5G Infrastructure Network Slicing: E2E Mean Delay Model and Effectiveness Assessment to Reduce Downtimes in Industry 4.0

Abstract

Fifth Generation (5G) is expected to meet stringent performance network requisites of the Industry 4.0. Moreover, its built-in network slicing capabilities allow for the support of the traffic heterogeneity in Industry 4.0 over the same physical network infrastructure. However, 5G network slicing capabilities might not be enough in terms of degree of isolation for many private 5G networks use cases, such as multi-tenancy in Industry 4.0. In this vein, infrastructure network slicing, which refers to the use of dedicated and well isolated resources for each network slice at every network domain, fits the necessities of those use cases. In this article, we evaluate the effectiveness of infrastructure slicing to provide isolation among PLs in an industrial private 5G network. To that end, we develop a queuing theory-based model to estimate the E2E mean packet delay of the infrastructure slices. Then, we use this model to compare the E2E mean delay for two configurations, i.e., dedicated infrastructure slices with segregated resources for each PL against the use of a single shared infrastructure slice to serve the performance-sensitive traffic from PLs. Also we evaluate the use of TSN against bare Ethernet to provide layer 2 connectivity among the 5G system components. We use a complete and realistic setup based on experimental and simulation data of the scenario considered. Our results support the effectiveness of infrastructure slicing to provide isolation in performance among the different slices. Then, using dedicated slices with segregated resources for each PL might reduce the number of the production downtimes and associated costs as the malfunctioning of a PL will not affect the network performance perceived by the performance-sensitive traffic from other PLs. Last, our results show that, besides the improvement in performance, TSN technology truly provides full isolation in the transport network compared to standard Ethernet thanks to traffic prioritization, traffic regulation, and bandwidth reservation capabilities.

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Citation: Chinchilla-Romero, L.;
Prados-Garzon, J.; Ameigeiras, P.;
Muñoz, P.; Lopez-Soler, J. 5G
Infrastructure Network Slicing: E2E
Mean Delay Model and Effectiveness
Assessment to Reduce Downtimes in
Industry 4.0. Sensors 2022,22, 229.
https://doi.org/10.3390/s22010229
Academic Editor: Yang Yue
Received: 15 November 2021
Accepted: 23 December 2021
Published: 29 December 2021
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
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Attribution (CC BY) license (https://
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4.0/).
sensors
Article
5G Infrastructure Network Slicing: E2E Mean Delay Model and
Effectiveness Assessment to Reduce Downtimes in Industry 4.0
Lorena Chinchilla-Romero 1,2,* , Jonathan Prados-Garzon 1,2 , Pablo Ameigeiras 1,2 , Pablo Muñoz 1,2
and Juan M. Lopez-Soler 1,2
1
Department of Signal Theory, Telematics and Communications, University of Granada, 18014 Granada, Spain;
jpg@ugr.es (J.P.-G.); pameigeiras@ugr.es (P.A.); pabloml@ugr.es (P.M.); juanma@ugr.es (J.M.L.-S.)
2Research Center on Information and Communication Technologies, University of Granada,
18014 Granada, Spain
*Correspondence: lorenachinchilla@ugr.es
Abstract:
Fifth Generation (5G) is expected to meet stringent performance network requisites of
the Industry 4.0. Moreover, its built-in network slicing capabilities allow for the support of the
traffic heterogeneity in Industry 4.0 over the same physical network infrastructure. However, 5G
network slicing capabilities might not be enough in terms of degree of isolation for many private
5G networks use cases, such as multi-tenancy in Industry 4.0. In this vein, infrastructure network
slicing, which refers to the use of dedicated and well isolated resources for each network slice at every
network domain, fits the necessities of those use cases. In this article, we evaluate the effectiveness of
infrastructure slicing to provide isolation among production lines (
PL
s) in an industrial private 5G
network. To that end, we develop a queuing theory-based model to estimate the end-to-end (
E2E
)
mean packet delay of the infrastructure slices. Then, we use this model to compare the
E2E
mean
delay for two configurations, i.e., dedicated infrastructure slices with segregated resources for each
PL
against the use of a single shared infrastructure slice to serve the performance-sensitive traffic
from
PL
s. Also we evaluate the use of Time-Sensitive Networking (
TSN
) against bare Ethernet to
provide layer 2 connectivity among the 5G system components. We use a complete and realistic
setup based on experimental and simulation data of the scenario considered. Our results support the
effectiveness of infrastructure slicing to provide isolation in performance among the different slices.
Then, using dedicated slices with segregated resources for each
PL
might reduce the number of the
production downtimes and associated costs as the malfunctioning of a
PL
will not affect the network
performance perceived by the performance-sensitive traffic from other
PL
s. Last, our results show
that, besides the improvement in performance,
TSN
technology truly provides full isolation in the
transport network compared to standard Ethernet thanks to traffic prioritization, traffic regulation,
and bandwidth reservation capabilities.
Keywords:
infrastructure slicing; network slicing; private networks; 5G; delay; response time;
isolation
1. Introduction
Fifth Generation (
5G
) is recognized as a key enabler for
Industry 4.0
(the fourth industrial
revolution) and its underlying industry digitisation. Smart factories need advanced wireless
connectivity to remove the access cabling, which is expensive and cumbersome, prohibits high
connection density, and inhibits the mobility of workers and machines. 5G will also enable a
myriad of emerging applications to unleash the full potential of the digital transformation
of the industry. For instance, wireless-enabled industrial applications include monitoring
and controlling cyber-physical systems, industrial Augmented Reality (
AR
)/Virtual Reality
(
VR
) services, Automated Guided Vehicles (
AGV
s), and plant monitoring and assessment
through massive wireless sensor networks, to name but a few. The heterogeneous and
stringent connectivity requirements in latency, connection density, and reliability of these
Sensors 2022,22, 229. https://doi.org/10.3390/s22010229 https://www.mdpi.com/journal/sensors

Sensors 2022,22, 229 2 of 29
industrial services can be uniquely delivered by
5G
to date [
1
]. According to [
2
], the service
provider addressable 5G-enabled market in the manufacturing industry is foreseen to be USD
132 billion in 2030 with a remarkable compound annual growth rate (CAGR) of 75 percent
over 2020–2030, which is concrete evidence that 5G in the industry holds out great promises
in terms of connectivity.
5G
includes network slicing capabilities to support the traffic heterogeneity expected
in the industry. To that end,
5G
enables the coexistence of multiple network slices, each
tailored for specific services. Although
5G
network slicing ensures a certain degree of
isolation among network slices, there are use cases that require a more robust level of
isolation than the one provided by the traditional network slicing technique. By way of
illustration, many
5G
industrial use cases require the deployment of several private
5G
networks for distinct tenants (multi-tenancy) within the same private venue. To realize
these use cases, infrastructure network slicing might be appealing as it offers a higher
degree of isolation than
5G
network slicing built-in capabilities. Infrastructure network
slicing can be regarded as an extension of the notion of network slice to offer a higher
degree of isolation, becoming a highly suitable option for multi-tenancy support in private
5G
networks. More precisely, an infrastructure network slice is an on-premise slice with
dedicated and well isolated resources at every network domain through the use of resource
quotas. Another meaningful application of infrastructure networks slicing is the creation of
independent and well isolated
5G
networks to serve the traffic from different parts of the
factory For instance, we can use a dedicated
5G
network per production line (
PL
). In this
way, any possible failure affecting one
PL
will not have an impact on the rest of the factory,
thus minimizing the production downtimes and the associated expenditures. Quite costly
unplanned downtimes might not be affordable by some industries.
The primary goal of this paper is to evaluate the degree of isolation offered by the
infrastructure slicing concept. To that end, we develop a Queuing Theory (
QT
)-based
model to estimate the end-to-end (
E2E
) mean response time of the infrastructure slices.
Specifically, we model a 5G System (
5GS
) deployed on an infrastructure slice as an open
queuing network. The resulting queuing network is solved (its
E2E
mean delay is estimated)
using the Queuing Network Analyzer (
QNA
) method. Then, we use this model to compare
the
E2E
mean packet delay for two configurations in an industrial scenario. In the first
configuration, we consider there is a dedicated infrastructure slice for each
PL
. In contrast,
in the second configuration, a single infrastructure slice serves the traffic generated by all the
PL
s. The industrial scenario considered for the evaluation is a factory floor with four
PL
s. In
this scenario, we simulate the failure of a
PL
that results in the generation of non-conformant
traffic. From the comparison described above, we can prove the effectiveness of the
infrastructure network slicing to provide isolation. In other words, for the assumed scenario,
verifying whether infrastructure slicing can avoid the malfunctioning of a
PL
negatively
affects the performance of the rest of the industrial manufacturing processes.
Regarding the experimental setup, we rely on empirical data from the literature and
realistic simulations to configure the different input parameters of the proposed analytical
model for estimating the
E2E
mean response time of the infrastructure slices. The resulting
complex configuration framework might serve the research community for carrying out, for
instance, proofs-of-concept and other evaluation studies. The obtained results support the
effectiveness of infrastructure slicing to provide a high degree of isolation in performance
among the different slices. From these outcomes, it can be deduced that the number and
cost of the production downtimes are reduced as the malfunctioning of a given
PL
does
not affect the others.
Furthermore, besides the two aforementioned configurations considered for the assessment
of the
E2E
mean packet delay, we also compare the performance of two different Transport
Network (
TN
) technologies to realize the midhaul network, namely, standard (bare) Ethernet
and asynchronous Time-Sensitive Networking (
TSN
). The midhaul network interconnects the
Next Generation NodeB (
gNB
)-Distributed Units (
DU
s) with the
gNB
-Central Units (
CU
s).
The results show that standard Ethernet fails to fully isolate the performance of the different

