ETSI TR 104 141 V1.1.1 (2026-03)

TECHNICAL REPORT
Practical Methods for Wireless Backhaul Planning
with New KPIs
2 ETSI TR 104 141 V1.1.1 (2026-03)

Reference
DTR/ATTMTMmWT-0031
Keywords
backhaul, BTA, microwave, millimetre wave,
new KPIs, wireless
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ETSI
3 ETSI TR 104 141 V1.1.1 (2026-03)
Contents
Intellectual Property Rights . 4
Foreword . 4
Modal verbs terminology . 4
Executive summary . 4
Introduction . 5
1 Scope . 9
2 References . 9
2.1 Normative references . 9
2.2 Informative references . 9
3 Definition of terms, symbols and abbreviations . 10
3.1 Terms . 10
3.2 Symbols . 10
3.3 Abbreviations . 13
4 An analytical procedure for deriving BTA lower bounds . 13
4.1 Overview . 13
4.2 Modelling the aggregated traffic demand of backhaul links through Beta distributions . 14
4.3 The analytical procedure for deriving BTA lower bounds . 16
5 Traffic demand distribution models through measurement campaigns on live networks . 20
5.1 Overview . 20
5.2 Data collection . 21
5.3 Data classification . 23
5.4 Clustering of traffic demand distributions . 26
5.5 Experimental results . 27
6 Link planning example . 29
6.1 Overview . 29
6.2 Derivation of the average and the peak values of the expected link traffic demand . 30
6.3 Scenario description . 31
6.4 Link planning with known traffic distribution. 32
6.5 Link planning with unknown traffic distribution. 35
7 Conclusions . 37
Annex A: Experimental validation of the analytical procedure for deriving BTA lower
bounds: methodology and results . 38
A.1 Overview . 38
A.2 Database description. 38
A.3 Methodology, system assumptions and test cases . 39
A.4 Numerical results . 41
Annex B: A methodology for analysing the impacts of New KPIs on Total Cost of Ownership . 47
Annex C: Method for determining the target BTAs on individual links in tree-shaped
backhaul network topologies . 50
C.1 Method for a simple network topology . 50
C.2 Method for all network topologies . 52
History . 53

ETSI
4 ETSI TR 104 141 V1.1.1 (2026-03)
Intellectual Property Rights
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ETSI in respect of ETSI standards", which is available from the ETSI Secretariat. Latest updates are available on the
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Foreword
This Technical Report (TR) has been produced by ETSI Technical Committee Access, Terminals, Transmission and
Multiplexing (ATTM).
Modal verbs terminology
In the present document "should", "should not", "may", "need not", "will", "will not", "can" and "cannot" are to be
interpreted as described in clause 3.2 of the ETSI Drafting Rules (Verbal forms for the expression of provisions).
"must" and "must not" are NOT allowed in ETSI deliverables except when used in direct citation.
Executive summary
The Radio Fixed Services community represented by the ETSI ATTM TM_mWT Working Group has recently defined
an innovative planning methodology for wireless backhaul links with the key benefit of enabling a cost-effective
network design by reducing the required system margins in most microwave and millimetre-wave transport scenarios,
compared to the current criteria, with negligible impact on the end-to-end Quality of Experience (QoE) of the Radio
Access Network (RAN) users.
The novel planning methodology (that will be also referred to as the "New KPIs methodology" in the present document)
reformulates the definition of two indicators already in use in current backhaul networks design - namely, the Peak
Information Rate (PIR) and the Committed Information Rate (CIR) - and introduces the Backhaul Traffic Availability
(BTA) as an innovative metric to assess the link performance by accounting for traffic-related information.
While on the one hand the BTA provides an effective representation of the probability that any backhaul link does not
cause congestion in the aggregated RAN data flows, on the other hand it requires to operatively choose a specific traffic
demand distribution to complete the assessment, thus possibly limiting the immediacy and in some cases the practical
applicability of the New KPIs approach.
