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Latency-Aware Dynamic Resource
Allocation Scheme for Multi-Tier 5G
Network: A Network Slicing-Multitenancy
Scenario
SUNDAY O. OLADEJO1(Student Member, IEEE) AND OLABISI E. FALOWO1(Senior
Member, IEEE)
1Department of Electrical Engineering, University of Cape Town, Cape Town, South Africa.
Corresponding author: Sunday O. Oladejo (email: oldsun002@myuct.ac.za)
This work was supported in part by the National Research Foundation, South Africa and Telkom, South Africa.
ABSTRACT In 5G slice networks, the multi-tenant, multi-tier heterogeneous network will be critical in
meeting the quality of service (QoS) requirement of the different slice use cases and in reduction of the
capital expenditure (CAPEX) and operational expenditure (OPEX) of mobile network operators. Hence,
5G slice networks should be as flexible as possible to accommodate different network dynamics such as
user location and distribution, different slice use case QoS requirements, cell load, intra-cluster interference,
delay bound, packet loss probability, and service level agreement (SLA) of mobile virtual network operators
(MVNO). Motivated by this condition, this paper addresses a latency-aware dynamic resource allocation
problem for 5G slice networks in a multi-tenant, multi-tier heterogeneous environment, for efficient radio
resource management. The latency-aware dynamic resource allocation problem is formulated as a maximum
utility optimisation problem. The optimisation problem is transformed and the hierarchical decomposition
technique is adopted to reduce the complexities in solving the optimisation problem. Furthermore, we
propose a genetic algorithm (GA) intelligent latency-aware resource allocation scheme (GI-LARE). We
compare GI-LARE with the static slicing (SS) resource allocation; the spatial branch and bound-based
scheme; and, an optimal resource allocation algorithm (ORA) via Monte Carlo simulation. Our findings
reveal that GI-LARE outperformed these other schemes.
INDEX TERMS Network Slicing, Multi-tier, Multi-tenancy, Resource Allocation
I. INTRODUCTION
A. BACKGROUND
NETWORK slicing (NS) refers to the abstraction of
the physical infrastructure and resources of a mobile
network into logical networks, which operate as autonomous
entities or networks. NS is envisioned to play a critical role
in the full implementation of IMT-2020 networks widely
regarded as the fifth generation (5G) mobile networks. 5G
networks will be pivotal in the Industry 4.0 revolution; hence,
5G networks will support diverse verticals and services to
reshape the way we live, transact businesses, and conduct
human-machine relationship [1].
Despite the positive economic impact of 5G NS, realising
effective NS schemes requires financial commitment [2], [3]
by key industry players such as the infrastructure providers
(InPs), mobile virtual network operators (MVNOs), backhaul
operators (BO), service providers (SP), and over-the-top
players (OTP). To make 5G networks profitable (i.e. by the
reduction of the capital expenditure (CAPEX) and operating
expenditure (OPEX) many business models [4], [5] have
been proposed, which revolve around multi-tenancy. In this
work, we adapt the models in [4], [5] to address multi-
tenancy in 5G NS as depicted in Fig. 1. Here, Fig. 1 depicts
a two-stage hierarchical business model for NS in a multi-
tenancy scenario where the InP leases out virtual network
resources to different MVNOs.
In this paper, we address the diverse service requirement via
three main slice use cases [6], [7]: (1) the enhanced mobile
broadband (eMBB); (2) the massive machine-type communi-
cations (mMTC); and, (3) the ultra-reliable low-latency com-
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InP
MVNO 1 MVNO h
...
FIGURE 1: InP-MVNO Model.
munications (URLLC) slice use cases. The eMBB use case is
bandwidth-crunching and supports applications such as high
definition (HD) video streaming and virtual reality (VR).
The mMTC use case is latency-dependent with intermittent
small-size data payloads. It supports applications such as
e-health and internet of things (IoT) devices. The URLLC
use case supports applications and services that require very
low-latency small-size payload transmissions with extremely
high reliability such as autonomous driving and vehicle-to-
everything (V2X).