Sensors 2022,22, 229 3 of 29
infrastructure slices in the Transport Network (
TN
). On the contrary,
TSN
not only ensures the
full isolation among the slices but also provides deterministic low-latency.
The contribution of this article is threefold:
(i)
We propose an analytical model for estimating the
E2E
mean response time of the
infrastructure network slices.
(ii)
Based on the developed model, we provide a delay evaluation study to show the
effectiveness of the infrastructure slicing to ensure isolation among
PL
s in order to
minimize the cost of production downtimes.
(iii)
Last, but not least, we consider a realistic configuration for an industrial scenario that
consists of a factory floor with several
PL
s. More precisely, we derive the configuration
of many parameters from experimental data extracted from the literature (accordingly
specified in the corresponding sections). Other parameters have been measured
through realistic simulations.
The remainder of the paper is organized as follows: Section 2provides some background
information on infrastructure network slicing and isolation. It also revisits the existing works
that address the analytical modeling of the
E2E
delay of network slices and isolation-related
assessment in 5G networks. Section 3includes the abstract model of the system assumed in
this work. Section 4describes the proposed
QT
-based model to estimate the
E2E
delay model
of the infrastructure slices in an industrial private
5G
network. Section 5details the methods,
the scenario, and specific configurations considered in our performance evaluation study. The
obtained results are reported and discussed in Section 6. Last,
Section 7
includes the future
work and concludes the paper.
2. Background and Related Works
This section introduces and motivates the infrastructure network slicing and isolation
concepts. Also, it gives an overview of the related works tackling the analytical modeling
of the E2E delay and isolation-related evaluations in virtualized mobile networks.
2.1. Network Slicing and Isolation
Network slicing concept relies on Software-Defined Networking (
SDN
) [
3
,
4
] and
Network Functions Virtualisation (
NFV
) [
5
,
6
] paradigms to enable the creation of several
E2E
virtual networks, referred to as network slices, each tailored for the necessities of
specific services, over a common underlying physical network infrastructure [
7
]. Network
slicing is broadly recognized as one of the most important key enablers of
5G
networks [
7
].
Besides supporting a high heterogeneity of services, network slicing allows for the existence
of multi-tenant networks in which over-the-top service providers, mobile network operators,
and different vertical industries share the same physical network infrastructure [
8
,
9
]. One
of the primary requirements and challenges to realizing network slicing is providing
isolation among the different network slices. Network slice isolation encompasses several
dimensions [10,11]:
•
The resources ring-fencing of a slice so as not to negatively impact the proper
performance of the rest of the slices.
•
The communication capabilities between slices, i.e., not supporting the communication
between them if full isolation is required.
•
Security capabilities in the sense of protection against deliberate attacks between slices.
This work focuses on the first of the three specified isolation dimensions, paying
attention to the performance isolation of slices delimiting their resources. In this way, no
matter the load or status of one slice, it will not interfere with other slices’ performance.
3rd Generation Partnership Project (
3GPP
) 5G standards include built-in capabilities
for network slicing support. A 5G network slice is defined as a set of network functions
tailored for specific services in terms of performance and functionality. In this vein,
3GPP
defines a slicing information model in
3GPP
TS 28.541 [
12
], specifying how to build network
slices from network functions to meet specific service requirements. However, it does
not address the segregation of resources at the network infrastructure stratum, which

Sensors 2022,22, 229 4 of 29
is of utmost importance to guarantee performance isolation among Ultra-Reliable and
Low Latency Communication (
URLLC
) slices and enable multi-tenancy support through
the allocation of dedicated and well-isolated resources to different tenants running their
services atop.
In this work, we adopt the infrastructure network slicing concept defined within the
5G-CLARITY project to enable multi-tenancy in private
5G
networks [
13
,
14
], with the
intention of fixing special attention in isolation, pursuing the ring-fencing of resources.
5G-CLARITY slicing concept allows for the creation of multiple
5GS
s on top of a common
physical network infrastructure comprising radio access, compute and transport nodes. A
5G-CLARITY slice is a logical partition of the network infrastructure layer that provides
an isolated execution environment for specific services or tenants. Each 5G-CLARITY slice
comprises a set of dedicated and well-isolated resources from the private
infrastructure [13,14].
To that end, 5G-CLARITY system includes a management and orchestration stratum for
provisioning infrastructure slices and leverages mechanisms to partition the resources across
the different network domains (e.g., Radio Access Network (
RAN
), Core Network (
CN
), and
TN
). Consequently, the resources belonging to an infrastructure network slice are defined
per resource domain through the use of resource quotas that delimit the amount of resources
for each slice:
•
Wireless quota: it refers to the spectrum allocated to each slice in each radio access
node.
3GPP
5G standards include functionality to abstract the complexity of non-
3GPP
wireless technologies (e.g., Wi-Fi and Li-Fi) access points making each appear as a
single
gNB
towards the User Plane Function (
UPF
). Using non-
3GPP
technologies
leveraging this 5G feature is appealing for enhanced throughput and reliability. Please
observe that the specification of the wireless quota depends on the Wireless Access
Technology (WAT) (e.g., 5G New Radio (NR), Wi-Fi, and Li-Fi).
•
Compute quota: it stands for the computational resources dedicated to each slice in
each compute node. It includes physical Central Processing Unit (
CPU
) cores, RAM,
disk, and networking resources.
•
Transport quota: it is the set of resources allocated to each slice in the
TN
. The
TN
provides connectivity among the
5G
components. Typically, these resources
might include transmission capacity at a given set of links and buffer space at the
corresponding transport nodes’ output ports. A Virtual Local Area Network (
VLAN
)
identifier (tag) can be assigned to each slice in order to differentiate traffic from
different slices at layer 2 (L2).
Below are three primary use cases in the context of industrial private 5G networks
that call for the highest level of isolation among slices as provided by infrastructure
network slicing:
(i)
Support of industrial
URLLC
critical services:
URLLC
critical services of Industry 4.0
impose the most demanding requirements in industrial networks. The restriction and
ring-fencing of resources for their dedication to
URLLC
services is crucial to guarantee
the stringent requisites demanded by these kinds of services and applications.
(ii)
Network performance isolation of the Operational Technology (
OT
) domain components:
The division/segmentation of an industrial network into well-isolated parts for supporting
the operation of disjoint
OT
components becomes essential to limit the scope of a
malfunctioning, thus reducing production downtimes and associated expenditures.
(iii)
Multi-tenancy support: Part of the success of private 5G networks will be the ability
to allow the provision of communication services from different customers (tenants)
with such an isolation level that guarantees the agreed performance and management
capabilities. Several use cases requiring multi-tenancy support have been proposed in
the literature [15].
2.2. Analytical Performance Models for Network Slicing
Some works have proposed analytical
E2E
delay models for virtualized wireless
networks and network slices [
16
–
27
]. Although there are also works providing performance

Sensors 2022,22, 229 5 of 29
models for a specific network domain (e.g.,
RAN
,
TN
, and
CN
) [
28
–
31
] or component
(e.g.,
gNB
and
UPF
) [
32
,
33
], here we will only review
E2E
delay models, i.e., those
considering every network domain. Analytical models are crucial to assist autonomous
solutions for the management and operation of the network and to perform offline network
performance assessments and optimization. On the one hand, analytical models are
essential to proactively compute the configuration and estimate the resources to be allocated
according to the expected workload in the near future [
34
,
35
]. Also, they serve to ensure
the cohesion and satisfiability of the configurations applied to the different network and
infrastructure domains. In this regard, the authors in [
36
] rely on analytical performance
models to develop a solution that guarantees smooth communications for
E2E
service
delivery when there is a wide variety of Quality of Service (
QoS
) classes in each network
domain. It shall be noted that alternative approaches such as real-time delay sensing [
37
]
can complement analytical models in many use cases through reactive solutions, i.e.,
real-time performance monitoring and actuation in case of any performance requirement
violation. On the other hand, analytical models serve to fast and effectively verify, for
example, whether a network architecture and built-in features meet the target performance
requirements. If not, an architectural redesign, optimizations, and new capabilities can be
proposed for the network.
Table 1includes a survey on the research literature addressing the analytical modeling
of the
E2E
delay of virtualized mobile networks and network slices. There are three primary
mathematical frameworks used in the literature to develop analytical
E2E
delay models,
namely,
QT
[
38
], Deterministic Network Calculus (
DNC
) [
39
], and Stochastic Network
Calculus (
SNC
) [
40
]. These three frameworks model the whole system as a network of
queuing facilities, each representing a shared resource (e.g., link capacity) in the system.
Broadly speaking,
QT
mainly addresses queuing systems with renewal arrival and service
processes and aims to provide the
E2E
mean delay. On the other hand,
DNC
relies on
alternative algebras (e.g., min-plus and max-plus) and inequalities to derive the worst-case
E2E
delay. Last, in contrast to
DNC
,
SNC
leverages the stochastic nature of the arrival
and service processes to estimate non-asymptotic statistical delay bounds of the form
P[d>D]≤e
[
41
], i.e., the probability that the delay of the system
d
be greater than a
given delay threshold
D
is bounded by the value of
e
. Table 1indicates the mathematical
framework used by each revised reference.
Overall, the proposed models in the literature either do not address the specificities
of the
RAN
, such as the co-channel interference, or the features of the
URLLC
traffic and
the respective
RAN
setup to serve it, which ultimately translate into the radio channel
capacity degradation. Similarly, they do not capture traffic prioritization at the
TN
domain. Deterministic network technologies like
TSN
are firm candidates to enable
the conveyance of the
URLLC
traffic while allowing for its coexistence with massive
machine type and enhanced Mobile Broadband (
eMBB
) communications over a common
TN
infrastructure. In this regard, traffic prioritization, which is a key feature of deterministic
transport technologies, plays a crucial role in isolating
URLLC
traffic. Also, the models
are tested under simplified or unrealistic setups for industrial private
5G
networks. Last,
focusing on the
QT
-based
E2E
delay models, most of them lack of generality as they
assume exponential packet inter-arrival times and exponential (M/M/1-based models) or
deterministic (M/D/1-based models) service times with a single server. In [
16
], the authors
consider arbitrary arrival and service processes but still a single server facility at every
queue (G/G/1-based model). Although a single server assumption might apply to model
the packet transmission in the wired network devices links (e.g.,
TN
links), it does not allow
for other potential bottlenecks, such as Virtual Network Functions (
VNF
s) with several
CPU
cores/threads processing packets in parallel or the radio interface transmitting several
packets simultaneously through orthogonal sets of Physical Resource Blocks (PRBs).