ETSI
5 ETSI TR 104 141 V1.1.1 (2026-03)
The present document takes up the challenge to overcome this hindrance by proposing practical methods to make the
assessment of the BTA an immediate and straightforward process, once few baseline features of the target backhaul
scenario are known. As a first key contribution, an experimentally validated analytical procedure for deriving the lower
bound of the BTA of any given backhaul link with unknown traffic demand distribution - that can be readily employed
for a conservative (i.e. worst-case) network planning - is disclosed. This method has the strategic advantage of relying
on the only knowledge of the average and the peak values of the traffic demand envisioned for the link under
investigation, thus making the choice of the complete statistical throughput distribution needed for computing the BTA
metric a completely transparent process for the end user. Furthermore, the proposed procedure is conceived to be easily
integrated into the software framework of the currently available backhaul planning tools, with the ultimate goal of
further promoting and accelerating the adoption of the novel design paradigm in present and next generation transport
networks.
As a second contribution, the present document describes a methodology for conducting measurement campaigns on
live backhaul links with the aim of deriving a dataset of traffic demand distributions to be possibly used as reference
statistics for the assessment of the BTA at least in a group of significant transport scenarios. In this context, the results
of an experimental activity carried out during the preparation of the present document are also disclosed, serving as an
example of how the proposed guidelines can be applied to build a proprietary database of backhaul traffic statistics to be
employed in the network design process.
Finally, a comprehensive planning procedure for an illustrative point-to-point E-band link developed in accordance with
the whole New KPIs paradigm is presented in order to provide a practical guide that can be adapted and scaled to more
complex network scenarios and configurations.
Introduction
The projected traffic volumes driven by the proliferation of 5G and Beyond Radio Access Technologies (RATs) have
raised serious concerns regarding the economic sustainability of transport infrastructures, particularly with respect to the
Total Cost of Ownership (TCO). In this context, enhancing the cost efficiency of wireless networks by reducing the
system margins often introduced by potentially over-engineered design methods has become imperative for telecom
operators.
The Radio Fixed Services community represented by the ETSI ATTM TM_mWT Working Group has recently devoted
significant efforts in this direction by finally defining an innovative planning methodology for wireless backhaul links
in ETSI GR mWT 028 [i.1]. This new approach has been shown to lead to the key benefit of enabling a cost-effective
network design by limiting the required system margins in most microwave and millimetre-wave transport scenarios,
compared to the current criteria, with negligible impact on the end-to-end Quality of Experience (QoE) of the Radio
Access Network (RAN) users.
The novel planning methodology (that will be also referred to in the following of the present document as the "New
KPIs methodology") reformulates the definition of two indicators already in use in current backhaul networks design -
namely, the Peak Information Rate (PIR) and the Committed Information Rate (CIR) - and introduces the Backhaul
Traffic Availability (BTA) as an innovative metric to assess the link performance by accounting for traffic-related
information. More specifically:
• The PIR is still defined as the maximum theoretical traffic that can be generated by the ensemble of the RAT
layers transported over a given backhaul link, and it can be readily computed according to the well-established
guidelines in, e.g., NGMN 0.4.2 [i.2] (figure 1 provides an overview of possible methods for the case of a
single RAN site with three sectors). Unlike the current planning approach for backhaul networks, the New
KPIs methodology does not associate the PIR with any availability requirement. Instead, it is dimensioned
using a practical system-level criterion by adopting a fade margin of 5 dB to 10 dB to ensure stable link
operation.
ETSI
6 ETSI TR 104 141 V1.1.1 (2026-03)

Figure 1: Overview of current methods for estimating the PIR for the case of
a single RAN site with three sectors
• The CIR is recommended to be tailored to the minimum amount of capacity exclusively targeted to guarantee
the survivability of the RAN and the essential and operator-specific top-priority services for the maximum
time in a year (i.e. with an availability higher than 99,99 %).
While the amount of traffic required to meet the first objective can be easily calculated for the different
RATs - since it corresponds to the necessary information flows to transfer the control, management and
synchronization planes to the base stations - top-priority services are more difficult to quantify as they mostly
depend on the specific propositions of Mobile Network Operators (MNOs) for their own customers and
could comprise voice traffic (including emergency calls), Guaranteed Bit Rate (GBR) applications
(e.g. mission-critical voice/video, real-time streams and 5G new use cases), as well as Service Level
Agreement (SLA) data sessions. In any case, it is important to emphasize that the target CIR values to be
employed in the novel wireless backhaul planning approach are highly dependent on the specific RAT
scenarios, and they cannot be blindly estimated as a fixed percentage of the PIR across all cases. For example,
in standalone 5G or mixed 4G and 5G sites baseline CIRs should be configured to fall between 1 % and 2 % of
the PIR - significantly lower than the 10 % to 20 % range usually considered in current design methodologies
(see ETSI GR mWT 028 [i.1] for a more detailed analysis on this matter).