In a multi-tenant multi-tier heterogeneous 5G slice network,
addressing the different quality of service (QoS) require-
ments of different verticals and several services could be an
uphill task. Moreover, owing to the stochastic characteristics
of the mobile network environment and the dynamic allo-
cation of network resources (such as bandwidth and power)
between the InP and the MVNOs; the respective MVNOs and
the numerous slice users could be very challenging. Besides,
unlike the widely investigated 2-tier heterogeneous network
environment in the study of 5G NS, we examine the concept
of NS deployed or implemented in a hierarchical multi-tier
clustered heterogeneous multi-tenant network. Furthermore,
unlike most works in the literature, we focus on both the
latency and received data rate QoS requirement of three slice
use cases.
B. RELATED WORK
There are a number of architectures and solutions that have
been proposed for NS. The authors in [8], [9] and [10] pre-
sented maximum capacity, profit-aware, and energy-efficient
resource allocation schemes for NS in a multi-tenancy sce-
nario. Slice priorities and bandwidth-power cost were con-
sidered; however, a static resource scheme between the InP
and MVNOs was adapted. Besides, the latency constraints
requirement of the respective slices was not considered. Also,
a single-tier homogeneous network was considered, which
does not entirely depict a 5G network and its complexities.
The authors in [11] proposed an incentive scheme for slice
cooperation based on the D2D communication in a multi-
tenant 5G network for achieving maximum system utility.
The authors did not address the multi-tier and multi-slice
peculiarities of 5G networks. Moreover, the latency-aware
requirements of the slice use case, such as the URLLC, were
not considered.
To meet the latency requirements of the cloud radio access
network (C-RAN), the authors in [12] proposed a queuing
delay model for front haul network dimensioning in 5G
networks. Kingman’s exponential law of congestion was
adopted by the authors to estimate the delay on the front-
haul.
In [13], a maximum-revenue resource allocation optimisation
problem was formulated for a virtual network in a 2-tier
heterogeneous network. In solving this problem, the authors
pre-allocated radio resources to the respective base stations
or access point. In [14], a dynamic resource sharing scheme
for a single-tier homogeneous C-RANs multi-tenancy was
proposed. A network utility maximisation problem was for-
mulated while considering the tenants’ priorities. Although
the proposed two-step sub-optimal approach improved the
network utility, users were not categorised based on their
slice requirements. The authors in [15] presented a dynamic
radio resource slicing scheme for a 2-tier heterogeneous
wireless network. An alternating concave search algorithm
was designed to solve the maximum network utility opti-
misation problem. The 2-tier heterogeneous network, due to
its simplistic model, may not fully represent a 5G network
environment with its many tiers of access networks in order
to meet the ever-rising user demands. Besides, the authors
did not address the concept of multi-tenancy, which is a
critical requirement for CAPEX and OPEX reduction in 5G
networks.
In [16], [17], [18], and [19], the authors considered a dynamic
allocation of radio resources in a network slicing scenario.
An auction game-based algorithm was proposed for efficient
resource allocation between the InP and MVNOs. Addition-
ally, the authors did not consider the challenge of latency
constraints in the resource allocation scheme. Although the
authors considered multi-tenancy, the multi-tier and multi-
slice features of the 5G network were not taken into consid-
eration in their studies.
In [20], an efficient RAN slicing strategy for a heterogeneous
network with eMBB and V2X services was investigated. The
authors proposed an off-line reinforcement learning scheme
which allocates radio resources to the eMBB and V2X slice
user case with the sole aim of maximising network resource
utilisation. However, the latency requirements of the V2X use
case were not considered. Besides, the small scale fading fac-
tors that significantly affect fast-moving devices and vehicles
were not included in their model. In addition, a single-tier
network was considered, which does not entirely depict a
5G network which is envisioned in [21] to be a multi-tenant
multi-tier network.
In [22], the authors discussed the different approaches to
realise URLLC use cases for V2X communications. The au-
thors adopted the large deviation theoretical (effective band-
width or capacity) framework of the MAC layer approach.
In [23], the authors proposed a cooperative communications
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scheme based on the average bit error probability (ABEP)
to enhance the performance of IoT communication systems.
The scheme relies on the capabilities of the back-propagation
neural network to predict the ABEP performance of the
investigated system.