Sensors 2022,22, 229 6 of 29
Table 1. Related literature addressing the analytical modeling of the network slices’ E2E delay.
References
Mathematical
Framework Description
QT DNC SNC
Schulz et al. [16]7
This work aims to provide an
E2E
delay model for a mobile network. To that end, it proposes a
model to estimate the sojourn time distribution of the GI/GI/1 queue and assumes Kleinrock’s
independence approximation. The model is tested and validated for a single M/D/1 queue with
different scheduling policies.
Ye et al. [25]7
This article models the
E2E
delay traversing a
VNF
chain. The primary assumption considered is
the system bottlenecks are the
CPU
processing and link transmission, both following a generalized
processor sharing discipline for service. The proposed model consists of an independent tandem of
M/D/1 queues for each flow.
Xu et al. [17,18]7
This paper derives statistical
E2E
delay bounds for network slicing considering Gaussian traffic
and deterministic service. This model is leveraged to perform dynamic resource provisioning, i.e.,
to adjust the slice allocated resources according to the traffic fluctuations. Specifically, resource
dimensioning is carried out using the derived performance bounds.
Yu et al. [19]7
This article provides stochastic performance bounds for network slices using martingale-based
approaches. The resulting bounds are employed to translate delay requirements into bandwidth
ones and to estimate the power allocation at the
RAN
considering an ALOHA-like medium access
technique for URLLC traffic.
Sweidan et al. [20]7
This work studies the joint problem of
E2E
networks slices composition, the mapping of
URLLC
applications to slices, and multiple disjoint paths to slices assignment. It models the
E2E
mean delay
of a network slice as an open network of M/M/1 queues.
Fantacci et al. [21]7
This article relies on martingale theory to derive statistical bounds of the slices
E2E
packet delay. The
model is applied for virtual network embedding. It focuses on ultimate
VR
services operated in 6G
Terahertz networks. They validate the bounds through simulation and compare their accuracy with
an equivalent Markov tandem queue model.
Liu et al. [23]7This paper presents a worst-case delay model for virtual wireless networks, including physical and
virtual nodes. It considers that different slices might receive differentiated treatment through the use
of virtual queues.
Picano [22]7
This work aims to evaluate the performance of the Sixth Generation (6G) pervasive edge computing
network for handling virtual reality traffic for two scheduling policies, namely, First Come, First
Served (
FCFS
) and earliest deadline first. To that end, it relies on a martingale-based model similar to
the one proposed in [21].
Chien et al. [24]7
This article proposes a solution for slices capacity allocation and traffic offloading from the
central office to the edge cloud. The solution relies on an
E2E
mean delay model consisting of
a feedforward network of M/M/1 queues, each standing for either a node or a link. The solution is
validated experimentally.
Kalør et al. [27]7
This paper focuses on modeling the
E2E
delay of
URLLC
network slices using
DNC
for deterministic
and switched networks. It presents an industrial medicine manufacturing system as a case study to
illustrate the usefulness of DNC for analyzing the worst-case E2E delay of network slices.
In this work, we cover the gaps mentioned above. To that end, we propose a
QT
-based
model to estimate the
E2E
mean packet delay of the network slices. More precisely, the
network slice is modeled as an open network of G/G/m queues, and the
E2E
mean
delay is estimated using the
QNA
method proposed by Whitt [
42
]. The model developed
in this work can be regarded as an extension of the one proposed in [
26
]. In [
26
], the
authors propose a G/G/m-based mean delay model for Softwarized Network Services
(
SNS
s) focusing on the computing domain (e.g., virtualized mobile network cores) and
experimentally validate its accuracy. In particular, they report their model achieves less
than half of the error in terms of accuracy compared to M/M/m-based models. This
is reasonable considering that the
QNA
method is consistent with the Jackson network
theory [
42
]. A simulation-based validation is also provided in [
43
]. Other works support
the usefulness and accuracy of the same modeling approach for the
SNS
s resource sizing.
Specifically, it is used for
SNS
s’ planning [
31
] and Dynamic Resource Provisioning (
DRP
)
in [
34
,
35
,
44
]. Here, we leverage the modeling approach in [
26
] to develop a generic
E2E
mean delay model of
5G
slices that captures the behavior and features of the
RAN
and
TN
network domains. The resulting model is quite general while preserving the simplicity and
exhibiting low computational complexity (please refer to the execution times measurements

Sensors 2022,22, 229 7 of 29
reported in [
43
]). The model is primarily intended to carry out performance evaluations
of
5G
network slices as those included in
3GPP
technical reports (TRs) (e.g., 3GPP TR
38.802 [
45
]) or the one included in this work. Furthermore, this work might serve as a basis
to extend other works proposing network calculus-based models through reproducing the
methods followed in this work for capturing the behavior of many 5G network features.
2.3. Network Slicing Isolation Assessment
Isolation is still a challenging requisite to be wholly met in today’s networks. Several
works have addressed the degree of isolation offered by network slicing for specific
network domains [
28
,
46
–
51
]. In [
46
], two resource allocation methods for isolation in
the
RAN
are presented. They guarantee resource isolation by limiting the maximum
allocated resources blocks to each slice and implementing slight modifications of the
ordinary packet scheduling algorithms. Their results show that the performance achieved
by these methods is improved, especially in high-resource utilization environments. The
work in [
47
] addresses the isolation problem between slices also in the
RAN
. The authors
demonstrate how isolation can be achieved in dynamic network slicing using an appropriate
Connection Admission Control (CAC) mechanism. In [
51
], the authors propose a novel
control framework for stochastic optimization based on the Lyapunov drift-plus-penalty
method for a wireless system with a time-varying number of users. This method enables
the system to minimize power, maintain slice isolation, and provide reliable and low latency
communications for the slices that require these requisites. The authors
in [28]
propose a
novel resource slicing scheme focusing on the performance isolation of network slices. To
that end, they developed a continuous-time Markov chain to estimate the performance
metrics, such as data rate, of the
RAN
. In contrast to our work that target industrial
URLLC
services, this work is centered around bandwidth-greedy services. Their results suggest
that the proposed approach might double the data rate compared to the complete static
segregation of resources. Nonetheless, throughput gains are not the main objective for
critical industrial services. Thus, resource sharing might not be justified for critical services
as it can compromise performance isolation and hinder the proper operation of them.
Regarding the transport domain, in [
48
] the authors develop a control plane architecture
for
TSN
networks able to support network slicing and show how to preserve slice isolation
over a
TSN
-based
TN
. With respect to the computing domain,
in [52]
the authors address
the optimal allocation of a slice in 5G core networks by tackling intra-slice function isolation
and guaranteeing the E2E delay for a slice.
To the best of our knowledge, up to date, very few works carry out an
E2E
isolation
evaluation. The authors
in [49]
develop a network slicing approach suitable for the
deployment in current
SDN
and
NFV
enabled communication infrastructures. The approach
is verified by empirical performance evaluation using a physical testing setup that showcases
slice isolation even during partial overloads. In [
50
], the authors present a prototypical
realization of
E2E
network slicing considering radio access and core networks based on
NFV
and
SDN
as key technologies. They also provide an empirical evaluation of the
proposed
E2E
network slicing solution based on real-world traffic patterns (e.g., smart
grids, intelligent transport, and best-effort (BE)).
3. System Model
This section describes the abstract model of the services and
5GS
deployed on an
infrastructure slice in an industrial factory floor, together with the main assumptions
considered. Broadly, a
5GS
provides the
OT
devices of a factory floor with radio connectivity.
Figure 1sketches a high-level view of the scenario under study in this work.
The factory floor with dimensions
W×L
m
2
includes
NPL PL
s. Each
PL
is composed
by
NURL LC
devices to automate the manufacturing process. The network traffic generated
by monitoring and controlling these devices has deterministic low-latency requirements,
i.e.,
URLLC
traffic. For example, motion control is a typical industrial service in which
an industrial controller communicates with remote sensors and actuators to control the

Sensors 2022,22, 229 8 of 29
motion of industrial machinery. This service has hard real-time requirements, i.e., cycle
times and latency are highly critical, to within milliseconds or even microseconds [53].
Figure 1.
System model: Private industrial 5G network with multi-
WAT RAN
and the 5G Core
deployed on the edge cluster.
Dedicated infrastructure network slices are deployed for specific services or set of
devices (e.g., sensors and actuators from a given
PL
). There might be one or several
infrastructure network slices to serve the
URLLC
traffic generated to control and monitor
the
PL
s. A given infrastructure slice might be dedicated for serving the traffic of one
PL
or
shared between several
PL
s. Each infrastructure slice has segregated resources for every
network domain (e.g.,
RAN
,
TN
, and computing domain), i.e., an infrastructure network
slice consists of a set of dedicated and well isolated computational (e.g., physical
CPU
cores, Random Access Memory (
RAM
), and disk), transport (e.g., buffer space, and link
capacity at every switch egress port) and radio (e.g., buffer space at the radio interface, and
bandwidth) resources.
Multi-
WAT
combining 5G
NR
and Wi-Fi technologies is considered. We assume Wi-Fi
technology does not include deterministic low-latency support, thus it only serves
eMBB
traffic. In contrast, 5G
NR
can serve any type of traffic, though in our setup (see Section 5)
we consider it only serves
URLLC
traffic. Although we consider dedicated resources for
each infrastructure slice, the
eMBB
traffic might degrade the performance of
URLLC
traffic
depending on the specific configuration. For instance, when there is no prioritization or
resource reservation in the
TN
, the
eMBB
traffic will compete for the transmission capacity
with URLLC one at some links.
The model description of each of the network domains (computing,
RAN
, and
TN
domains) that conform the
E2E
network layout is included in the subsections below
(Sections 3.1–3.3, respectively).
3.1. Computing Domain
The computing domain comprises the compute nodes to host the set of
VNF
s. Here,
we consider the same configuration as that considered in [
26
,
33
] for the
VNF
s of the
5GS
.
The 5G
VNF
s (e.g.,
gNB
-
CU
and
UPF
) instances have one or several dedicated
CPU
cores
(
CPU
pinning) in the Physical Machines (
PM
s) or servers. There is a processing thread
per dedicated
CPU
core allocated to allow for the parallel processing of the packets at the
corresponding
VNF
. There are also
CPU
physical cores dedicated to the virtualization
container housekeeping. We assume software-based with run-to-completion (
RTC
) pipeline
for the
VNF
s, i.e., all the processing tasks to process each packet are executed at once,
followed by the processing of the next packet picked for processing (
FCFS
discipline).
RTC
approach for packet processing is highly suitable for the scenario due to the following
reasons [33]:

Sensors 2022,22, 229 9 of 29
(i)
Processing of packets, for instance, in
gNB
-
CU
and
UPF
instances, from each 5G
stream is quite independent from other streams. Then, there is no need to divide
processing into smaller pieces to spread it across cores.
(ii)
RTC
mode minimizes the context switchings and maximizes the cache hit rate, which
results in a lower packet processing delay.
3.2. Radio Access Network Domain
For the User Plane (
UP
) of the
RAN
, we consider the baseband functions are split into
three components, namely,
gNB
-
CU
,
gNB
-
DU
, and
gNB
-Radio Unit (
RU
). We assume the
splitting options #2 and #7 for the F1 (interconnecting
gNB
-
CU
and
gNB
-
DU
instances)
and Fx (interconnecting
gNB
-
DU
and
gNB
-
RU
instances) [
54
] interfaces, respectively.
In this way, the
gNB
-
CU
is in charge of the per packet processing associated with the
Radio Resource Control (
RRC
), Service Data Adaptation Protocol (
SDAP
), and Packet Data
Convergence Protocol (
PDCP
) protocols. The operation considered for the virtualized
gNB
-
CU
is the same as the virtualized
UPF
’s implementation described in [
33
] and
compatible with the one assumed in [
29
] for the Cloud
RAN
’s Baseband Unit (
BBU
) pool.
Thus, the processing of these upper layers is the main potential bottleneck of the
gNB
-
CU
.
On the other hand, the
gNB
-
DU
is responsible for the Radio Link Control (
RLC
), Medium
Access Control (
MAC
), and part of the physical layer (e.g., equalization and Multiple-Input
Multiple-Output (
MIMO
) precoding). In contrast to the
gNB
-
CU
whose packet service
time only depends on the workload, the
gNB
-
DU
packet processing rate also depends on
the carrier bandwidth and Modulation and Coding Scheme (
MCS
) index [
55
–
57
]. Last, the
gNB
-
RU
realizes the Fast Fourier Transform (
FFT
)/Inverse Fast Fourier Transform (
IFFT
),
resource mapping and Radio Frequency (
RF
) functionalities. The packet service time of the
gNB
-
RU
depends on the carrier bandwidth and the virtualization layer when the function
is virtualized [54–56].
There might be multiple
gNB
instances through the coverage area. The available
bandwidth, denoted as
BW
, is split into
N
channels of
BWc=BW/N
bandwidth. Several
channels are allocated to each
gNB
instance. A given channel might be shared by multiple
gNB
instances, resulting in co-channel interference. The attainable data rate for a
URLLC
device
j
at the radio interface is a function of its allocated bandwidth
BWj
, its perceived
Signal-to-Interference-plus-Noise Ratio (
SINR
)
SI NRj
, the packet size and the block length.
For low latency applications, there is always a probability of packet drop due to noise.
In addition, data must be encoded at a rate significantly lower than that given by the
Shannon’s capacity formula in order to get a higher reliability [
58
,
59
]. The authors
in [59],
based on [
58
], derives the following performance model for the User Equipment (
UE
)
achievable rate:
Rj=BWj· log2(1+SI NRj)−rCj
n·Q−1(e)·log2(e)!(1)
where
n
is the blocklength for a given duration
τ
of the time slot. For instance, a resource
block in a Long-Term Evolution (
LTE
) system contains 84 symbols and lasts 0.5 ms [
60
].
5GS
allows for the use of flexible numerology which can be translated into configurable
values of the time slot duration
τ
.
Q−1(·)
is the inverse of the Gaussian Q function.
e
is the
transmission error probability.
log2(e)
refers to the logarithm in base 2 of number e.
Cj
is
the channel dispersion of the UE j, which is given by:
Cj=1−1
(1+SI NRj)2(2)
Observe that
(1)
adds a correction factor to the Shannon’s capacity formula in order
to consider the specific physical layer behaviour for
URLLC
s with small packet sizes, as
previously mentioned.

Sensors 2022,22, 229 10 of 29
Last, as in [
32
], we assume that packets are transmitted without errors. In other words,
there are no Hybrid Automatic Repeat Request (HARQ) retransmissions.
3.3. Transport Network Domain
The 5G components are interconnected through the Transport Network (
TN
). Here,
we consider an asynchronous bridged network (traditional Ethernet or asynchronous
TSN
networks) for realizing the
TN
segments shown in Figure 1(e.g., midhaul and backhaul).
On the one hand, traditional Ethernet does not include traffic differentiation capabilities.
Then, all types of traffic receive the same treatment. This technology is affordable and
easy to configure, but it is hard to support deterministic
QoS
in these networks [
30
]. What
is more, the computation of the
E2E
worst-case delay is an nondeterministic polynomial
time (
NP
)-hard problem [
61
]. On the other hand, asynchronous
TSN
is more complex to
configure [
62
,
63
], but provides deterministic
QoS
through per-link traffic regulation and
traffic prioritization [
30
]. Asynchronous
TSN
is suitable to serve non-periodic deterministic
traffic patterns and enables its coexistence with the best effort one [
64
]. Thus, it is a perfect
candidate to realize the 5G
TN
s as the traffic types mentioned above are expected to be
dominant there [
65
]. In asynchronous
TSN
, the transmission of the frames at each link is
handled by an Asynchronous Traffic Shaper (
ATS
). Each
ATS
has several priority queues
to apply strict traffic prioritization [
66
,
67
]. Eight priority levels are considered by default in
standards [
68
]. Also, each
ATS
has a maximum number of shaped buffers for carrying out
per-flow traffic regulation. The maximum number of these buffers might limit the number
of implementable priority levels [
66
,
67
]. We refer the interested reader to [
65
–
68
] for further
details on the ATS operation.
The queue to place each frame at a given output port of a
TSN
switch in the
TN
is taken according to the Priority Code Point (
PCP
) of the
VLAN
tag. We assume there
is a mechanism in charge of doing the mapping of
5G
streams onto
PCP
s according to
some criteria.
4. E2E Mean Delay Model
This section includes the analytical performance model employed for estimating
the
E2E
mean response time of the network slices. A network slice comprises several
components (e.g.,
UPF
,
gNB
-
CU
,
gNB
-
DU
,
gNB
-
RU
, and
TN
bridge) at the data plane. In
turn, every component might have several instances, each with multiple resources (e.g.,
CPU
,
RAM
, disk, and link capacity) supporting the operation of the data plane. We model
a network slice as an open queuing network. Each queue in the network models a Primary
Resource Access Delay Contribution (
PRADC
), i.e., the queuing time involved to access a
resource associated with a given component instance (for instance, the CPU time at a given
UPF
instance) supporting the data plane operation that has a non-negligible dependency
on the workload.
PRADC
s are related to the potential bottlenecks of the system. That is,
those resources that can potentially have the highest utilization in the system and become
the primary source of delay. By way of illustration, the switching fabric of the networking
devices, such as bridges, is typically designed to operate at the line rate, and the associated
processing is almost constant with the traffic load. Consequently, the packet transmission
at the links is usually the
PRADC
for the networking devices instances in the
TN
, while
the switching packet processing delay can be regarded as constant.
Figure 2shows an example of the queuing model for the downlink of a slice. For
simplicity, the figure only depicts the
PRADC
s, but not the constant delay components,
e.g., propagation delay at every link. There is only one instance for each
VNF
(e.g.,
UPF
and
gNB
-
CU
) and two small cells encompassing
gNB
-
DU
and
gNB
-
RU
functionalities. We
assume
5GS
components execute CPU-intensive tasks for the packet processing, being the
CPU
time the only
PRADC
of the
5GS
components instances. Then, the queuing servers of
each
5GS
component instance in Figure 2stand for physical
CPU
cores and the respective
processes or threads running the tasks associated with each packet processing in parallel.
For example, the service time of every queuing server at the
UPF
represents the processing
time required by the
CPU
core/thread to run the packet processing task, which is ultimately

Sensors 2022,22, 229 11 of 29
given by the total number of task instructions to be executed and the processor computing
power. Exceptionally, besides CPU processing, the packet transmission at the radio interface
is considered another
PRADC
in the
gNB
-
RU
instances. The queuing servers at the radio
interface correspond to
PRB
s and the service time is the time slot duration, which is given
by the configured numerology. For the
TN
segments, the example considers asynchronous
TSN
as L2 technology. There is a
PRADC
at each
TSN
bridge output port related to the
frames handling and transmission at a given
TN
link. Each
TSN
bridge port is modeled as
a non-preemptive multi-priority queuing node, where the server represents the link packet
transmission process, whose service time is given by the nominal transmission capacity
of the link. The only external packet arrival process to the slice downlink is at the
UPF
,
and the packets leave the queuing network right after they are transmitted through the
radio interface.
Figure 2. Example of queuing network to model the downlink of a network slice.
To solve the resulting network of queues modeling the downlink of the slices, i.e., to
estimate the
E2E
mean delay, we rely on the queuing network analyzer (QNA) method
proposed in [
42
]. This method can be regarded as an extension of the methodology to
solve Jackson’s open networks, which consists of M/M/c queuing nodes, to general
open networks composed of G/G/c queuing nodes. The most important feature of this
method is that it provides approximations to efficiently compute the first and second-order
moments of the internal arrival processes at every queue. In [
26
], this methodology
has been experimentally validated to estimate the mean response time of softwarized
network services.
Please note that, for generality, we use the indexes
k
and
i
, which represent integer
numbers, in the subsequent analysis to differentiate the queues in the queuing network.
Let us recall that a queue stands for a PRADC of a given component instance. Please note
that the mapping of queues onto indexes (queue-to-index assignment) might be arbitrary,
though it has to remain the same for all the computations. The primary notation used
through this section is defined in Table 2.