• The BTA is defined as the probability that a given backhaul link is capable to deliver the entire aggregated
traffic demand with no impacts on the RAN end-users QoE and, under a mathematical standpoint, it is
expressed by the following weighted sum:
�
����� ��� ���
��� ����� ���� ��� , (1)
�� �� ��
���
���
where � is the total number of backhaul capacities that can be delivered, � represents the availability of the
��
��� ��� ��� ��� ����� ���
�th backhaul capacity � (with � �� � .�� ), and ��� ���� � denotes the probability
�� �� �� �� �� ��
����� ��� ���
that the aggregated traffic demand � lies in the range between � and � , being � �0 bit/s the link
�� �� ��
���
failure state. Terms � can be derived by applying the well-established guidelines and methods described in
��
����� ���
Recommendation ITU-R P.530-19 [i.4] and references therein, while probabilities ��� ���� � can
�� ��
� �
be easily computed from the cumulative distribution function � � of the link aggregated traffic demand as
�
(with ��1,2,…,�):
����� ��� ��� �����
��� ���� ��� �� ��� �� � (1a)
� �
�� �� �� ��
ETSI
7 ETSI TR 104 141 V1.1.1 (2026-03)
A massive number of system-level simulations accounting for different network conditions and aggregated
RAN traffic demand profiles carried out in ETSI GR mWT 028 [i.1] have demonstrated that wireless backhaul
links with BTA values above the 99,7 % to 99,9 % range do not introduce any perceivable degradation in the
average end-to-end QoE performance of the RAN users even under highly demanding application scenarios.

Figure 2: A comparison between current and novel planning methodologies
for wireless backhaul links
The three check points characterizing the novel backhaul planning methodology described above are summarized in
figure 2, that also presents a comparison with the current design approach.
On the one hand, the BTA offers an effective means of representing the probability that a given backhaul link does not
cause congestion in the aggregated RAN data flows. On the other hand, though, it requires to operatively choose a
����� ���
specific traffic demand distribution to complete the assessment (i.e. for computing probabilities ��� ���� �
�� ��
in equation (1)), thus possibly limiting the immediacy and in some cases the practical applicability of this approach,
ultimately leading to a potential reluctance among MNOs to adopt the New KPIs methodology.
The present document takes up the challenge to overcome this hindrance by proposing practical methods for enabling a
fast and straightforward assessment of the BTA, based solely on few baseline features of the target backhaul scenario.
As a first key contribution, clause 4 discloses an experimentally validated analytical procedure for deriving the lower
bound of the BTA of any given backhaul link on the basis of the sole knowledge of its average and peak expected
aggregated traffic demands. The proposed approach offers the key benefit of leading to the derivation of a worst-case
(i.e. minimum achievable) BTA value that does not depend on any specific assumption on the actual and complete
traffic statistical distribution characterizing the link under inspection, and that can be readily employed for a
conservative and effective network planning.
NOTE: It is remarked that, both in the last sentence and in similar contexts throughout the entire present
document, the term "conservative" refers exclusively to the BTA evaluation. It does not extend to the
overall New KPIs methodology, which is instead specifically designed to avoid introducing unnecessary
system margins compared to current backhaul planning approaches.
As a second contribution, clause 5 describes a methodology for conducting measurement campaigns on live transport
networks with the aim of generating a dataset of traffic demand distributions that can serve as reference statistics for the
assessment of the BTA at least in a group of representative backhaul scenarios. In this context, the results of an
experimental activity carried out during the preparation of the present document are also disclosed as a practical
example of how to apply the proposed guidelines.
ETSI
8 ETSI TR 104 141 V1.1.1 (2026-03)
The use of the above-mentioned strategies for assessing the BTA is then exemplified in clause 6, that is entirely devoted
to the description of a comprehensive planning procedure of a point-to-point link operating in E-band according to the
whole New KPIs approach.
Finally, annex B presents a methodology targeted at a general assessment of the benefits, in terms of cost of ownership,
of the New KPIs paradigm, with the ultimate goal of encouraging and accelerating its adoption in current and
next-generation wireless backhaul networks.