In [24], the authors investigated a slice-aware admission
scheme for multi-tenant radio access networks, which sup-
ports guaranteed eMBB and mission-critical services. A
Markovian model was proposed to characterise resource
sharing in a multi-tenant network slicing environment. How-
ever, in addition to considering only the single-cell sce-
nario, authors did not address the latency requirement of the
mission-critical use case.
Furthermore, in [25], the authors examined dynamic resource
allocation in a virtualised network slicing environment. A
dynamic resource allocation scheme based on deep reinforce-
ment learning was proposed to address the challenge, as men-
tioned earlier. Nevertheless, they did not address the multi-
tenancy scenario and its challenges. Moreover, it was not
shown how the average delay utility of the delay constrained
slice was guaranteed or ensured.
In [26], the authors proposed a dynamic network slicing
and resource allocation scheme for video streaming and IoT
applications, which is based on the Lyapunov Optimisation in
a single cell scenario. However, the URLLC use case, which
is highly latency-dependent and requires extreme-reliability,
was not considered. In addition, multi-tenancy, which is a
critical feature in NS, was not considered.
The authors in [27] showed that low error rates and low
latencies are attainable and practicable over an air interface.
Moreover, the authors emphasised the importance of channel
error rates and short transmission intervals in achieving low
latency.
The authors in [28] considered the challenge of latency in
the allocation of resources to users in a multi-access edge
computing network. A virtual network function placement
assignment algorithm based on the polynomial-time com-
binatorial algorithm was proposed to guarantee user satis-
faction. However, a multi-slice multi-tier 5G network, in
which slice users require different latency thresholds, was
not considered. Besides this point, the authors also did not
consider the peculiarities of multi-tenancy in their problem
formulation.
In [29], the authors studied network slicing resource allo-
cation challenges in vehicular networks. The eMBB and
URLLC slice-use cases were considered in the proposed
scheme, which is based on the effective capacity theory.
However, the vehicular network was not studied in the
context of a multi-tier multi-tenant network. The vehicular
network cannot exist in isolation [30], [31] because of its
interaction with other slice users in other tiers such as macro,
pico and femto tiers. In addition, dynamic resource allocation
was not considered.
In [32], the authors proposed a dynamic resource allocation
scheme for eMBB and URLLC slice-use cases. The pro-
posed scheme is based on optimal power control for latency-
aware resource allocation. The dynamic allocation of the
bandwidth, which is a scare resource, was not addressed.
The authors did not consider the peculiarities of multi-tenant
multi-tier in their problem formulation.
In [33], the authors addressed the challenge of slice users’
quality of experience and resource allocation in a vehicular
network. The authors partitioned vehicles into multiple logi-
cal networks based on a network slicing clustering algorithm.
A multi-tier network which reflects one of the 5G features
was not considered. Moreover, static partitioning of radio re-
sources was adopted rather than dynamic resource allocation
of resources which can easily adapt to traffic variation.
In satisfying the diverse demand requirements of the respec-
tive slice use cases, the authors in [34] proposed an on-
demand cooperation scheme among multi-tenants in a net-
work slicing scenario. The proposed framework was centred
on complex network theory to obtain the topology related
information of networks for efficient resource management.
However, the latency requirement of the slice use cases was
not addressed.
Different from the above-mentioned works, in the present
paper we investigate the latency-aware dynamic resource
allocation problem in a multi-tier clustered heterogeneous
network for multi-tenancy network slicing.
C. CONTRIBUTIONS
The main contributions of the present paper are summarised
as follows:
1) We consider radio resource allocation concerning the
three broad slice use cases, namely the eMBB, mMTC,
and URLLC respectively, in a multi-tier multi-tenant
5G slice network. A latency-aware dynamic resource
allocation scheme is developed as an optimisation
framework to maximise the total utility of the network.
This framework efficiently allocates radio resources to
the different slice use cases by considering the data
rate and latency requirements of the respective slice use
cases. In meeting the slice user QoS requirements, the
network bandwidth is sliced by taking into considera-
tion the users’ location and distribution, slice use case
QoS requirements, cell load, tier load, intra-cluster
interference, delay bound, packet loss probability, and
the service level agreement of the respective MVNOs
(i.e. tenants).