Sensors 2022,22, 229 12 of 29
Table 2. Main notation.
Notation Description
Variables related to the E2E mean response time computation
KNumber of queues in the queuing network.
ΦConstant delays in the system.
TMean response time of a network slice.
TkMean sojourn time at queue k.
VkVisit ratio of queue k.
λ0kMean external arrival rate at queue k.
c2
0kSCV of the external arrival process at queue k.
mkNumber of servers at queue k.
c2
ak SCV of the inter-arrival packet times at queue k.
µkAverage service rate at queue k.
µ(p)
kAverage service rate at queue kfor priority class p.
c2
sk SCV of the service time at queue k.
c2(r)
sk SCV of the service time at queue kfor priority class p.
pik Probability that a packet leaves node ito node k.
νiMultiplicative factor for the flow leaving queue i.
dik Link delay between queues iand k.
C(m,ρ)The Erlang’s C formula.
ak,bik
System of equations coefficients for computing the mean and squared coefficient
of variation (SCV) of the inter-arrival packet times to every queue.
ωk,xi,γkAuxiliary variables for akand bik computation.
q0kProportion of arrivals to node kfrom its external arrival process.
qik Proportion of arrivals from node ito node k.
ρkLink utilization at queue k.
ρ(p)
kLink utilization for queue kfor priority class p.
T(p)
NP MP−MG1Mean delay of a non-preemptive multi-priority queue for priority class p.
TGGm Mean delay estimation of a G/G/m queue.
λkAggregated arrival rate at queue k.
λ(p)
kAggregated mean packet arrival rate of queue kfor priority class p.
Variables of service processes related input parameters
LAverage packet size.
CNominal link capacity.
µUPF UPF packet processing rate per physical CPU core.
IUPF Number of instructions to be executed to process a single packet.
PUP F CPU power.
µCU gNB-CU serving rate.
PCPU CPU power.
GCPU
Number of Giga OPerationss (
GOP
s) required to process a single packet in a given
gNB-CU instance.
µDU gNB-DU average packet rate.
usDynamic processing component.
urRemainder user processing component.
µRU RU packet processing rate.
CRU Base offset for the cell processing.
PRU Base offset for the platform processing.
m(ri f )
kNumber of servers in the radio interface.
NPRB Number of PRBs available at the radio interface
EbAverage number of PRBs required to serve a single packet.
µRI F Service rate at the radio interface.
τTime slot duration.

Sensors 2022,22, 229 13 of 29
4.1. Network Slice End-to-End Mean Response Time
The
E2E
mean response time
T
of a network slice in the downlink direction can be
estimated by adding up the
PRADC
s, each associated with a given resource in a network
component instance, and the constant delay contributions:
T=Φ+
K
∑
k=1
Tk·Vk(3)
where
•Φ
stands for the constant delays in the system, i.e., those delay components that do
not depend on traffic load (e.g., propagation delays) or those whose dependency on
the traffic load is negligible (e.g., switching fabric processing time of the physical L2
bridges or RAM accesses in VNFs when they execute CPU-intensive tasks).
•Tk
is the mean sojourn time of the queue
k
. As previously mentioned, a queue
k
is
associated with a given data plane component or functionality (e.g.,
UPF
,
gNB
-
CU
,
gNB
-
DU
,
gNB
-
RU
, and
TN
bridge), an instance of the respective component, and a
resource within that instance. There is no pre-established rule to perform the queues
to numerical indexes mapping, though this assignment shall remain the same for all
the computations.
•Vk
denotes the visit ratio of the queue
k
(a specific resource), i.e., the average number of
times a packet or the respective processing task visits the queue
k
since it enters until
it leaves the network slice. For instance, a
VNF
packet processing could be modeled
as three queues related to the
CPU
,
RAM
, and disk resources, each accessed a given
number of times on average to run the packet processing task.
Next, we will specify the mean delay
Tk
computation for each individual queue or
PRADC k.
4.2. Mean Sojourn Time per Queue Computation
The
PRADC
s might be modeled as G/G/m queues. That is, a queuing facility with
general distributions for both the packet inter-arrival and service times and an infinite
FCFS
queue. The mean response time of this queuing node can be estimated using the
following heavy traffic approximation [38]:
TGGm =0.5 ·c2
ak +c2
sk·Cmk,λk
µk
mkµk−λk
+1
µk
(4)
where
λk
and
c2
ak
are the aggregated arrival rate and the
SCV
of the inter-arrival packet
times at queue
k
, respectively. In other words, the first and second order moments of the
internal arrival process at queue
k
. Regarding the service process characterization,
µk
,
c2
sk
,
and
mk
denote the mean service rate,
SCV
of the service time, and the number of servers at
queue
k
, respectively. Last,
C(m
,
ρ)
is the Erlang’s C formula for a queuing node with
m
servers and utilization ρ, which is given by:
C(m,ρ) = (m·ρ)m
m!·1
1−ρ
∑m−1
n=0
(m·ρ)n
n!+(m·ρ)m
m!·1
1−ρ(5)
To model resources including traffic prioritization, for instance, the packet transmission
at the asynchronous
TSN
-based bridges’ output ports includes this feature, we consider
the use of non-preemptive multi-priority M/G/1 queues in the resulting queuing network.
This queuing node comprises a single server with
PFCFS
priority queues or priority classes.
The packets are served from these queues according to a non-preemptive strict priority
scheduling. That is, the packets with higher priority are served before packets with lower
priority. However, the service process of any packet is not interrupted until it is completed,

Sensors 2022,22, 229 14 of 29
even though a packet with higher priority arrives meanwhile. Each priority class
p∈[
1,
P]
might have a different service process characterized by the mean service rate
µ(p)
k
and
SCV
of the service times
c2(p)
sk
. It is assumed that priority class
P
corresponds to the lowest
priority. The mean response time experienced by a packet with priority class
p
at this
queuing node is given by:
T(p)
NP MP−MG1=



























P
∑
r=1
λ(r)
k·c2(r)
sk +2·µ(r)
k−1/µ(r)
k2
2·1−ρ(1)
k+1
µ(p)
k
i f p =1
P
∑
r=1
λ(r)
k·c2(r)
sk +2·µ(r)
k−1/µ(r)
k2
2·µ2
k·1−∑p−1
r=1ρ(r)
k·1−∑p
r=1ρ(r)
k+1
µ(p)
k
i f 1<p≤P
(6)
where
λ(p)
k
and
ρ(p)
k=λ(p)
k/µ(p)
k
are the aggregated mean arrival rate and utilization at
priority level pof the non-preemptive multi-priority queue k.
In a nutshell, we use the G/G/m queue to model a resource that do not support traffic
prioritization (i.e., its number of priority levels
Pk
equals one), whereas non-preemptive
multi-priority M/G/1 queuing model is employed to estimate the mean response at the
priority class p∈[1, Pk]for resources supporting traffic prioritization:
Tk=(TGGm (λk,c2
ak,µk,c2
sk,mk)if Pk=1
T(p)
NP MP−MG1(λ(p)
k∀p∈[1, P],µ(p)
k∀p∈[1, P],c2(p)
sk ∀p∈[1, P]) i f Pk>1(7)
In the following subsections, we describe the estimation of the first and second order
moments for both the aggregated arrival and service processes of every queue. Observe
that these moments are the primary input parameters to estimate the mean response
time per queue in the expressions
(4)
–
(7)
introduced above. On the one hand, the
QNA
method includes approximations to efficiently estimate the aggregated packet arrival
rate and
SCV
of the interarrival packet times at each queue. On the other hand, we rely
on the combined use of simulation, experimentation, and analysis to obtain the service
processes characteristics of the main
PRADC
s. It is worth noting that many features of the
system behavior considered in this work and presented in Section 3, especially for the
5GS
operation, can be captured through the service-related input parameters (i.e., mean and
SCV of the service times).
4.3. First and Second Order Moments Computation of the Internal Arrival Processes
First, similar to the Jackson’s method to solve open network of M/M/m queues, we
calculate the aggregated arrival rate for each queuing facility. Let
λk
denote the total arrival
rate to queue
k
. As in the case of Jackson’s networks, we can compute
λk
,
∀ {k∈N|
1
≤
k≤K}by solving the following set of linear flow balance equations:
λk=λ0k+
K
∑
i=1
λiνipik (8)
To estimate the
SCV c2
ak
of the aggregated arrival process to each queuing node
k
, QNA
relies on approximations to derive the following set of linear equations [42]:
c2
ak =ak+
K
∑
i=1
c2
aibik, 1 ≤k≤K(9)

Sensors 2022,22, 229 15 of 29
ak=1+ωk(q0kc2
0k−1) +
K
∑
i=1
qik [(1−pik) + νipik ρ2
ixi](10)
bik =ωkqik pik νi(1−ρ2
i)(11)
xi=1+m−0.5
i(max{c2
si, 0.2} − 1)(12)
ωk=1+4(1−ρk)2(γk−1)−1(13)
γk= K
∑
i=0
q2
ik !−1
(14)
Please note that the first and second order moments for all the internal arrival processes,
i.e., the aggregated arrival process to every queuing node in the queuing network, can
be computed from the set of linear equations above given the external arrival processes
(incoming arrival processes to the queuing system) and the service processes related
parameters of the different queues. Table 2includes the description of the notation
considered in the expressions above.
4.4. Estimation of the Service Processes Related Input Parameters
Finally, here, we describe methods to estimate the first and second-order moments
related to the
PRADC
s considered in this work. These service times moments are input
parameters for both computing the internal arrival processes moments and the per-queue
response time described in the previous subsections. Because of the complexity and high
domain knowledge required to model some of these input parameters together with their
dependency on the scenario specificities (e.g., processor architecture in the second-order
moment of the packet processing times), we rely on simulation and experimentation
methodologies or combine any of them with mathematical analysis to model many
of them. Additionally, we list the factors that most affect them. Please note that the
expressions provided next for the service processes related input parameters apply to all
the queues modeling the same resource in a given component, even though they refer to
different instances.
4.4.1. Packet Transmission at the Transport Network Bridges’ Ouput Ports
Here we consider the packet transmission at the
TN
bridges’ egress ports as the only
PRADC
of these components. In this case, the service time is given by the average packet
size
L
and the nominal link capacity
C
as
L/C
. For bridges supporting traffic prioritization
as
TSN
ones, each priority class might have different values of
L
. Regarding the
SCV
of
the packet transmission times, it is mainly given by the packet length distribution, but it is
also affected by deviations in the nominal transmission capacity of the link. Experimental
measurements can be performed to characterize it.
4.4.2. Packet Processing Times Characterization at the User Plane Function
The primary potential bottleneck of the
UPF
is related to the higher layers protocols
(e.g., GTP-U and PDU) processing. Here, we assume the
UPF
is deployed as a
VNF
with
one or several dedicated physical CPU cores. The packet processing rate of the
UPF
per
physical CPU core is given by the average number of instructions
IUPF
to be executed to
process a single packet divided by the CPU core power
PUP F
expressed in instructions
per second:
µUPF =IUP F
PUP F
(15)
On the other side, the
SCV
of the
UPF
’s processing time
c2
s,UPF
is a function of the
PM
configuration (e.g., CPU governor, C-States, and processor architecture and operation) [
26
],
and the virtualization layer (e.g., Kernel-based Virtual Machine (
KVM
)). Given the complexity