ETSI
9 ETSI TR 104 141 V1.1.1 (2026-03)
1 Scope
The present document has the goal of defining practical and effective methods for planning wireless backhaul links
according to the novel approach detailed in ETSI GR mWT 028 [i.1]. One key area of investigation and contribution is
the design of appropriate prediction models of the aggregated traffic demand statistics of any backhaul link as a
function of few high-level and easy-to-know RAN-related behavioural features, such as the average and the peak values
of the transported throughput, or the configuration of the various radio access technologies implemented in the
connected sites. The derived prediction models are conceived with the goal of being easily embedded within the
software framework of the currently available backhaul planning tools, thus pursuing the strategic benefit of making the
choice of the link traffic demand distribution required for enabling the New KPIs methodology (namely, for computing
the BTA metric) a completely transparent process for the end user.
In this context, the present document discloses an analytical procedure targeted at deriving a pessimistic estimation of
the BTA of any backhaul link on the basis of the sole knowledge of the average and the peak values of its traffic
demand, that could be used for a conservative and practical network planning. Secondly, the present document
describes a methodology for conducting measurement campaigns on live transport networks and for processing the
collected data in order to create a discrete set of reference throughput demand distributions to be used in the assessment
of the BTA of any backhaul link, after a proper identification and classification of its main deployment features
(e.g. number and type of transported radio access layers) and statistical properties.
2 References
2.1 Normative references
Normative references are not applicable in the present document.
2.2 Informative references
References are either specific (identified by date of publication and/or edition number or version number) or
non-specific. For specific references, only the cited version applies. For non-specific references, the latest version of the
referenced document (including any amendments) applies.
NOTE: While any hyperlinks included in this clause were valid at the time of publication ETSI cannot guarantee
their long-term validity.
The following referenced documents may be useful in implementing an ETSI deliverable or add to the reader's
understanding, but are not required for conformance to the present document.
[i.1] ETSI GR mWT 028 (V1.1.1): "New KPI's for planning microwave and millimetre wave backhaul
network".
[i.2] NGMN 0.4.2 FINAL (July 2011): "Guidelines for LTE Backhaul Traffic Estimation".
[i.3] A. K. Gupta and S. Nadarajah: "Handbook of Beta Distribution and Its Applications", Boca Raton,
FL, USA: CRC Press, 2004.
[i.4] Recommendation ITU-R P.530-19 (09/2025): "Propagation data and prediction methods required
for the design of terrestrial line-of-sight systems".
[i.5] Recommendation ITU-R P.676-13 (08/2022): "Attenuation by atmospheric gases and related
effects".
ETSI
10 ETSI TR 104 141 V1.1.1 (2026-03)
3 Definition of terms, symbols and abbreviations
3.1 Terms
For the purposes of the present document, the following terms apply:
peak (aggregated) traffic demand: maximum value of the aggregated traffic demand process experienced by a given
backhaul link
3.2 Symbols
For the purposes of the present document, the following symbols apply:
�,�,�,ℓ generic indices
� ∈ � � is an element of set �
��� Backhaul Traffic Availability
� total number of capacities that can be delivered by a given backhaul link
��� (�) (�) (�)
� �th capacity that can be delivered by a given backhaul link (with � < � < .< � )
�� �� �� ��
� �
�
� link failure state
��
(�) ���
� availability of the �th backhaul capacity �
�� ��
�(�) probability that event � occurs
� random variable representing the aggregated traffic demand of a given backhaul link
� �
� � cumulative distribution function of a generic random variable �, evaluated at the argument �
�
� �
� �,�,� probability density function of a generic Beta-distributed random variable � with parameters �
�
and �, evaluated at the argument �
� first shape parameter of the Beta distribution
� second shape parameter of the Beta distribution
��� gamma function evaluated at the argument �
� ��,�,�� cumulative distribution function of a generic Beta-distributed random variable � with parameters
�
� and �, evaluated at the argument �
� �
� �,�,� regularized incomplete Beta function with parameters � and �, evaluated at the argument �
���� expected value of a generic random variable �
�
� exponential function evaluated at the argument �
�
�(�)�� integral of a generic real-valued function �(�) with respect to the real variable � on an interval
