Energy-efficient Joint Computational and Network Resource Planning in Beyond 5G Networks

Abstract

Network Function Virtualization (NFV) is expected to be a crucial enabler of Beyond 5G (B5G) networks, supporting new services with stringent requirements, while offering high flexibility and configurability. In this paper, we consider the joint problem of Virtual Network Function (VNF) placement alongside computational and communication resource allocation in a mobile network to minimize total power expenditure while satisfying the Service Function Chain (SFC), throughput and delay requirements. We explicitly account for the Access Network (AN) and formulate a general Mixed Integer Linear Program (MILP). Due to the high complexity of the latter, we propose an efficient heuristic, which is shown to significantly outperform the State-of-Art (SoA), while achieving up to 78% of the optimal energy efficiency with up to 742 times lower complexity.

Full text

Energy-efficient Joint Computational and Network
Resource Planning in Beyond 5G Networks
M. Gatzianas?,†, A. Mesodiakaki?,†, G. Kalfas?,†, and N. Pleros?,†
?Department of Informatics, Aristotle University of Thessaloniki, Thessaloniki, Greece
†Center for Interdisciplinary Research and Innovation, Thessaloniki, Greece
Email: {mgkatzia, amesodia, gkalfas, npleros}@csd.auth.gr
Abstract—Network Function Virtualization (NFV) is expected
to be a crucial enabler of Beyond 5G (B5G) networks, supporting
new services with stringent requirements, while offering high
flexibility and configurability. In this paper, we consider the
joint problem of Virtual Network Function (VNF) placement
alongside computational and communication resource allocation
in a mobile network to minimize total power expenditure while
satisfying the Service Function Chain (SFC), throughput and
delay requirements. We explicitly account for the Access Network
(AN) and formulate a general Mixed Integer Linear Program
(MILP). Due to the high complexity of the latter, we propose
an efficient heuristic, which is shown to significantly outperform
the State-of-Art (SoA), while achieving up to 78% of the optimal
energy efficiency with up to 742 times lower complexity.
Index Terms—Mobile Edge Computing, Virtual Network Func-
tion, Service Function Chaining, Mixed Integer Linear Program.
I. INTRODUCTION
Beyond 5G (B5G) networks are expected to meet a plethora
of service requirements supporting high resource and tech-
nology heterogeneity, while adopted architectural paradigms,
such as Centralized-Radio Access Network (C-RAN) and
Network Function Virtualization (NFV), have introduced new
challenges (e.g., Virtual Network Function (VNF) placement
[1]) to traditional user association and traffic routing problems.
A service can be viewed as an ordered set of VNFs
(e.g., firewall, NAT, etc.), referred to as Service Function
Chain (SFC), which should be deployed at the network so
that not only the correct VNF ordering is ensured (SFC
chaining) but the capacity constraints of the host nodes and
links are also satisfied [2]. The NFV-supporting physical
infrastructure contains a number of nodes, including traffic-
forwarding switches and computational nodes of different
capabilities able to host VNFs in the form of Virtual Machines
(VMs), containers or unikernels. Although traditional cellular
architectures were mainly equipped with cloud servers, located
at distant locations offering high computational power at low
cost, the need for supporting ultra-low latency B5G services
has motivated Multi-Access Edge Computing (MEC) [3].
MEC nodes offer computational capabilities very close to the
user, often being attached to Base Stations (BSs), and are able
to achieve ultra-low latency at the expense of high cost, thus
leading to a non-trivial cost/distance trade-off.
In addition, B5G is expected to include a variety of different
technologies of distinct characteristics that should be jointly
studied. Hence, apart from fiber links interconnecting the
physical machines, wireless links may also be deployed as an
X-haul transport solution, to offer high flexibility close to the
Access Network (AN). Millimeter wave (mmWave) constitutes
a very promising candidate to serve this purpose, due to its
very high bandwidth availability and antenna gains that are
able to compensate for the higher path loss in this band.