2) As stated, the latency-aware dynamic resource allo-
cation problem is formulated as a maximum utility
optimisation problem. In solving the maximum utility
optimisation problem, we transform and decompose
the main problem via hierarchical decomposition [35]
to reduce the complexity of the main problem. Con-
sequently, we optimally associate slice users with the
different tiers in the clustered multi-tier multi-tenant
network. We exploit the matching game theory to
optimally associate slice users to the respective access
points. The selection, crossover, mutation and elitism
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Cat.I:
Cat.II:
Cat.III:
Cat.IV:
MacroBase
Station,
m
PicoBase
Station,
p
FemtoBase
Station,
f
Clustered-
FemtoBase
Station,
pf
V2V
Intra-Cluster
Interference
Co-Tier
Interference
Co-Tier
Interference
V2I
Interference Link
Signal Link
FIGURE 2: System Model.
processes of the Genetic Algorithm are adapted to
solve the transformed maximum utility problem.
3) Through extensive Monte-Carlo simulations, we
demonstrate the performance of the proposed latency-
aware dynamic resource allocation framework in a
clustered multi-tier multi-tenant network. We also
compare the proposed GI-LARE with three other
schemes, namely: a static slicing scheme (SS) [36], a
spatial branch and branch scheme (sBB) [37], and an
optimal resource allocation algorithm (ORA) [38].
D. ORGANISATION
We organised the remainder of this paper as follows. In
Section II, we give a detailed explanation of the system
model. In Section III, the latency-aware and dynamic re-
source model is discussed. The latency-aware dynamic radio
resource allocation problem is formulated in Section IV. In
Section V, the proposed solutions are discussed in detail. To
this end, we discussed the computational complexities of the
proposed algorithms in Section VI. Simulation results are
shown and discussed in Section VII. Finally, we draw the
conclusion of this paper in Section VIII.
For convenience, the notations used in this paper are sum-
marised in Table 1.
II. SYSTEM MODEL
In this section, a multi-tier multi-tenant heterogeneous net-
work system model is presented. Table 1 shows the main
notations to be used in the following sections.
A. GENERAL MODEL
We describe the system model considered in this paper, as de-
picted in Fig. 2. The considered scenario assumes a clustered
multi-tier heterogeneous network whose physical resources
are owned by an InP. The InP provides services to a set of
MVNOs H={h|h∈ N ,1≤h≤ |H|}. Each MVNO,
h∈ H is uniquely independent of each other; that is, h6=h0,
and hhas its own set of network slice use cases, Sh, it offers
to its slice users. However, Sh={E∪M∪R}, in which Ede-
notes the eMBB slice user case, Mindicates the mMTC slice
use case and Rstands for the URLLC. Subsection II-B gives
a detailed explanation of the slice use case specifications.
The multi-tier network comprises femtocells, picocells, clus-
tered femtocells, a macrocell and a device-to-device (D2D)
based V2X communication layers. The set of unclustered
femtocells located in the coverage of the macrocell only is
numbered as F={f|f∈ N ,1≤f≤ |F|}, while the set
of picocells is denoted as P={p|p∈ N ,1≤p≤ |P |}.
Owing to the relatively large radius of pcompared to f,
we consider that there are femtocells in the coverage of a
p. These femtocells we call clustered femtocells, such that
a set of clustered femtocell in the coverage of picocell is
numbered as PF ={pf|pf ∈ N ,1≤pf ≤ |PF |}. The
coverage area of a phelps to create a cluster area for a set of
clustered femtocells, pf. It is essential to state that the users
of an MVNO, h, are categorised according to their requested
slice use case {E ∪ M ∪ R} and geographical position in the
multi-tier network.