�
�
[�, ]
! maximum (or peak) value of the generic aggregated traffic demand �
���
ℳ continuous subspace of the re-scaled Beta distributions family where parameters � and � are
�
related according to equation (10)
� normalized average traffic demand value
ETSI
11 ETSI TR 104 141 V1.1.1 (2026-03)
" total number of possible values for the shape parameter � in the analytical procedure for deriving
BTA lower bounds
� #th possible value for the shape parameter �
�
$ discrete set of " possible values for the shape parameter �
� #th possible value for the shape parameter �
�
% discrete set that contains all the pairs (� ,� ) satisfying constraint (13) on the derivative of the
� �
corresponding cumulative distribution functions
& first parameter used in the analytical procedure for deriving BTA lower bounds
’ second parameter used in the analytical procedure for deriving BTA lower bounds
��(�)
derivative of a generic function �(�) with respect to variable �
��
�(�)| value of a generic function �(�) evaluated at � = �̅
���̅
* #th BTA value
�
+�#��� minimum among all the real values contained in a generic discrete set �
,� ,� ,� - discrete set with values � , � , �
� � � � � �
�
,� - discrete set with all values � for indices # from 1 to "
� �
���
� random variable representing the maximum values of the link input traffic observed with a given
���
time granularity
� random variable representing the minimum values of the link input traffic observed with a given
���
time granularity
� random variable representing the average values of the link input traffic observed with a given
���
time granularity
��
� (!) cumulative distribution function of the average link input traffic observed with a time granularity
�
on the order of 1 second
. total number of bits transmitted over a backhaul link in a given time interval
/ number of seconds in a generic time interval
�0� 1 average throughput exchange (in bit/s) that is expected during busy hours over a given backhaul
����
link
2 coefficient representing the portion of the day classified as "busy hours"
�
2 coefficient representing the anticipated traffic reduction during off-peak periods with respect to
�
busy hours
2 coefficient expressing the ratio between the expected peak traffic ! and the average traffic
� ���
demand �[�] for a given backhaul link
� �th radio site of a generic backhaul network
�
3 total number of possible radio configurations utilized in a link planning example
4(�) metric value for the �th radio link configuration
���
� (�) maximum transmit power (in dBm) of the radio equipment available in the �th radio link
��
configuration
5 (�) transmit antenna gain (in dB) of the radio equipment available in the �th radio link configuration
��
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12 ETSI TR 104 141 V1.1.1 (2026-03)
5 (�) receive antenna gain (in dB) of the radio equipment available in the �th radio link configuration
��
�� (�) PIR fade margin (in dB) guaranteed by the �th radio link configuration
� �
� �
� ��� transmit power relative to the PIR (in dBm) of the radio equipment available in the �th radio link
��
configuration
�6 free-space path loss (in dB) experienced over a given backhaul link
56 attenuation due to atmospheric gases (in dB) experienced over a given backhaul link
� �
/ (�) receiver sensitivity threshold relative to the PIR (in dBm) of the radio equipment available in the
��
�th radio link configuration
� maximum capacity delivered by a given backhaul link
��,���
7 coefficient expressing the ratio between the actual peak traffic value ! and the maximum
���
capacity � delivered by a given backhaul link
��,���
5 overall antenna gain in dB (namely, including both the receive and the transmit side) of a given
!"!
backhaul link
� distance covered by a given backhaul link
��� �5 � actual link BTA obtained for the ℓth traffic time series and the link distance �, considering an
ℓ,# !"!
overall antenna gain equal to 5
!"!
6 total number of time series included in the �th test dataset
�
8 cardinality of the set of pairs of parameters (&,’) used in the numerical analysis
(& ,’ ) �th choice of a pre-defined set of 8 pairs of parameters (&,’)
� �
6� (5 ) BTA lower bound obtained for the ℓth traffic time series, the link distance � and the
ℓ,#,� !"!
�th pair (& ,’ ) to be used in constraint (13), considering an overall antenna gain equal to 5
� � !"!
9 relative error between the BTA lower bound and the actual link BTA obtained for the ℓth time
ℓ,#,�
series, the link distance � and the �th pair (& ,’ ) to be used in constraint (13)
� �
Δ excess gain in dB needed to achieve a BTA lower bound 6� (5 ) numerically equal to the
ℓ,#,� ℓ,#,� !"!
actual link BTA ��� (5 ), obtained for the ℓth time series, the link distance � and the
ℓ,# !"!