Moreover, for the AN, comprised of gNodeBs (gNBs) densely
overlaid with Small Cells (SCs), 5G-New Radio (5G-NR)
proposes the use of multiple frequencies (including mmWave).
In this context, network resource planning should jointly
consider i) all different types of technologies, e.g., 5G-NR,
mmWave, fiber, along with their benefits and constraints, and
ii) the allocation of all different resource types, i.e., com-
munication, computational and storage. It is also crucial to
consider the whole network path from the traffic source to the
destined User Equipment (UE), so as to satisfy the service
latency constraint and offer true End-to-End (E2E) optimality.
Furthermore, achieving high energy efficiency is of utmost
importance not only to limit the network operator’s operational
costs (thus, increasing its revenue) but also to decrease the
ICT carbon footprint, leading to eco-friendly B5G networks.
Consequently, energy-efficient network resource planning so-
lutions are needed that will jointly solve the user association,
VNF placement (SFC chaining) and traffic routing problem in
the highly heterogeneous B5G networks.
A. Related work and Contribution
The joint problem of VNF placement, SFC chaining and
routing in wired networks, mostly targeting cloud environ-
ments in the network core, has been widely studied with tools
such as Dynamic Programming [4], knapsack algorithms [5]
and Benders decomposition [6]. The above works, including
the recent ones in [7], [8], [2], formulate NP-hard Mixed
Integer Linear (MILP) and Non-Linear Programs, for which
heuristic algorithms are proposed and numerically evaluated.
Hence, their essential differences lie in the considered con-
straints and objectives (i.e., minimum total network power
consumption in [7], link utilization, overhead and server power
consumption in [8], monetary profit in [2]). However, most of
these works do not consider mobile networks and, even when
they do, they ignore the wireless AN segment. Models with a
distinct MEC/cellular flavor appear in [9], [10]; however, [9]
does not consider power consumption, while [10] models the
link constraints more abstractly than in our paper and uses a
different objective (i.e. minimize maximum link utilization).

The last remark motivates our paper, which also studies
joint VNF placement and routing in a MEC/cloud-enabled
heterogeneous mobile network consisting of macro BSs and
SCs. We explicitly include the AN, as well as potential wire-
less X-haul links, while accounting for the inherent wireless
channel fluctuations. Hence, this paper extends the concrete
and detailed communication model of [11] by adding all
necessary controls for the computational resources and by
modeling the associated delay and capacity constraints.
The paper’s contribution lies in the formulation of a con-
crete optimization problem, with minimal assumptions, that
accounts for both communication and computation resources
in the AN, edge and core segments of a mobile network. Due
to the NP-hardness of the resulting problem, we also propose
a heuristic algorithm, evaluate its performance via simulations
and demonstrate its superior performance compared with other
State-of-the-Art (SoA) algorithms. Our formulation and algo-
rithm can also be employed by a mobile network operator
as an offline tool, during the network planning stage, to
provide quantitative answers on the power expenditure and
computational resources (both of them major components of
OPEX/CAPEX) required to support a given set of services.
The rest of the paper is structured as follows: Section II
describes the system model and problem formulation, while
Section III presents the proposed heuristic, which is com-
pared to the optimal solution and other SoA algorithms in
Section IV. Section V concludes the paper. Notation-wise, sets
are denoted as V,Fetc. and M
=denotes equality by definition.
II. SY ST EM M OD EL A ND P ROB LE M STATE MENT
We consider the RAN and Core segments of a mobile
network and model them as a graph G(V,E), where Vis
the set of nodes (excluding mobile users) and Eis the set of
(non-access) edges/links among them, as illustrated in Fig. 1
(which also shows access links, for completeness). The nodes
in Vcomprise gNB and/or SCs (hereafter referred to as BSs)
in the RAN, as well as switches/routers and other middlebox
devices (e.g., load balancers, firewalls, etc.) in the Core. These
devices typically operate as VNFs running in virtual instances
(e.g., VMs, containers etc.) utilizing computational resources
collocated with network nodes.