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TABLE 1: List of Notations
Symbol Description
h,HMVNO, Set of MVNO
ShSet of Slices offered by a MVNO
E,M,ReMBB, mMTC, URLLC Slice
m,f,p,pf Macro, femto, pico and clustered femto-
cells
F,P,PF Set of femtocell, picocell, and clustered
femtocell
Eh,m,Eh,f ,
Eh,p,Eh,pf
Set of eMBB users in the macro, femto,
pico and clustered femto tiers
Mh,m,Mh,f ,
Mh,p,Mh,pf
Set of mMTC users in the macro, femto,
pico and clustered femto tiers
Rh,m Set of URLLC Slices
di,j,h Distance of user iin MVNO hfrom access
point j
ρi,j,h,ρr,m,h Path loss of the link between user iand
access point
γi,j,h Spectrum efficiency
Γi,j,h Channel Gain
ψj,h,ψwTx. power of an access point, V2V car in
Tx mode
Tw,TrEffective antenna height of a V2V car in
Tx mode, V2I in Rx mode
XcCarrier frequency in GHz
WSet of paired vehicles in V2V communica-
tion
αr,m,αw,r Small scale fading components of a Rh,m
slice user engage in a V2V and V2V com-
munication.
λi,h Packet arrival rate
Dmax Maximum delay bound
µDelay-bound violation probability thresh-
old
θi,h QoS Exponent
Li,h Packet size
BTotal Bandwidth of the network
βt,h Network Slice ratio per tier tfor each
MVNO h
ϕi,p,h user slice ratio
Pm,Pe,PcProbability of mutation, elitism, crossover
APopulation of chromosomes in CGA
yNumber of chromosomes
|t|Number of tiers
UFitness vector of A
gMaximum number of iterations
B. SLICE USER CATEGORISATION
Considering the slice use-case requested by QoS require-
ment and its geographical location of the users, we categorise
users into four:
1) Cat. I: Eh,m is the set of eMBB users belonging
to MVNO h, attached to the macro-tier. In addition,
the set of users requesting mMTC slice belonging to
MVNO hand attached to the macro base station, m,
in the macro-tier, is denoted by Mh,m. Furthermore,
the set of vehicles pre-installed with Subscriber Iden-
tity Module (SIM) of MVNO hrequesting URLLC
services is denoted by Rm,h.
2) Cat. II: The set of MVNO heMBB users in the
coverage of a femtocell, f∈ F, is denoted as Eh,f
and similarly, Mh,f for the set of mMTC slice users in
the coverage of a femtocell f∈ F.
3) Cat. III: For the set of slice users belonging to MVNO
h, in the coverage area of a picocell p∈ P, however
which do not fall under the coverage of a clustered
femtocell, pf, is denoted as Eh,p. Likewise, Mh,p
denotes the set of mMTC slice users which are under
the coverage area of p∈ P and not under the coverage
area of a clustered femto cell pf.
4) Cat. IV: Similar to the other categories, Eh,pf denotes
the set of MVNO husers requesting eMBB slice in
the coverage of a clustered femtocell pf ∈ PF . For
MVNO h, users requesting mMTC slice in a clustered
femtocell pf, its set is denoted by Mh,pf . The total
number of cluster c∈ C is the same as |P|.
C. V2X COMMUNICATION MODEL
The set of URLLC users and devices, Rm,h, is modelled
using the D2D-based V2X communication. In this work, we
assume that V2X communication is based on the Cellular-
V2X (C-V2X) rather than the Dedicated Short Range Com-
munications (DSRC). Our assumption is due to the growing
popularity of C-V2X in the vehicle-communications and
manufacturing industry and other reasons in [39], [22], and
[40].
We assume the V2X communication-enabled cars are under
the coverage of the macro base station alone to minimise
the handover signalling. The V2X layer comprises a set
of vehicles (i.e. URLLC slice users engaged in Vehicle-to-
Network (V2N)) R={r|r∈ N ,1≤r≤ |R|} connected to
the macro base station requesting for the URLLC slice. In ad-
dition to the V2X layer, the set of paired vehicles that engage
in Vehicle-to-Vehicle (V2V) communications using the PC5
sidelink is numbered as W={w|w∈ N ,1≤w≤ |W|}.
D. CHANNEL MODEL
Specifically, our paper draws on the downlink of multi-tier
heterogeneous networks based on the link layer model given
in [41], [42] and mobility characteristic of slice users in
modelling the channel. We categorise the channel modelling
into two; (i) Static and moderately mobile Slice users and
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(ii) highly mobile slice users. Without loss of generality, we
assume mMTC and eMBB slice users are in the first category
and the URLLC users in the latter.
