 S1 X2 S1 X2

ACK(n) sent 0 1 2 2 3 3 4

TCP needs at least three consecutive ACKs with the samesequence number to start a fast-recovery (TCP Reno) or slow-start (TCP Tahoe) process. TCP won’t thus have any impacton our enhancement.

2) RTP: Real Time Protocol (RTP) is used for real-timeflows (VoIP, video streaming, real-time gaming...) and can beused over UDP (User Datagram Protocol). We will supposethat this protocol goes along with a reordering buffer with sizeγ (in seconds): it is possible to reorder two consecutive packetsif their distance is lower than γ. The end user will experiencecongestion if the collision time between flows from S1 andX2 is higher than γ; that is if the overall transmission time onthe X2 link is higher than γ + δ. To experience congestion, aclass-i user must thus have an X2 data rate Di

X2such that

DiX2

< diβi

γ + δ(18)

If ∀i, γ + δ ≥ βi, RTP won’t have any impact on ourenhancement. Consider now the case where ∃i|γ + δ < βi.

If we suppose that the eNB has a proportionally fairscheduler, a class-i UE has a data rate di

CX2∑j kjdj

and thecondition of eqn. (18) becomes:

C∑j=1

kjdj > CX2

γ + δ

βi(19)

The congestion probability, given by (15), is now:

Pc(i, CX2) = P iexit

∑l∈Ωi

CX2

Pr(l,n− ei) (20)

where:

ΩiCX2=

k ∈ Hn−ei

∣∣∣ C∑j=1

kjdj + di > CX2

γ + δ

βi

(21)

IV. COMPARISON WITH WIDJAJA AND LA ROCHE’SMODEL [14]

In [14], the authors propose a richer stochastic model. Basedon a traffic model using the Kaufman-Roberts formula [8],they give the number of UEs leaving the cell per unit time.As in our model, they consider that in case of congestionflows are blocked. However, they drop all excess flows whoarrive while we accept these flows during a time slot s beforestopping them at the end of this slot.

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Fig. 3. Blocking probabilities for both models.

Their mobility model is based on the fluid flow model,according to which the UE crossing rate out of an enclosedregion with perimeter length L is ρvL/π where ρ is the UEsdensity. If we adapt their model to a model with a fixed numberof active UEs, the offered load for class-i UEs becomes:

ai =2vδniπR

(22)

We can notice that if we replace Pexit by the mean numberof handover during a communication 2v∆i/πR [12] in eqn.(8), we obtain the same parameter. While we consider inour model the probability of leaving the cell, Widjaja andLa Roche consider the mean number of handover during acommunication. Another major difference between stochasticmodels is that Widjaja and La Roche use the classical multi-Erlang model developed by Kaufman and Roberts [8] inplace of a simpler comprehensible model and easy to use bynetworks planners. Figure 3 compares blocking probabilitiesfor both models, with the same mobility model (which is ourmobility model). In this figure, ’BKR’ denotes our enhancedmodel and we have taken CX2

= 1280 Kbps. We can observethat blocking probabilities are really close, and thus the sameX2 bandwidth is required in both models.

In [14], the authors also propose a model with batchedarrivals: UEs are moving in groups (batches) with randomsize, and they observe the impact of such a behaviour onthe X2 link. A state of the art of the Erlang multi-rate lossmodel with batched arrivals can be found in [4]. However, nomodel has been developed for batches with different classes ofservice, which led Widjaja and La Roche to consider a singleservice class for their batch study. A complete study of batchesarrivals needs a consequent development. Another reason fornot studying deeply the batches arrivals lies in the fact thateven if active UEs are travelling in batches, it is unlikely thatthey will all leave the cell on the same slot. If we consider ahigh speed train (300 km/h) or a commuter train (80 km/h),a 25 ms slot represents approximately 2 meters for the firstone, and only 0.5 meter for the second. These distances makeit unlikely for few active UEs from the same train to leavethe cell simultaneously and induce congestion. For instance,with the classes of service VoIP, video, data, if CX2 = 1024kbps, we can have k∗ = 0, 0, 1 or 2, 3, 0 or 32, 0, 0...