Each link e= (u, v)∈ E , where u, v ∈ V, can be wired
or wireless (the latter enables wireless X-hauling, typically
mmWave), has a communication capacity ceand induces a
delay δe(the sum of transmission and propagation delays)
to all packets traversing it. We partition Einto the sets Ef i ,
Ewl of wired/fiber and wireless links, respectively, and denote
with Vsw ⊆ V the set of nodes in Vthat have at least one
incident link in Efi (i.e., u∈ Vsw iff there exists w∈ V
such that (u, w)∈ Ef i).1For modeling reasons, and although
all physical links are inherently bidirectional, we explicitly
distinguish between links (u, v)and (v, u)in E(and also for
Efi,Ewl ). We denote with h(e) = uand t(e) = vthe head
and tail, respectively, of directed link (u, v).
1We abstractly refer to these nodes as “switches” since most fiber links in
a mobile Core are typically Point-to-Point links among switches or routers.
: Middleboxes (VNF-
implemented)
: Fiber link
: gNB, SC : MEC resources
: Fog resources
: Switch
Aggreg.
Layer 1
Aggreg.
layer 2
: Cloud resources : X-haul
wireless link
: Access link
Fig. 1. Mobile network of heterogeneous communication and computation
nodes along with middlebox functionality offered by deployed VNFs. Dashed
color lines indicate 2 illustrative E2E paths selected for 2 highlighted UEs.
The UEs are not included in Vbut rather in J(we also
define ˜
VM
=V ∪ J ). Each UE j∈ J connects to a BS a∈
A(j)⊆ V, where the dependence on jcaptures the typical
signal level-based association rules. We define AM
=∪j∈J A(j)
as the set of all BSs and S(a)M
=j:a∈ A(j)⊆ J as the
set of UEs which may be served by BS a∈ A. We focus
on Downlink (DL) and consider the set of DL AN links EAN
M
=(a, j) : a∈ A, j ∈ S (a)with ˜
EM
=E ∪ EAN . We also
assume that each BS a∈ A has a maximum number of ¯
N(RB)
a
Resource Blocks (RBs) to allocate to the UEs in S(a).
Let Vc⊆ V be the set of network nodes which also have
computational (i.e., CPU2) resources able to host one or more
VNFs. For each node y∈ Vc, we denote with cythe amount
of CPU resources (measured in GFLOPS).
We denote with Fthe set of all available VNFs (viewed as
complete software stacks) that can be deployed and allow for
multiple instances of a given VNF in the same or different
nodes depending on network traffic. Each VNF f∈ F is
described by the tuple fM
= (Tf, πf, wf, τf), where Tfis an
identifier of the VNF’s functionality (e.g., NAT etc.), πf>0
is the data processing capacity of the VNF (in Mbps), wf>0
is the amount of CPU resources (in GFLOPS) required for
the VNF’s operation, and τf>0is the data processing
delay experienced by an individual data packet as it passes
through the VNF. To ensure proper service endpoints, we also
introduce the set Fdum
M
={fdum1, fdum2}of two “dummy”
VNFs and include it into F. The VNFs f∈ Fdum ⊆ F are
characterized by πf=∞,wf= 0,τf= 0, which implies
that the “dummy” VNFs work transparently w.r.t our model.
Let Cbe the set of SFCs, where SFC ρ∈ C is described
by the ordered sequence ρM
=hfdum1, f (ρ)
1, . . . , f (ρ)
Nρ, fdum2i,
where Nρis the number of non-dummy VNFs in ρand
f(ρ)
i∈ F \Fdum. The traffic of ρis properly served only if it
passes through the VNFs in ρexactly matching the specified
order. We also write f ρto state that VNF fis contained
in ρand define Rρ
M
={f∈ F :f ρ}. An equivalent
description for ρis via a directed graph G(ρ)with the virtual
node set V(ρ)containing the VNFs in ρand the virtual edge
2Additional computational resources such as memory and storage can be
similarly handled and are omitted for simplicity and without loss of generality.