1) Static Slice Users
We consider a slice user ihwith a path loss given as [43]:
ρi,j,h =
30 + 35 log(di,j,h),∀ih∈ {Em,h,Mm,h }, j =m
35 + 35 log(di,j,h),∀ih∈ {Ep,h,Mp,h }, j =p
40 + 35 log(di,j,h),
∀ih∈ {Ef,h ,Epf,h ,Mf,h ,Mpf,h }
(1)
where di,j,h denotes the distance of the slice user, ih, belong-
ing to MVNO, hfrom an access point, j∈ {m, f, p, pf }.
The spectrum efficiency of a user ih∈ {Em,h,Mm,h}is
expressed as:
γi,j,h = log21 + ψj,hΓi,j,h
σ2,∀j=m(2)
where ψj,h is the transmit power and Γi,j,h denotes the chan-
nel gain associated with a user ihwhich belongs to MVNO h
and an access point in tier j∈ {m, f, p, pf }. Similarly, for a
user ih∈ {Ef,h ,Mf,h }, its spectrum efficiency is given as:
γi,j,h = log21 + ψj,hΓi,j,h
σ2+X
k∈{F}
j6=k
ψk,hΓi,k ,h (3)
Likewise, for a user ih∈ {Ep,h,Mp,h}, its spectral effi-
ciency is given as:
γi,j,h = log21 + ψj,hΓi,j,h
σ2+X
k∈{P}
j6=k
ψk,hΓi,k ,h (4)
where the terms X
k∈{F}
j6=k
ψk,hΓi,k ,h and X
k∈{P}
j6=k
ψk,hΓi,k ,h in
(3) and (4) denote the co-tier interference associated with the
femto and pico tiers.
For a user ih∈ {Epf,h,Mpf ,h}who subscribes to the
services of MVNO, h, its spectrum efficiency is given as:
γi,j,h = log21 + ψj∈c,h Γi,j∈c,h
σ2+X
p0∈c0
c6=c0X
k∈{PF 0}
j6=k
PF 6=P F 0
ψk,hΓi,k ,h (5)
where ψj,h is the transmit power of the access point in tier
j∈ {m, f, p, pf }.Γi,j,h denotes the channel gain associated
with a user ihwhich belongs to MVNO hand an access point
in tier j∈ {m, f, p, pf }. The double-summation term in (5)
is the inter-cluster interference with respect to the clustered
femtocells in the coverage of the picocells.
2) Highly Mobile Slice Users
Without loss of generality, we assume that the URLLC users
are based on V2X communication [22]. V2X communication
is characterised by highly mobile users or vehicles in this
case. Unlike the static or moderately mobile slice users,
we include the small-scale fast fading component in the
channel model in addition to the large scale factors. For a
URLLC slice user, r∈ R, (engaged in V2N communications
otherwise known as V2I as shown in Fig. 2) the path loss (i.e.
the large scale fading) is expressed as [44]:
ρr,m,h = 128.1 + 37.6 log(dr,m,h)(6)
where dr,m,h is the distance between the URLLC slice user
rand the macrocell m. However, for a vehicle in transmit
mode in the V2V set, W, its path loss model is dependent
on its respective distance from the URLLC slice user-vehicle
and it is given [45] as:
ρw,m,h =
40 + 22.7 log(dr,w,h)
+ 20 log Xc, dr,w,h ≤dthr es
9.45 + 40 log(dr,w,h)−17.3 log(Tw)
−17.3 log(Tr)+2.7 log(Xc), dthres ≤dr,w,h
(7)
where dr,w,h is the distance between the URLLC slice user
rengaged in V2N and a car in transmit mode in the V2V
set. Xc,Twand Trdenote the carrier frequency in GHz,
effective antenna height of the transmit vehicle, w, in V2V
communication and effective antenna height of the receive
vehicle, r, requesting for URLLC slice engaged in V2N. The
threshold distance, dthres, is given as [45]:
dthres =4(Tw)(Tr)Xc
speed of light (8)
Hence, for URLLC slice users, that is for vehicles engaged
in V2N communication, the spectrum efficiency is given as:
γr,m,h = log21 + ψm,hΓr,m,h|αr,m|2
σ2+X
w∈{W}
w6=r
ψwΓw,r,h|αw,r |2(9)
where ψm,h and ψwdenote the transmit powers of the macro
base station in the macro-tier and the transmitting vehicle w
in the V2V set, W. Here, αr,m and αw,r denote the small-
scale fading component. We assume that the small-scale fast
fading component is independent and identically distributed
(i.i.d) as CN (0,1).