Sensors 2022,22, 229 16 of 29
of deriving a model considering all these variables, we rely on experimental measurements of
the c2
s,UPF in this work.
4.4.3. Packet Processing Times Characterization at the Central Unit
The primary potential bottleneck of the
CU
is associated with the
gNB
higher-layers
protocols (e.g., SDAP and PDCP) processing. We also assume the
CU
is deployed as a
VNF
with one or several dedicated physical CPU cores. Let
PCPU
and
GCU
denote the processing
power of a CPU core expressed in Giga Operations Per Second (
GOPS
) and the number of
GOP
s required to process a single packet in a given
gNB
-
CU
instance. Then, the service
rate of the gNB-CU instance is given by:
µCU =PCPU
GCU
(16)
As the virtualized
UPF
, the
SCV
of the virtualized
CU c2
s,CU
will also depend on the
PM
configuration and the specific virtualization layer. Additionally, it depends on the
per
UE SINR
distribution of the particular scenario. Again,
c2
s,CU
is obtained through
experimental measurements.
4.4.4. Packet Processing Times at the Distributed Unit
Based on the model presented in [
56
], we distinguish two components in the
DU
processing delay, namely, dynamic processing and remainder user processing. On the one
hand, the dynamic processing is related to the user processing, i.e., (de)modulation and
(de)coding, which is a linear function of allocated
PRB
s and
MCS
[
56
]. On the other hand,
the remainder of user processing includes scrambling, Downlink Control Indicator (
DCI
)
coding, and Physical Downlink Control Channel (
PDCCH
) coding [
56
]. Then, we estimate
the gNB-DU average packet rate as:
µDU =1
(us+ur)·10−6(17)
where
us
and
ur
are the dynamic processing and remainder user processing components
associated with the processing of a single packet, respectively. Several linear fittings of
the form
us(NPRB
,
MCS) = as(NPRB)·MCS +bs(NPRB)
to estimate
us
are provided
in [56]
for an Intel-based Sandy Bridge architecture with the CPU frequency set to 3.2 GHz. As
observed,
us
is a function of the number of
PRB
s
NPRB
and the
MCS
index
MCS
. For
instance, for downlink and
NPRB =
25
PRB
s,
as(
25
) =
4.9 and
bs(
25
) =
24.4. Regarding
ur
, some measured values are reported in [
56
] for different virtualization environments
and values of
NPRB
. Since these data roughly suggest
ur
depends linearly on
NPRB
, we
estimate
ur
as
ur=ar·NPRB +br
, where
ar
and
br
are fitting parameters that depend on
the virtualization environment considered (e.g., Linux Container (LXC), Docker or KVM).
4.4.5. Packet Processing Times Characterization at the Radio Unit
The
RU
packet processing rate
µRU
is related to the processing of the physical layer
and depends on the carrier bandwidth and the virtualization layer [
54
–
56
]. We adopt the
base processing model proposed in [56] to estimate µRU as below:
µRU =1
(CRU +PRU)·10−6(18)
where
CRU
and
PRU
are the base offsets for the cell and platform processing, respectively.
CRU
is a function of the number of
PRB
s.
PRU
also depends on the virtualization environment
and platform.
Regarding the
SCV
of the
RU
processing time, it mainly depends on the computing
capacity drift of the PM.

Sensors 2022,22, 229 17 of 29
4.4.6. Packet Transmission Times Characterization at the Radio Interface (NR-Uu)
The radio interface is modeled as a GI/D/m queuing system, i.e., general distribution
for the arrival process, deterministic service time,
m
servers and infinite room for packets.
Then, we can use
(4)
to estimate the mean response time of the radio interface by considering
the
SCV
of the service time equals zero (
c2
sk =
0 in
(4)
). The number of servers
m(ri f )
k
in the
queuing model is estimated as:
m(ri f )
k=NPRB
Eb(19)
where
NPRB
is the number of
PRB
s available at the radio interface and
Eb
is the average
number of
PRB
s required to serve a single packet through the radio interface. The parameter
Eb
can be estimated either experimentally or through simulation as in this work. Either
way, observe that this parameter includes the co-channel interference effect. Trivially, the
higher the co-channel interference, the greater the number of required
PRB
s to serve a
packet will be.
On the other hand, the service time of the radio interface is given by the chosen
numerology, which, in turn, determines the time slot duration
τ
. Thus, the service rate at
the radio interface is given by:
µRI F =1
τ(20)
QT
-based performance models have been proposed and validated in [
32
,
57
]. More
precisely, the authors in [
57
] model the radio interface as an M/M/m/K queuing system,
i.e., a system with Poissonian arrival and service processes,
m
servers and finite queue
length. In [
32
], the authors propose a more accurate model at the expense of a higher
complexity. However, it shall be noted that the accuracy of the M/M/m/K model to
estimate the channel Packet Loss Ratio (
PLR
) is still quite fair according to the results
reported in [
32
] (see [Figure 1.a]). Here, we compute the number of servers as in [
57
],
but we consider deterministic service times as in [
32
] as we assume there is no
HARQ
retransmissions. In contrast to [
32
,
57
] that consider Poissonian arrival processes, we do not
make any assumption on the packet arrival process. In this regard, the model used here is
more general.
5. Experimental Setup
This section details the scenarios, methods, and configurations considered in this work
to carry out our experimentation.
Figure 3shows the scenario employed in our evaluation. More precisely, it includes
the layout of the factory floor considered in our setup. As observed, it consists of four
PL
s, each with fifty-six motion control devices and twenty
eMBB
users. Moreover, four
5G
gNB
s and five Wi-Fi Access Points (
AP
s) are part of the industrial scenario
RAN
. This
layout is inspired by the one considered in [69].
Figure 4depicts the underlying network infrastructure together with the placement of
the 5G
VNF
s (e.g.,
gNB
-
CU
and
UPF
). The servers and bridges depicted in this figure are
physically placed in the technical room shown in Figure 3. The figure also includes the paths
followed by each slice in the midhaul network, that is, the
TN
segment interconnecting
the
CU
s with the
gNB
-
DU
s. For the sake of clarity, the path followed by the aggregated
traffic from each cluster of servers to a given
gNB
or
AP
is specified all along the network.
Nonetheless, actually, there is a single full-duplex link interconnecting each bridges pair at
most. Then, for instance, the aggregated traffic from
URLLC
slices #2, #3, and #4 shares the
link between TSN switch #6 and TSN switch #7.
We evaluate the
E2E
mean delay for the following two configurations with the aim of
assessing the effectiveness of slicing in terms of isolation:
•
Configuration 1: The URLLC traffic generated by each of the four
PL
s in the factory
floor is served by a segregated slice, thus providing isolation between the production
lines. The
PL
#1 generates an aggregated non-conformant traffic that does not meet
the aggregated committed data rate due to a failure in its operation.

Sensors 2022,22, 229 18 of 29
•
Configuration 2: The URLLC traffic generated by all of the four
PL
s in the factory floor
is served by a single slice. The production line #1 generates non-conformant traffic
due to a failure in its operation.
Figure 3. Industrial scenario layout.
Figure 4. Infrastructure setup for the evaluation.
We also consider the following two variants for each scenario configuration in
order to compare the transport network technologies (e.g., standard (bare) Ethernet, and
asynchronous TSN):
•
Variant A: The midhaul network in Figure 4is realized as a standard IEEE 802.1Q
Ethernet network where there is no traffic prioritization.

Sensors 2022,22, 229 19 of 29
•
Variant B: The midhaul network in Figure 4is implemented as an asynchronous
TSN network, whose building block is the
ATS
. There is an
ATS
instance at every
TSN bridge egress port. The
ATS
includes a per-flow traffic regulation through the
interleaved shaping and traffic prioritization.
The combination of each of the configurations 1 and 2 with the two variants of the
TN
results in four different scenarios to be evaluated, namely: (i) configuration 1.A (dedicated
slice for every
PL
and standard Ethernet for the midhaul network), (ii) configuration 1.B
(dedicated slice for every
PL
and
TSN
for the midhaul network), (iii) configuration 2.A
(single slice serving the traffic of all the
PL
s and standard Ethernet for the midhaul network),
and (iv) configuration 2.B (single slice serving the traffic of all the
PL
s and
TSN
for the
midhaul network).
A dedicated
5GS
is deployed for each
URLLC
slice. This
5GS
includes dedicated
virtualized
UPF
and
gNB
-
CU
instances to serve the traffic generated by the respective
production line(s). There are also isolated radio and
TN
resources destined for the slice.
The upper layers of the virtualized
UPF
and
gNB
-
CU
instances follow a
FCFS
discipline to
serve the packets following a
RTC
strategy. They are instantiated at the edge cluster (placed
at the technical room) and have dedicated physical
CPU
cores for this task (
CPU
pinning).
The
gNB
-
DU
and the radio unit are deployed as a small cell (physical network function
-PNF-) operating at 3.5 GHz and 100 MHz of bandwidth. For the
TN
, we consider both
standard Ethernet and asynchronous TSN technologies, as commented previously. The
constituent TSN bridges of the TSN network include an
ATS
at every egress port. Every
ATS
includes eight priority levels and sixteen shaped buffers. The transmission capacity
for every link was set to 1 Gbps. Additionally, the
PRADC
s considered for the downlink
at each slice are the
UPF
upper-layers processing,
gNB
-
CU
upper-layers processing, the
transmission process at every involved link in the
TN
,
gNB
-
DU
processing,
gNB
-
RU
processing, and radio interface transmission process. Considering these bottlenecks, we
used the model (3)–(20) described in Section 4to estimate the E2E mean response time.
The main configuration parameters are included in Table 3. It is worth highlighting
that a realistic configuration of the industrial scenario parameters has been taken into
consideration. In our setup, we assumed the expected throughput generated by each
PL
is the same and we performed the dimensioning of the resources for each slice and
configuration accordingly. In the same way, each
eMBB
slice generates the same amount
of aggregated traffic for each
AP
. The quality radio signal-related parameters (e.g., mean
number of
PRB
s required to transmit a
URLLC
packet at the radio interface (
Eb
), average
spectral efficiency per user, average
SINR
per user) in Table 3were measured through
simulation considering the layout shown in Figure 3. Figure 5includes the Cumulative
Distribution Function (
CDF
) of the per-
UE SINR
and the Probability Mass Function (
PMF
)
of the PRBs required to transmit a single packet obtained via simulation for the industrial
scenario considered.
-10 -5 0 5 10 15 20 25 30
SINR (dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cumulative Distribution Function (CDF)
(a) CDF of the per UE SINR
0.05
0.1
0.15
0.2
0.25
Probability Mass Function (PMF)
0 10 20 30 40 50 60 70 80 90
Number of PRBs
(
b
)
PMF
of the required number of
PRB
s to transmit
a packet
Figure 5. CDF of the SINR and PMF of the number of PRBs obtained through simulations.