set E(ρ)describing the relative order of the VNFs (see, e.g.,
Fig. 2 of [10]). For any virtual edge e0∈ E(ρ), we denote
with h(e0),t(e0)∈ F the respective VNFs at the head and
tail of e0. Each UE j∈ J requests a service type qj∈ Q,
with qj
M
= (sqj, rqj, δqj, ρqj), where sqj∈ V is the “source”
node of the service (the “destination” node of service qjis
UE j), rqj>0is the E2E required throughput, δqj>0
is the E2E maximum allowed latency, and ρqj∈ C is the
required SFC. We explicitly allow for sharing a VNF instance
among two (or more) different SFCs.Also, for each UE j, we
use our knowledge (or estimates) of the SINR σa,j of link
(a, j)∈ EAN and the requested service rate rqjto compute
the number of RBs N(RB)
a,j needed to achieve this rate on link
(a, j). Assuming frequency-flat slow fading [11], we consider
the simple case of uniform BS power allocation among the
RBs, so that each RB is assigned a power of p(RB)
a.
A. Power consumption model and problem formulation
Unless otherwise stated, we consistently use the following
indices ranging over the respective sets: j∈ J ,a∈ A,q∈ Q,
y∈ Vc,˜y∈ Vc∪ J ,f∈ F,q∈ Q,u, v, w ∈ V,m, n ∈
Vsw. We introduce the decision variables xj,a as the Boolean
indicator of whether UE jattaches to BS a, and φ˜y,f,q as the
Boolean indicator of whether VNF frequested by service q
is deployed on node ˜y. Also, θe0,q
e(or θe0,q
u,v ) is the Boolean
indicator variable of whether the directed physical link e=
(u, v)∈ E belongs to the physical path in Gonto which the
virtual link e0∈ E(ρq)is mapped for SFC ρq. Finally, Nf, ˜y
is the number of instances of VNF fdeployed on node ˜y.
Towards superior energy-saving performance, we employ
resources, devices and links only when needed. Specifically,
collocated CPU resources at node yare employed only when
yactually runs deployed VNFs, as captured by the Boolean
indicator variable ξy. Hence, the power consumed by CPU
processing at node yis given by P(CP U )
y=P(CP U,i)
yξy+
P(CP U,m)
y−P(CP U,i)
y·Uy, where P(CP U,m)
y,P(CP U,i)
yare
the maximum and idle power of the CPU deployed at yand
Uy
M
=Pf∈F
Nf,y wf
cvis the CPU load factor at y[7].
Similarly, for a fiber link (n, m)∈ Efi, the Boolean variable
zn,m indicates whether the link actually carries traffic, in
either link direction, for any request. To examine whether
link (n, m)∈ Efi carries any traffic in the specific direction
from nto m, we introduce the Boolean variable wn,m, which
implies that zm,n ≥wm,n,zm,n ≥wn,m for all (n, m)∈ Ef i.
We also denote with ψnthe Boolean variable of whether the
switch of node n∈ Vsw is actually used. There exist certain
consistency relations between these variables as shown in (1)
below, where C1>0is a sufficiently large constant.
X
q∈Q X
e0∈E(ρq)
θe0,q
e≤C1we,∀e∈ Efi,
X
e∈Efi :h(e)=n
we+X
e∈Efi :t(e)=n
we≤C1ψn,∀n∈ Vsw.(1)
The total power consumed by the switch in node nis
P(sw)
n=P(sw)
idle ψn+Pport Pm∈Vsw :(n,m)∈Ef i zn,m, where
P(sw)
idle denotes the switch idle power and the second term
accounts for the active fiber links of the switch, with Pport
being the power consumed by each active port [7].