III. LATENCY-AWARE AND DYNAMIC RESOURCE
MODEL
In this section, we explain the latency and dynamic resource
allocation model. First, we discuss the Latency and Delay
Model and later the dynamic resource model.
A. LATENCY AND DELAY MODEL
In order to guarantee the service rate of the mMTC and
URLLC slice users within a latency threshold and a trans-
mission delay bound, we consider the link-layer model and
apply the effective capacity theory in [41], [42] which is
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based on the theory of large deviations. We employ the link-
layer model owing to its ease of translating QoS metrics such
as delay bounds and packet loss probability into guarantees;
simple implementation process and high accuracy. The effec-
tive capacity of a slice use case is the maximum arrival rate it
can accommodate to guarantee a QoS requirement which is
specified by a QoS exponent. The effective capacity, being a
robust statistical approach for QoS analysis, employs the QoS
triplets of packets arrival rate λi,h, a maximum delay bound
Dmax and, a delay-bound violation probability threshold µ.
The stochastic behaviour of the mMTC and URLLC slice
user can be modelled by their effective capacity, which is
expressed as [41]:
φ(θi,h) = lim
t→∞
1
t
1
θi,h
log Eeθi,hQt
i,h (10)
where θi,h is the QoS exponent, and Qt
i,h is the source data
(i.e. packet arrivals) over a time interval of [0, t). In this work,
we assume a Poisson traffic process with an arrival rate of
λi,h packets/s. In computing large deviations, we apply the
Moment Generating Function of a Poisson process Qt
i,h with
an arrival rate of λi,h, which is given as [46]:
MQi,h (θi,h) = eλi,h (eθi,h −1) (11)
Substituting (11) into (10), therefore, (10) can be rewritten
as:
φ(θi,h) = 1
t
1
θi,h
log eλi,ht(eθi,h −1) (12)
We simplify (12) and can be expressed as:
φ(θi,h) = λi,h
θi,h eθi,h −1(13)
To ensure that the delay QoS requirement is met, the delay
violation probability should always be less than a given
threshold of µsuch that:
Pr{D(∞)≥Dmax} ≤ µ(14)
Dmax and D(∞)are the maximum delay-bound of a slice a
use case (mMTC and URLLC) and the steady-state delay of
a slice use case. Expression (14) is approximately equal to:
Pr{D(∞)≥Dmax} ≈ e−θi,h λi,hDmax (15)
However, we denote the packet size Li,h and hence
the minimum achievable rate for a bounded de-
lay violation probability of slice user (i.e. ih∈
Mm,h,Mp,h ,Mf,h ,Mpf,h ,Rm,h) is given as:
ϑthres
h=−Li,h log(µ)
Dmax loge(1 −log(µ)
Dmaxλi,h )(16)
The proof of ϑthres
his provided in Appendix A.
B. DYNAMIC RESOURCE ALLOCATION MODEL
In this work, the network resources of the clustered multi-
tier multi-tenant heterogeneous network are pooled and vir-
tualised to a cloud server by the InP and then allocated to the
respective MVNOs contracted to it. The bandwidth allocated
to each MVNO hin each tier tis given as:
X
t∈{m,F,P,PF }
βt,hB(17)
where Bis the total bandwidth of the network and βt,h is the
network slice ratio of the MVNO h, in tier t. For the entire
network, the sum network slice ratio is given as:
X
h∈H X
t∈{m,F,P,PF }
βt,h = 1 (18)
The slice network ratio being dynamic is a function of slice
user distribution and location, cell load characteristics, user
slice use case QoS requirement; BS-User association, Inter-
ference and slice user mobility characteristics. For a user with
a user-slice ratio, ϕi,j,m, which is dependent on the above
mentioned factors, its logarithmic utility is given as:
log ϑi,j,h= log Bβt,h ϕi,j,h γi,j,h (19)
Then, the question arises, how can network resources be
dynamically allocated to MVNO and slice users while guar-
anteeing the slice use case QoS requirement?