�th pair (& ,’ ) to be used in constraint (13)
� �
: lower bound efficiency, defined as the percentage of cases in which the proposed analytical
�
procedure employing the �th pair (& ,’ ) in constraint (13) succeeds in generating actual BTA
� �
lower bounds
;(�) step function evaluated at the argument �
��< total cost of ownership of a target backhaul network when the traditional planning methodology is
applied
� number of resolvable intervals of the link lengths distribution of a target backhaul network
= cost of the least expensive transport technology that can be employed to cover all the connection
�
distances included in the �th interval while satisfying the target conditions of the traditional
planning methodology
� relative number of links in a target backhaul network with distances included in the �th interval
�
��< total cost of ownership of a target backhaul network when the New KPIs planning methodology is
��$ %� �
applied
= cost of the least expensive transport technology that can be employed to cover all the connection ̃�
distances included in the �th interval while satisfying the target conditions of the New KPIs
planning methodology
ETSI
13 ETSI TR 104 141 V1.1.1 (2026-03)
ℒ #th subset of links of a given backhaul network
�
� generic aggregation node in a given backhaul network
? target end-to-end BTA to be guaranteed for the traffic generated by a generic radio site � of a
� �
given backhaul network
@@@@@@
��� target BTA to be guaranteed over the #th link of a given backhaul network
�
A number of radio sites in a generic backhaul network
3.3 Abbreviations
For the purposes of the present document, the following abbreviations apply:
nd
2G 2 Generation
rd
3G 3 Generation
th
4G 4 Generation
th
5G 5 Generation
ACM Adaptive Coding and Modulation
ATTM Access, Terminals, Transmission and Multiplexing
BH Backhaul
BTA Backhaul Traffic Availability
CDF Cumulative Distribution Function
CIR Committed Information Rate
DL Downlink
ETSI European Telecommunications Standards Institute
FDD Frequency Division Duplex
FWA Fixed Wireless Access
GBR Guaranteed Bit Rate
KPI Key Performance Indicator
LTE Long Term Evolution
MIMO Multiple-Input-Multiple-Output
MNO Mobile Network Operator
mWT millimetre Wave Transmission
PAR Peak-to-Average Ratio
PIR Peak Information Rate
QoE Quality of Experience
RAN Radio Access Network
RAT Radio Access Technology
RTPC Remote Transmit Power Control
SLA Service Level Agreement
TCO Total Cost of Ownership
TDD Time Division Duplex
UL Uplink
4 An analytical procedure for deriving BTA lower
bounds
4.1 Overview
The aim of this clause is to present a quick and straightforward analytical procedure for deriving the lower bound of the
BTA of any given backhaul link on the basis of the sole knowledge of its expected average and peak aggregated traffic
demands. The proposed approach offers thus the key benefit of leading to the derivation of a worst-case (i.e. minimum
achievable) BTA value that can be readily employed for a conservative and effective planning whenever an estimation
of the complete statistical distribution of the expected link traffic demand is not available.
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14 ETSI TR 104 141 V1.1.1 (2026-03)
The disclosed analytical procedure builds upon the possibility to reliably capture the statistical model of the traffic
demand of any transport link through a conveniently selected Beta probability distribution, as debated in [i.1]. An
overview of the use of the Beta distributions family to model backhaul traffic demand dynamics is given in clause 4.2,
while the method for deriving conservative BTA values is detailed in clause 4.3.
4.2 Modelling the aggregated traffic demand of backhaul links
through Beta distributions
The Beta distribution is a family of parametric continuous probability distributions defined on the interval [0,1]. The
analytical expressions of the probability density function
&’� (’�
� �1−��
(2)
� ��,�,�� = �� +��,
�
� � � �
Γ � Γ �
the cumulative distribution function
� � � �
� �,�,� = � �,�,� , (3)
�
and the expected value
�
���� =
(4)
� +�
of a generic Beta-distributed random variable � depend on the value of the two positive parameters � and �, being
+
)’� ’*
��� =B� � �� (5)
�
the gamma function, and
�
�� +��
&’� (’�
� � � �
� �,�,� = ×B� 1−� �� (6)
������
�
the regularized incomplete Beta function with parameters � and � [i.3], with � ∈[0,1].
Previous studies conducted by the ETSI ATTM TM_mWT community [i.1] argue that the statistical behaviour of the
random variable representing the traffic demand of any backhaul link can be accurately modelled by a properly
re-scaled Beta distribution. This implies that, based on relations (2), (3), and (4), the probability density function, the
cumulative distribution function and the expected value of any traffic demand variable � with maximum (peak) value
! can be approximated as:
���
&’� (’�
� �
1 ! ! ! −!
���
� �!,�,�� = ×� C ,�,�D = Γ�� +��, (7)
� �
&,(’�
! ! �! � ������
��� ��� ���
!