The power expenditure model for the mmWave links in
Ewl follows [11] (see eq. 7-10 therein); specifically, the
power consumed on link e∈ Ewl is given by P(mmW)
e=
N(mmW )
RF χeP(mmW,i)
e+ ∆(mmW )
eF(`e), where N(mmW )
RF
is the number of RF chains in the link, P(mmW,i)
eis the idle
power of the link’s transmitter, `e
M
=Pq∈Q Pe0∈E(ρq)θe0,q
e/be
(where beis the utilized bandwidth of link e) is a load-
dependent variable, ∆(mmW )
eis a slope parameter depending
on the power electronics used in the link’s transmitter, and
F(·)is a piecewise-linear function accounting for the non-
linear dependence between achieved throughput and power
expenditure. Finally, χeis a Boolean indicator variable for
whether link eis actually used to serve any traffic.
The power expenditure for the AN links in EAN
is similarly modeled as follows: the power expended
by a gNB BS a∈ A is P(gNB)
a=N(gN B)
RF ·
µaP(gN B,i)
a+∆(gN B)
aPj∈S(a)xj,a p(RB)
aN(RB)
a,j , where
µais the Boolean indicator for whether BS ais deployed
and N(gN B)
RF , P (gN B,i)
a,∆(gN B)
ahave the same semantics as
in Ewl. For an SC BS, it similarly holds P(S C)
a=N(SC)
RF ·
µaP(SC,i)
a+ ∆(SC )
aPj∈S(a)xj,a p(RB)
aN(RB)
a,j . We use the
clever trick of [11] to convert the activation/power saving
constraints into a set of linear constraints by introducing
auxiliary Boolean variables χe, for e∈ Ewl, and νa, for a∈ A
χe+C2σe≥1,∀e∈ Ewl,
1−C2χe≤X
q∈Q X
e0∈E(ρ)q
θe0,q
e≤C2(1 −σe),∀e∈ Ewl (2)
1−C1νa≤X
j∈J
xj,a ≤C2(1 −νa), µa+C1νa≥1,∀a∈ A.
In addition to basic self-consistency conditions (omitted here
due to lack of space), we also impose the constraints:
X
y∈Vc
φy,f,q = 1,∀q∈ Q,∀f∈ Rq\ Fdum ,
X
a∈A(j)
xj,a = 1, xj,b = 0,∀j∈ J ,∀b6∈ A(j),(3)
X
q∈Q:f ρq
φy,f,q rq≤Nf,y πf,∀f∈ F ,∀y∈ Vc,
X
f∈F
Nf,y wf≤cy,X
f∈F\Fdum
Nf,y ≤C1ξy,∀y∈ Vc,(4)
X
q∈Q,
e0∈E(ρq)
θe0,q
erq≤ce,∀e, X
j∈S(a)
N(RB)
a,j ≤¯
N(RB)
a,∀a(5)
X
v:(u,v)∈˜
E
θe0,q
u,v −X
w:(w,u)∈˜
E
θe0,q
w,u =φu,h(e0),q −φu,t(e0),q ,
∀q∈ Q,∀e0∈ E(ρq),∀u∈˜
V,
(6)
X
y∈Vc,
f∈Rqj
φy,f,qjτf+X
e∈E,
e0∈E(ρqj)
θe0,qj
eδe+X
a∈A(j)
xj,aδ(a,j )≤δqj,∀j
(7)

where (3) requires that each requested VNF must be deployed
and that each UE must properly attach to exactly one BS.
Eq. (4) ensures that the number of deployed VNF instances on
a node is sufficient to meet the data processing requirements
for the incoming traffic and does not exceed the amount of
available CPU resources, while ensuring that the computa-
tional node is deployed only when needed. The link and BS
capacity constraints are captured in (5), while (6) is a flow
conservation and routing condition which ensures that the
packets of each requested SFC meet the corresponding VNFs
in the correct order as they are routed through the selected
path. The E2E delay constraint is captured in (7).