Sensors 2022,22, 229 20 of 29
Table 3. Main configuration parameters.
Parameters Value
Number of production lines 4
Number of URLLC flows per production line 56
URLLC service Motion Control (MC) [70,71]
Packet delay budget MC 1 ms [70,71]
Packet length MC 80 bytes
Sustainable rate per MC flow 1.55 Mbps [70,71]
Burstiness per MC flow 2592 bits
eMBB traffic generated from server #3 to each Wi-Fi
AP
AP#1: 330 Mbps, AP#2: 330 Mbps, AP#3: 330 Mbps
AP#4: 800 Mbps, AP#5: 800 Mbps
eMBB packet size 1500 bytes
UPF service rate per processing unit (CPU core) 357,140 packets per second (from data included in [33])
SCV of the UPF service time 0.65 (from experimental measurements in [26])
gNB-CU service rate per processing unit
(CPU core) 601,340 packets per second (from data included in [55])
SCV of the gNB-CU service time 0.65 (from experimental measurements in [26])
CPU core power (Intel Xeon Platinum 8180) 25.657 GOPS
gNB-DU service rate per processing unit
(CPU core)
Substitute as=0.097 ·Eb+2, bs=1.6 ·Eb−14, and ur=1.3 ·Eb+23 in (17)
(fittings derived from experimental data in [56])
SCV of the gNB-DU service time 1
gNB-RU service rate per processing unit Substitute CRU =1.2 ·Eb−11, and PRU =0.03 ·Eb+4.3 in (18)
(fittings derived from experimental data in [56])
SCV of the gNB-RU service time 1
Processing units allocated to each network
component.
The number of processing units were designed
to ensure that the utilization of the computing
resources for every component is lower than 75%.
Configuration 1:
UPF: 1 CPU core (Intel Xeon 8081)
gNB-CU: 1 CPU core (Intel Xeon 8081)
gNB-DU: 24 CPU cores (Intel SandyBridge i7-3930K @3.20Ghz
gNB-RU: 3 CPU cores (Intel SandyBridge i7-3930K @3.20Ghz)
Configuration 2:
UPF: 3 CPU cores (Intel Xeon 8081)
gNB-CU: 2 CPU cores (Intel Xeon 8081)
gNB-DU: 96 CPU cores (Intel SandyBridge i7-3930K @3.20Ghz)
gNB-RU: 10 CPU cores (Intel SandyBridge i7-3930K @3.20Ghz)
Visit ratios of the UPF and gNB-CU 1
Visit ratios of the gNB-DU, gNB-RU and
radio interface 0.5
TSN links capacities All links have a capacity of 1 Gbps
MC traffic-to-priority level assignment at every
TSN bridge output port 1 (1 is the highest priority level and 8 is the lowest)
eMBB traffic-to-priority level assignment at every
TSN bridge output port 8
PRB bandwidth 180 kHz
Radio interface time slot duration 142.8 µs
Number of PRBs dedicated for each URLLC
slice per gNB
Configuration 1:
Slice#1: gNB#1: 166, gNB#2: 166, gNB#3: 0, gNB#4: 0
Slice#2: gNB#1: 166, gNB#2: 166, gNB#3: 0, gNB#4: 0
Slice#3: gNB#1: 0, gNB#2: 0, gNB#3: 166, gNB#4: 166
Slice#4: gNB#1: 0, gNB#2: 0, gNB#3: 166, gNB#4: 166
Configuration 2:
Slice#1: gNB#1: 333, gNB#2: 333, gNB#3: 333, gNB#4: 333
Mean number of PRBs required to transmit
a URLLC packet at the radio interface (Eb)15.8
Average spectral efficiency per user 2.8173 bps/Hz (MCS index=22)
Average SINR per user 3.5368 dB
External arrival process (to the UPF) Poissonian

Sensors 2022,22, 229 21 of 29
6. Results
This section includes the numerical results obtained from the evaluation of the
E2E
mean response time for the four configurations presented in the previous section.
Figure 6depicts the
E2E
mean packet delay per production line (
PL
) for the
configuration 1.A (see Section 5). The abscissae axis in the figure represents the
throughput excess generated by the
PL
#1 due to a malfunctioning. The results show
that only the mean packet delay of the
PL
#1 is primarily affected by the non-conformant
traffic, thus suggesting the effectiveness of infrastructure slicing for ensuring the
isolation among slices.
0 0.5 1 1.5 2 2.5
Unexpected throughput excess from production line #1 (Mbps)
0.5
1
1.5
2
2.5
3
3.5
4
E2E mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
Figure 6. E2E mean delay for configuration 1.A (dedicated slices + std. Ethernet for the midhaul).
Table 4includes a breakdown of latency per considered
PRADC
and per studied
configuration. Each cell in the table includes the minimum and maximum mean packet
delay (expressed in microseconds) obtained per
PL
in the evaluated range of throughput
excess for the respective identified bottleneck and configuration. The entries in the table that
include only one value instead of an interval stand for a constant or roughly constant mean
delay for all the throughput excess values assessed. As observed, the traffic excess from
PL
#1 is not impacting the mean packet delay of the 5G components and radio interfaces
(i.e., NR-Uu) of the
PL
s #2, #3, and #4 as their serving slices have dedicated computing and
radio resources, respectively. Nonetheless, the non-conformant traffic results in an increase
of the
TN
packet delay for the
PL
#2. This fact can be clearer observed in Figure 7a. The
explanation of this fact is that the standard Ethernet network considered cannot provide
per link traffic isolation, i.e., there are no means to reserve a segregated link capacity per
slice. Please note that the traffic from
PL
s #1 and #2 share the same paths in the
TN
(see
Figure 4). Therefore, using bare Ethernet as transport network technology does not ensure
the full isolation among slices.
Also, it is remarkable that the
TN
delay of the slices serving
PL
s #1 and #2 is significantly
higher than the one experienced by the traffic from
PL
s #3 and #4. That is due to the fact
that slices #1 and #2 are sharing the link from switch #1 to switch #4 with
eMBB
traffic (see
Figure 4) and there is no traffic prioritization.
The main bottleneck in configuration 1.A is the radio interface (see Figure 7b). Please
note that, even considering there are dedicated radio resources for each
PL
, in a real scenario
it is expected to observe an increase in the mean packet delay at the radio interface of the
slices serving
PL
s #2, #3 and #4 with the
PL
#1 traffic load excess. This is because of the
interference and it depends on the per gNB radio resources to slices assignment.

Sensors 2022,22, 229 22 of 29
Table 4.
Mean delay (expressed in microseconds) contribution per component and per
production line.
ConFigure 1.A ConFigure 1.B ConFigure 2.A ConFigure 2.B
TN PL#1-2: 111.10-121.40
PL#3-4: 2.25
PL#1-2: 40.16-41.87
PL#3-4: 2.07
PL#1-2: 40.16-41.87
PL#3-4: 2.07
PL#1-2: 12.18
PL#3-4: 2.07
UPF PL#1: 4.22-4.28
PL#2-4: 4.21
PL#1: 4.41-183.20
PL#2-4: 4.21 PL#1-4: 3.18-3.23 PL#1-4: 3.21
CU PL#1: 2.09-2.10
PL#2-4: 2.09
PL#1: 2.13-4.36
PL#2-4: 2.09 PL#1-4: 2.04-2.08 PL#1-4: 2.06-7.94
DU PL#1: 13.25
PL#2-4: 13.25 PL#1-4: 132.50 PL#1-4: 132.50 PL#1-4: 132.50
RU PL#1:1-2: 13.13-13-16
PL#2-4: 13.13 PL#1-4: 13.13 PL#1-2: 12.88-12.93
PL#3-4: 12.88 PL#1-4: 12.87
NR-Uu PL#1: 379.80-3229.00
PL#2-4: 367.60 PL#1-4: 367.60 PL#1-2: 174.20-1114.00
PL#3-4: 174.20 PL#1-4: 172.60
0 0.5 1 1.5 2 2.5
Unexpected throughput excess from production line #1 (Mbps)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
TN mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
(a) TN mean delay
0 0.5 1 1.5 2 2.5
Unexpected throughput excess from production line #1 (Mbps)
0
0.5
1
1.5
2
2.5
3
3.5
NR-Uu mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
(b) NR-Uu mean delay
Figure 7.
TN and NR-Uu mean delay for configuration 1.A (dedicated slices + std. Ethernet for
the midhaul).
Figure 8a shows the
E2E
mean packet delay per
PL
for the configuration 1.B. In contrast
to configuration 1.A, in this configuration
TSN
is used as
L2
technology in the
TN
. In this
case, the results also suggest that the traffic excess from
PL
#1 does not have any impact
on the rest of
PL
s. It is noteworthy that this configuration requires a higher throughput
excess to significantly degrade the performance perceived by
PL
#1 traffic. This is related to
the fact that the asynchronous
TSN TN
performs a per flow traffic regulation at every
TSN
bridge egress port, thus filtering the non-conformant traffic. As a consequence, the
UPF
becomes the main bottleneck of the network as shown in Figure 8b. For the same reason,
the mean packet delays of the
TN
,
gNB
-
DU
,
gNB
-
RU
, and radio interface for
PL
#1 do not
depend on the traffic excess. Last, please note that the traffic from
PL
s #1 and #2 experiences
the longest
TN
delays (see Table 4). Although the asynchronous
TSN TN
includes traffic
prioritization, the transmissions are non-preemptive and therefore the
eMBB
traffic still
degrades the performance of
PL
s #1 and #2 traffic in the link interconnecting switches #1
and #4 (see Figure 4).
Figure 9a depicts the
E2E
mean packet delay for configuration 2.A. In contrast to
configurations 1.A and 1.B, the non-conformant traffic from the
PL
#1 severely degrades
the performance perceived by the traffic from
PL
#2. This fact further highlights the
effectiveness of infrastructure slicing for providing isolation. On the other hand, the mean
packet delay of
PL
s #3 and #4 seems to remain independent of the
PL
#1 traffic excess
despite there is a single slice to serve the traffic from all the
PL
s. As in configuration 1.A,
the primary bottleneck of configuration 2.A is the radio interface as shown in Figure 9b.
The traffic from
PL
#1 is only sharing the computational and radio resources at the
RAN
with
PL
#2. Consequently, the traffic from
PL
s #3 and #4 only perceives an increase in its
delay at the
UPF
and
gNB
-
CU
. However, the utilization of the
UPF
and
gNB
-
CU
resources