� �!,�,�� =�C ,�,�D,
(8)
�
!
���
and
�
���� = ! ,
(9)
���
� +�
respectively, for a convenient choice of the shape parameters � and �, and with the independent variable ! ∈[0,! ].
���
NOTE 1: Throughout the present document, the traffic carried over any link at any given time instant is modelled
as a random variable � characterized by a statistical distribution that is assumed to remain constant over
time.
NOTE 2: Terms maximum and peak are used interchangeably within the present document when referring to traffic
demand random variables.
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15 ETSI TR 104 141 V1.1.1 (2026-03)

Figure 3: Illustrative probability density functions and cumulative distribution functions of
Beta-distributed traffic demand random variables with fixed ���

Figure 4: Illustrative probability density functions and cumulative distribution functions of
Beta-distributed traffic demand random variables with fixed ���
ETSI
16 ETSI TR 104 141 V1.1.1 (2026-03)

Figure 5: Illustrative probability density functions and cumulative distribution functions of
Beta-distributed traffic demand random variables with ���
Figures 3, 4 and 5 show illustrative probability density functions and cumulative distribution functions of
Beta-distributed traffic demand random variables with maximum value � = 2 Gbit/s, for different choices of the
���
parameters � and , according to equations (7) and (8). It is remarked that some combinations of � and  can lead to
unrealistic traffic demand distribution shapes where high capacities tend to become more probable than values in the
low-to-medium range (for example, for �0,5 in figure 4-(a) and �� �0,5 in figure 5-(a)). These preliminary
graphical considerations will be further expanded and elaborated in the following clause 4.3 and annex A devoted to the
disclosure of the analytical procedure for deriving BTA lower bounds.
4.3 The analytical procedure for deriving BTA lower bounds
The possibility of using the Beta distributions family to approximate the statistical behaviour of any backhaul traffic
demand allows to derive the analytical method disclosed in the present clause, targeted at associating any transport link
with a worst-case BTA value that can be readily used for a conservative but effective planning.
According to equation (9), the ensemble of traffic demand random variables characterized by a maximum value �
���
and an average value "#�$ can be statistically described by a continuous subspace ℳ of the re-scaled Beta
�
distributions family where parameters � and  are related according to the following rule:
1�&
� �, (10)
&
being
&�"#�$/� (11)
���
the normalized average traffic demand value. By way of example, the coloured area in the chart of figure 6 illustrates
the ensemble of the re-scaled Beta cumulative distribution functions belonging to the continuous subspace ℳ , that
���,�
can be used to represent the statistical behaviour of any traffic demand random variable with normalized average value
# $
&�" � /� �0,3.
���
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17 ETSI TR 104 141 V1.1.1 (2026-03)

� �
Figure 6: Ensemble of the re-scaled Beta cumulative distribution functions ) *,�,� belonging to
�
the continuous subspace +
���,�
Once fixed the backhaul technology, which determines the ordered set of transport capacities
� �
��� ��� ��� ��� ���
,� - (with � �� � .�� ) and the corresponding availabilities ,� - (the latter obtainable through
�� �� �� �� ��
��� ���
the application of the well-established guidelines and methods in Recommendation ITU-R P.530-19 [i.4]), the ensemble
of BTA values associated with all the cumulative distribution functions belonging to the continuous subspace ℳ lie
�
within a closed interval for any value of the normalized average traffic demand &, as sketched in figure 7 for the
illustrative case of a 3,4 km E-band backhaul connection employing 500 MHz bandwidth (therein, a peak traffic
demand value � = 3 100 Mbit/s is assumed). This consideration is at the basis of the analytical procedure described
���
in table 1, that aims, for an input pair of average and peak expected traffic demand values, at finding the BTA lower
bound (i.e. the BTA worst-case) of any link under investigation by conducting a convenient search on the space of
��, � parameters satisfying equation (10).

� �
��� ���
NOTE: In this figure, the set of transport capacities �� � and the corresponding availabilities �� �
�� ��
��� ���
characterizing a 3,4 km E-band connection operating with a 500 MHz bandwidth have been utilized for
deriving the ensemble of BTA values associated with all the traffic cumulative distribution functions
belonging to the continuous subspaces ℳ , for different values of the normalized average demand � on
�
the abscissa (f = 0,1, 0,2, …, 0,9), with � = 3 100 Mbit/s.
���
Figure 7: Ensemble of BTA values
...