Hence, the total power expenditure in the network
is Ptotal
M
=Pn∈Ssw P(sw)
n+Py∈VcP(CP U )
y+
Pe∈Ewl P(mmW )
e+Pa∈A P(gN B/SC )
aand we formulate our
problem as the following NP-hard MILP
minimize Ptotal,
s.t. (1)–(7),(8)
Due to the high complexity of solving (8), we next propose a
low-complexity heuristic algorithm and use (8) as a yardstick
against which the heuristic’s performance is evaluated.
III. PROP OS ED ENERGY-EFFIC IE NT VNF PLACEMENT,
TR AFFI C ROU TI NG A ND U SE R AS SO CI ATIO N (HERO)
Our proposed Heuristic for Energy-efficient VNF place-
ment, traffic Routing and user assOciation (HERO) aims at
maximizing the network energy efficiency while ensuring low
UE blocking probability. HERO consists of two stages, as
shown in Fig. 2. In the first stage, the traffic path is selected
(i.e., user association and routing), while in the second one
VNF placement takes place, ensuring correct VNF ordering.
Initially, to ensure high UE acceptance ratio, the UEs are
sorted based on their service demands, giving priority to the
UEs with the most delay-intolerant services. For UEs with the
same delay requirements, priority is given to the UEs with
higher rate demands. Then, for each UE, a weighted graph is
constructed from the service traffic source to the UE with all
feasible links and their respective power consumption acting
as weights. HERO calculates the kshortest-weighted paths and
starts with the first, as long as it satisfies the delay and link
capacity constraints, taking into account the decisions for the
already examined users. Otherwise, the next path is selected
until either a path that satisfies all constraints is found or there
are no other paths. In the latter case, the UE is blocked and
HERO proceeds with the next as long as there is one.
After a valid path is found for the current UE, HERO
proceeds to the second stage, where the UE VNFs are being
placed. To that end, for each VNF, following the order of
the UE SFC, a list is constructed with all the available
computational nodes based on a parameter, denoted by H. This
parameter is equal to the sum of the normalized node centrality
(closeness), the normalized node computational capabilities
(cy) and the node CPU utilization. The latter is equal to a)
1 when the studied VNF can be placed in the examined node
without initiating a new VNF instance, b) 0.1 when there is
Input
For each UE:
Construct a weighte d graph including:
Feasible AN links, X -haul transport links, and Fiber links
Edge weights: Link power consumption t aking into account any networ k change
Calculate the
k
shortest-weighted paths
First stage
Output
Move to the next
path
Satisfies
delay &
capacity
constraints?
Other
VNFs?
YES NO
Put UE to unsatisfied users
Define UE examination order
YES
NO
Other
paths
available?
User association &
traffic routing
We select the (next) node with the highest
H
to place the
VNF ensuring correc t VNF ordering
YES
YES
NO
Change
selected path
For each VNF of the UE we sort the computing nodes
of the path based on parameter
H
that considers:
•Node centrality (Closeness)
•Computational power
•Utilization
Other nodes
available in
the path?
NO
Comp.
capacity
constraint
satisfied?
Place the
VNF
Second stage
VNF placement
Select t he (next) shortest-weighted path
Other
UEs?
NO
YES
NO
YES
NO NO
Update the networ k
conditions
Fig. 2. Flowchart of the proposed energy-efficient VNF placement, traffic
routing and user association algorithm (HERO).
enough computational capacity to host the studied VNF in
the examined node, but a new VNF instance is required, and
c) 0 otherwise. Subsequently, the node with the highest H
for the selected VNF is selected, as long as it has sufficient
computational resources to host it. Otherwise, the node with
the next highest His selected, until either the VNF is placed
or there is no other node to examine in the selected path. In the
latter case, the algorithm returns to stage 1 and the next path
out of the kcalculated is examined. The process is repeated for
the new path until either all VNFs of the UE are placed or there
is no other path to study and the UE is blocked. In case all
UE VNFs are placed the network conditions are updated, and
the algorithm proceeds to the next UE. The aforementioned
steps are repeated until all UEs are examined.