Sensors 2022,22, 229 23 of 29
is low compared to the radio ones and the performance degradation experienced by
PL
s #3
and #4 traffic is negligible in the range of throughput excess studied.
0 20 40 60 80 100 120 140
Unexpected throughput excess from production line #1 (Mbps)
0.5
0.55
0.6
0.65
0.7
E2E mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
(a) E2E mean delay
0 20 40 60 80 100 120 140
Unexpected throughput excess from production line #1 (Mbps)
0
50
100
150
200
UPF mean delay ( s)
Production line #1
Production line #2
Production line #3
Production line #4
(b) UPF mean delay
Figure 8. E2E and UPF mean delay for configuration 1.B (dedicated slices + TSN for the midhaul).
0 2 4 6 8 10 12 14
Unexpected throughput excess from production line #1 (Mbps)
0.2
0.4
0.6
0.8
1
1.2
1.4
E2E mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
(a) E2E mean delay
0 2 4 6 8 10 12 14
Unexpected throughput excess from production line #1 (Mbps)
0
0.2
0.4
0.6
0.8
1
1.2
NR-Uu mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
(b) NR-Uu mean delay
Figure 9. E2E
and NR-Uu mean delay for configuration #2.A (shared slice + std. Ethernet for
the midhaul).
Finally, in contrast to the previous configurations, the traffic excess from
PL
#1
significantly increases the
E2E
mean packet delay of all the
PL
s in configuration 2.B (see
Figure 10a).
0 50 100 150 200 250 300 350
Unexpected throughput excess from production line #1 (Mbps)
0.3
0.35
0.4
0.45
0.5
0.55
0.6
E2E mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
(a) E2E mean delay
0 50 100 150 200 250 300 350
Unexpected throughput excess from production line #1 (Mbps)
0
0.05
0.1
0.15
0.2
0.25
UPF mean delay (ms)
Production line #1
Production line #2
Production line #3
Production line #4
(b) UPF mean delay
Figure 10. E2E and UPF mean delay for configuration 2.B (shared slice + TSN for the midhaul).
As in configuration 1.B, the
UPF
becomes the primary bottleneck since the
TSN TN
does not allow the traffic excess pass through (see Figure 10b). Notably, it is apparent,
especially for low values of the throughput excess, that the
E2E
mean packet delay is
slightly higher for
PL
s #1 and #2. This is because of non-preemptive transmissions of
the
eMBB
traffic at the
TSN TN
as explained for configuration 1.B. Also, it shall be noted
that the throughput excess to overload the bottleneck is greater than in the configurations
previously discussed due to the two following reasons:
(i)
Compared to configurations 1.A and 2.A, the bottleneck in this configuration is the
UPF
, which has an initial utilization much lower than radio resources given our setup.

Sensors 2022,22, 229 24 of 29
(ii)
The throughput excess in this configuration leverages statistical multiplexing to
utilize the
UPF
computational resources surplus allocated to
PL
s #2, #3, and #4 in
configuration 1.B.
7. Conclusions and Future Work
In this article, we have proposed a queuing theory-based model to estimate the
end-to-end mean delay of 5G infrastructure network slices. Then, using this model, we
have investigated the effectiveness of infrastructure in terms of the degree of isolation in
industrial private
5G
networks. To that end, we have considered a reasonably complete
and realistic setup whose main parameters have been obtained from experimentation and
simulation. The use case addressed in this work aims to show the benefits brought by using
segregated infrastructure slices, each with dedicated resources at every network domain,
for serving the traffic generated by the different
PL
s in the factory floor. In this way, we
might reduce the number of production downtimes and the corresponding associated
expenditures. This is because the traffic excess from any
PL
due to any malfunctioning will
not negatively affect the operation of the rest of
PL
s as a consequence of a
QoS
degradation
in the network.
As concluding remarks, our results suggest the effectiveness of infrastructure network
slicing in ensuring a quite fair degree of isolation among segregated slices. Nonetheless,
the use of standard (bare) Ethernet does not ensure the complete isolation of the slices as it
does not include support for traffic prioritization and resources reservation. In this way, for
example, the
eMBB
cross traffic at the different links of the
TN
interferes and degrades the
performance of
URLLC
services. This might potentially result in production downtimes. To
overcome this issue,
TSN
technology might be used to enable a per link dedicated resources
assignment to every slice. Furthermore,
TSN
enhances the performance of the
TN
segments
due to its traffic prioritization capability, thus drastically reducing the adverse effects of the
interfering eMBB traffic.
As future work, several challenges lie ahead. One of the central challenges is to
devise, develop and validate a solution for automating the management and operation
of the industrial infrastructure slices. The principal objective might be to minimize
the expenditures associated with the production downtimes while using the minimum
resources necessary to ensure the target
QoS
metrics for the proper operation of the
involved industrial services. Solving this challenge requires further research to address
many currently open issues. First, it is necessary to integrate the knowledge from
OT
,
Information Technology (
IT
), and economic domains to model the production downtimes
cost as a function of the network performance metrics. Then, the resulting model could
drive the solution towards the aforementioned goal. Second, network calculus-based
models for the delay and jitter (delay variation) must be developed to holistically capture
the network slices’ behavior. Existing related works only capture network parts of the
features and operation of the slice. These models are needed for a feasibility check of the
configurations issued by the solution, i.e., to verify whether a given configuration meets
the delay and jitter requirements of the involved industrial services. Similarly, stochastic
models are a must to estimate the network slice availability. Then, the solution could
harness them to compute, for instance, the required redundancy to ensure the availability
requirements. Last, likely, the use of Machine Learning (
ML
) techniques is required to
assist the optimization process in coping with its complexity.
The challenge of realizing a zero-touch solution for managing industrial network
slices is accentuated in industrial networks that integrate 5G and
TSN
. The integration
of 5G with TSN, which 3GPP is addressing (see 3GPP TS 23.501), is crucial to realize
tomorrow’s converged industrial networks, providing both wired and wireless access with
deterministic
QoS
support. In this way, these networks will satisfy the needs of almost any
industrial service. In this scenario, the
5GS
is regarded as a set of virtual TSN bridges that
can be logically configured by the TSN controller through the TSN application function at
the 5G control plane. This scenario brings further problems. For example, the coordination

Sensors 2022,22, 229 25 of 29
and cohesion of the configurations of 5G and TSN segments must be ensured. On the one
hand, the delay and jitter budgets of the industrial services have to be properly distributed
between these two segments. On the other hand, the deterministic QoS requirements and
configurations issued by the TSN controller for the 5G virtual TSN bridges have to be
translated into a valid setup for the 5GS.
Author Contributions:
Conceptualization, L.C.-R., J.P.-G., P.A., P.M. and J.M.L.-S.; methodology,
L.C.-R., J.P.-G., P.A. and P.M.; software, L.C.-R., J.P.-G. and P.M.; validation, L.C.-R., J.P.-G.,
P.A. and P.M.; formal analysis, L.C.-R., J.P.-G., P.A. and P.M.; data curation, L.C.-R. and J.P.-G.;
writing—original draft preparation, L.C.-R. and J.P.-G.; writing—review and editing, L.C.-R.,
J.P.-G., P.M., P.A. and J.M.L.-S.; supervision, P.A., P.M. and J.M.L.-S.; project administration, P.A.
and J.M.L.-S.; funding acquisition, P.A. and J.M.L.-S. All authors have read and agreed to the
published version of the manuscript.
Funding:
This work has been partially funded by the H2020 project 5G-CLARITY (Grant No. 871428)
and the Spanish national project TRUE-5G (PID2019-108713RB-C53).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
Acronym Acronym expansion
3GPP 3rd Generation Partnership Project
4G Fourth Generation
5G Fifth Generation
5GS 5G System
AGV Automated Guided Vehicle
AP Access Point
AR Augmented Reality
ATS Asynchronous Traffic Shaper
BBU Baseband Unit
BE best-effort
CBS Credit-Based Shaper
CDF Cumulative Distribution Function
CN Core Network
CPU Central Processing Unit
CU Central Unit
DCI Downlink Control Indicator
DNC Deterministic Network Calculus
DU Distributed Unit
DRP Dynamic Resource Provisioning
E2E end-to-end
eMBB enhanced Mobile Broadband
EPC Evolved Packet Core
FCFS First Come, First Served
gNB Next Generation NodeB
GOP Giga OPerations
GOPS Giga Operations Per Second
HARQ Hybrid Automatic Repeat Request
IFFT Inverse Fast Fourier Transform
IT Information Technology
KVM Kernel-based Virtual Machine

Sensors 2022,22, 229 26 of 29
L2 layer 2
LXC Linux Container
LTE Long-Term Evolution
MAC Medium Access Control
MCS Modulation and Coding Scheme
MIMO Multiple-Input Multiple-Output
ML Machine Learning
MTBF Mean Time Between Failures
NF Network Function
NFV Network Functions Virtualisation
NP nondeterministic polynomial time
NR New Radio
NS Network Softwarization
OP Operational Technology
PCP Priority Code Point
PDCP Packet Data Convergence Protocol
PL production line
PLR Packet Loss Ratio
PMF Probability Mass Function
PM Physical Machine
PRADC Primary Resource Access Delay Contribution
PRB Physical Resource Block
QoS Quality of Service
QN Queuing Network
QNA Queuing Network Analyzer
QT Queuing Theory
RAM Random Access Memory
RAN Radio Access Network
RF Radio Frequency
RLC Radio Link Control
RRC Radio Resource Control
RTC run-to-completion
RU Radio Unit
SCV squared coefficient of variation
SDN Software-Defined Networking
SDAP Service Data Adaptation Protocol
SINR Signal-to-Interference-plus-Noise Ratio
SNC Stochastic Network Calculus
SNS Softwarized Network Service
TAS Time-Aware Shaper
TN Transport Network
TR Technical Report
TSN Time-Sensitive Networking
UE User Equipment
URLLC Ultra-Reliable and Low Latency Communication
UP User Plane
UPF User Plane Function
VLAN Virtual Local Area Network
VNF Virtual Network Function
VNFC Virtual Network Function Component
VR Virtual Reality
WAT Wireless Access Technology
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