V. NUMERICAL ANALYSIS

For this chapter, we use the enhanced model (paragraphIII-B) and the following numerical inputs: R = 250 m andv = 12 km/h. The various classes of service are VoIP,video, data with a distribution of 25%, 25%, 50%, withcorresponding data rates of 32, 320, 1024 Kbps and com-munications duration ∆ of 100, 200, 5 seconds. We alsoconsider ∀i, βi = 100 ms, and δ = 25 ms.

A. Variation of the number of active UEs N

Until now, the number of active UEs has always beenconsidered steady. In this section, we will consider that Nfollows a Poisson distribution. Table II shows the maximumnumber of active UEs that we can have for a maximumcongestion probability set to 0.01%. We can observe that thosenumbers are very close, which confirms our hypothesis of asteady number of active UEs.

CX2(Kbps) Nmax original amax with Poisson distribution

1024 1 11376 25 242080 135 134

TABLE IIIMPACT OF A POISSON DISTRIBUTION OF THE NUMBER OF ACTIVE UES

WITH THE ENHANCED MODEL

B. Enhanced model and impacts of transport protocols

In what follows, numerical inputs will be the same as before.We also consider γ = 25 ms (real-life systems have usually abigger γ, this small value is used for showing the impact ofRTP in a worst-case scenario).

Fig. 4. The impact of RTP on congestion probabilities for N = 100.

Fig. 4 shows congestion probabilities in terms of X2 band-width for a population N = 100 UEs, for the enhancedmodel and with the impact of RTP. The original multi-servicemodel has the same congestion probabilities than the enhancedmodel, but for a X2 bandwidth multiplied by βi/δ = 4. Wecan notice that with a very small γ, RTP has a non negligibleimpact on X2 dimensioning.

For example, a maximum congestion probability pi = 0.5%for all classes requires a X2 bandwidth of 1344 Kbps for theenhanced model and 2650 Kbps if we take into account RTP.

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C. Variation of the maximum congestion probability

It could be interesting to see the impact of a rise ofparameter pi (here considered as the same for all classes)on the needed X2 bandwidth. Fig. 5 shows this impact forthe enhanced model (without RTP impact) for N = 100.We observe that the X2 bandwidth still vary by steps; thisis consistent with the bandwidth evolution illustrated on Fig.4 for separate services.

Fig. 5. Impact on the X2 dimensioning of the variation of the maximumcongestion probability

D. Ratio X2/S1

From an operational point of view, finding a relation be-tween S1 and X2 capacities can be very useful. However,the presence of congestion on the S1 link changes the actualbit rate and thus the needed X2 bandwidth. In the absenceof congestion (

∑i nidi ≤ CS1

), each class-i UE receives itsmaximum bit rate di. The ratio X2 capacity over bandwidthused on the S1 link, denoted by CX2

/BS1, is then

∑i k

∗i diβi/δ∑i nidi

.In case of congestion (

∑i nidi > CS1

), assuming a propor-tional share of the capacity, each UE receives on S1 a bit rateof di

CS1∑j djnj

, but the ratio CX2/BS1

remains the same; it isthus independent of the S1 link state. This explains why wewere able to consider a non-congested S1 link.

Fig. 6. Evolution of the CX2/BS1

ratio according to v and BS1

Fig. 6 shows the evolution of the CX2/BS1 ratio accordingto the UEs’ speed v and different values of bandwidth usedon the S1 link BS1

. We can notice that the ratio is quite smalland the X2 interface can thus be carried with the S1 interfaceon the same physical link. Moreover, if the value for BS1

isgiven, we can easily find the needed X2 bandwidth.

VI. CONCLUSION

In this paper, we provide an analytical model that quantifiesthe impact of UE mobility on the dimensioning of a LTEmobile network. Based on QoS requirements, dimensioningrules are given for the X2 link, and also for relating directly theX2 capacity to the S1 traffic. The simplicity of the approachmakes it easy to integrate in existing network planning tools.Indeed, network planners must just have the number of activeUEs in the cell and the dimension of the S1 link to estimatethe capacity needed on the X2 link. The comparison with thericher model proposed in [14] shows a quite small differenceson the results. Furthermore, our discrete model can be approx-imated by a Poisson distribution, allowing a verification of theassumptions made previously.

Future work include a study where all handover flows wouldbe considered as elastic and never be blocked and the impactof radio interface conditions on handover rates. We also planto investigate the dimensioning of the X2 interface in LTE-Advanced networks, where inter-cell interference coordination(ICIC) schemes will be used, thus increasing the load on theX2 interface.

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