IV. PERFORMANCE EVALUATION
A. Simulation scenario
In our results, the heuristics have been developed in MAT-
LAB, while the optimal solution in IBM CPLEX. The simu-
lation scenarios consider a gNB sector area of 500 m radius
overlaid with two SC clusters [11], as shown in Fig. 3.
Each cluster consists of four possible SC positions, which
are uniformly dropped in an 100-m-radius from the cluster
centers. The minimum allowable distances are given in [11].
A subset of BSs, one SC (randomly selected) per cluster and
the gNB in this case, are assumed to be able to have fiber
access to the aggregation network. mmWave X-haul links can
be deployed among BSs as long as their distance is lower
than 200 m. The aggregation network consists of two layers
each one comprising four possible node positions, as shown in
Fig. 3. The aggregation layer nodes are fiber-connected among

TABLE I
SFC DE TAIL S [7]
Type VNF ordering Throughput Delay Share
(Mbps) (ms) (%)
Web NAT-FW-TM-WOC-IDPS [0.6-1] 500 20
VoIP NAT-FW-TM-FW-NAT [0.384-0.64] 100 20
Streaming NAT-FW-TM-VOC-IDPS [5-24] 100 39
Gaming NAT-FW-VOC-WOC-IDPS [0.24-0.5] 60 6
Ultra RT AI/ML NAT-NAT [15-25] 1 15
them and with the BSs having fiber access so that there is no
disconnected node. Hotspot UE traffic is also assumed [11].
We consider 5 different SFCs of specific VNF ordering
(NAT: Network Address Translator, FW: Firewall, TM: Traffic
Monitor, WOC: WAN Optimization Controller, IDPS: Intru-
sion Detection Prevention System, VOC: Video Optimization
Controller), data rate demand (uniformly distributed in the
provided set), E2E delay requirement and share of the total
requests, as shown in Table I. The data processing capacity as
well as the GFLOPS requirement of each VNF type are given
in Table II. For given number of UEs, we run 10 different
scenarios, with 5 different UE distribution snapshots each.
We assume 100 RBs allocated per gNB or SC (µ=0 in 5G
numerology). The operating frequency of the gNB and SCs is
2 GHz, assuming orthogonal channels between the gNB and
the SCs. However, the SCs of different clusters may interfere
with each other. The mmWave X-haul links operate at 60
GHz, with 200 MHz channel bandwidth. For the AN and the
mmWave links, we employ the link budget equation and the
related parameter values of [11]. The number of cores is equal
to 8, 24 and 48 for the MEC, 1st and 2nd Aggregation Layer
nodes, respectively. Parameter P(CP U,m)
yis selected randomly
from the set {55, 70}for the MEC nodes, from {150, 220}for
the 1st Aggregation Layer and from {200, 278}for the 2nd
Aggregation Layer nodes, while the idle power is assumed to
be equal to 10%of the assigned maximum power values. The
fiber link capacity is 10 Gbps, while the rest of the simulation
parameters are summarized in Table III.
The optimal solution and the proposed heuristic (HERO)
will be compared with the following SoA algorithms [7]:
a) Holu: This heuristic first performs the VNF place-
ment based on the node centrality (closeness) and the CPU
utilization of computing nodes and then decides upon traffic
routing targeting at minimizing the power consumption, while
satisfying the E2E service delay constraint.
b) BCSP: It considers node centrality (betweeness) for
the VNF placement and the shortest-path in terms of delay for
routing, while meeting the E2E service delay constraint.
Given that both reference algorithms do not handle user
association, we employ the default user association criterion
for both, i.e., the UEs are connected based on the highest
received signal. In addition, for a fair comparison, their UE
examination order is selected to be the same with HERO.
B. Simulation results
In Fig. 4 and 5, we show the energy efficiency (bits/Joule)
and the computational time (s, in logarithmic scale), respec-
1
2
3
45
67
8
9
10
11
12
13
14
15
16
17
Fig. 3. Simulation scenario example.
TABLE II
VNF DE TAIL S [7]
Type NAT FW TM VOC WOC IDPS
Process Capacity (Mbps) 500 400 200 578 300 600
GFLOPS Requirement 110 440 55 110 110 440
TABLE III
SIMULATION PARAMETERS [7], [11], [12]
Parameter Value Parameter Value Parameter Value
P(sw)
idle 315 W Pport 7 W Packet length 1.5 KB
N(gN B)
RF 8N(SC)
RF 4N(mmW )
RF 64
∆(gN B)
a4.7 ∆(SC)
a4∆(mmW )
e100
P(gN B,i)
a6.8 W P(SC ,i)
a130 W P(mmW,i)
e3.9 W
tively, of all algorithms for different number of UEs. As can
be seen, HERO provides a very good trade-off between energy
efficiency and complexity compared to other approaches,
achieving up to 78%of the optimal value, with up to 742 times
lower complexity. All algorithms have 100%user acceptance
ratio in all cases except for BCSP that presents 96%for N=20,
93%for N=40, and 91%for N=40. This is due to the fact that
in BCSP the CPU utilization of the computing nodes is not
taken into account, resulting in less efficient VNF placement,
which under higher traffic load can lead to few UEs being
blocked. The inefficiency of BCSP VNF placement is also
shown in Fig. 6, where the power break down of all algorithms
under low and high traffic is presented. As shown, inefficient
BCSP VNF placement leads to a higher number of deployed
computational nodes, and thus, higher power consumption.
Compared to Holu and BCSP, HERO achieves up to 60%
and 86%higher energy efficiency, respectively, while keeping
the complexity low, as shown in Fig. 5. This is due to the

60%
86%
Fig. 4. Energy efficiency (bits/Joule) of all algorithms for different number
of UEs per gNB area.
Fig. 5. Execution time (s) in logarithmic scale of all algorithms for different
number of UEs per gNB area.
fact that HERO jointly considers user association leading to
higher flexibility at the expense of a little higher complexity.
On the other hand, in both Holu and BCSP, the serving BSs
are already decided (based on the best SINR criterion) and
then the optimal VNF placement and traffic routing from the
UE traffic source to its serving BS are performed. This is also
demonstrated in Fig. 6, where the Optimal and HERO do not
deploy the gNB in any case, but rather use SCs as serving
BSs (in contrast to Holu and BCSP), hence, leading to much
lower power consumption. We can also observe that the power
consumption of the Optimal and HERO are scaling better than
the SoA with increasing load (HERO still achieves 68%of
the Optimal energy efficiency value when N=40). This further
justifies the motivation of our work that user association, VNF
placement and traffic routing should be jointly considered to
guarantee true optimal E2E network performance.
V. CONCLUSION
In this paper, we studied the joint VNF placement, user
association and traffic routing in B5G networks targeting
at energy efficiency maximization, while ensuring high UE
acceptance ratio. We modeled the aforementioned problem as
a MILP with minimal assumptions, which captures all charac-
teristics of the employed technologies, resource and service
Fig. 6. Power (W) break down of all algorithms for low traffic (N=10) and
high traffic (N=40).
types as well as their constraints and power consumption.
To tackle the prohibitive complexity of the studied problem,
we proposed HERO, an energy-efficient resource planning
heuristic, which was shown to significantly outperform the
SoA, while achieving up to 78%of the optimal value, with
up to 742 times lower complexity.
ACKNOWLEDGMENT
This work is supported by H2020 5G-COMPLETE (GA
871900).
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