IV. PROBLEM FORMULATION
In this section, the problem of latency-aware requirement
and dynamic allocation of radio resources in a multi-tier
multi-tenant heterogeneous 5G Network in a network slicing
scenario is examined. In order to fully maximise the capacity
of the network, we formulate a joint user-association InP-
MVNO resource allocation problem in (20).
max X
h∈H "X
i∈(Em,h∪Mm,h ∪Rm,h)
log ϑi,m,h+X
f∈F X
i∈(Ef,h∪Mf ,h)X
j∈{m,f}
δi,j,h log(ϑi,j,h)
+X
p∈P X
i∈(Ep,h∪Mp,h )X
j∈{m, p}
δ0
i,j,h log ϑi,m,h+X
p∈P X
pf∈PF X
i∈(Epf,h∪Mpf ,h)X
j∈{m, p, pf}
δ00
i,j,h log ϑi,m,h#
(20)
s.t.
C1:ϑi,m,h ≥λh,EmLh,Em∀i∈ Em,h,∀h∈ H
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C2:ϑi,m,h ≥ϑthres
h∀i∈ Mm,h,∀h∈ H
C3:ϑi,m,h ≥ϑth
h∀i∈ Rm,h,∀h∈ H
C4:δi,j,hϑi,m,h −ϑthres
h≥0∀i∈ Mf,h , j ∈ {m, f },∀h∈ H
C5:δi,j,hϑi,m,h −λh,EmLh,Em≥0∀i∈ Ef ,h, j ∈ {m, f },∀h∈ H
C6:δ0
i,j,hϑi,m,h −ϑthres
h≥0∀i∈ Mp,h, j ∈ {m, p},∀h∈ H
C7:δ0
i,j,hϑi,m,h −λh,EpLh,Ep≥0∀i∈ Ep,h , j ∈ {m, p},∀h∈ H
C8:δ00
i,j,hϑi,m,h −ϑthres
h≥0∀i∈ Mpf,h , j ∈ {m, p, pf},∀h∈ H
C9:δ00
i,j,hϑi,m,h −λh,Epf Lh,Epf ≥0∀i∈ Epf ,h, j ∈ {m, p, pf },∀h∈ H
C10:X
j∈{m,f}
δi,j,h = 1 ∀i∈(Ef,h ∪ Mf,h )
C11:X
j∈{m, p}
δ0
i,j,h = 1 ∀i∈(Ep,h ∪ Mp,h)
C12:X
j∈{m, p, pf}
δ00
i,j,h = 1 ∀i∈(Epf,h ∪ Mpf,h )
C13:δi,j,h ∈ {0,1} ∀ i∈(Ef,h ∪ Mf,h ), j ∈ {m, f },∀h∈ H
C14:δ0
i,j,h ∈ {0,1} ∀ i∈(Ep,h ∪ Mp,h), j ∈ {m, p},∀h∈ H
C15:δ00
i,j,h ∈ {0,1} ∀ i∈(Epf,h ∪ Mpf,h ), j ∈ {m, p, pf},∀h∈ H
C16:X
i∈(Em,h∪Mm,h ∪Rm,h)
ϕi,m,h +X
f∈F X
i∈(Ef,h∪Mf ,h)
δi,j,hϕi,m,h +X
p∈P X
i∈(Ep,h∪Mp,h )
δ0
i,j,hϕi,m,h +
X
p∈P X
pf∈PF X
i∈(Epf,h∪Mpf ,h)
δ00
i,j,hϕi,m,h = 1
C17:X
f∈F X
i∈(Ef∪Mf)
δi,f,h ϕi,f,h = 1 ∀h∈ H
C18:X
p∈P X
i∈(Ep,h∪Mp,h )
δ0
i,p,h ϕi,p,h +X
p∈P X
pf∈PF X
i∈(Epf,h∪Mpf ,h)
δ00
i,p,hϕi,p,h = 1 ∀h∈ H
C19:X
p∈P X
pf∈PF X
i∈(Epf,h∪Mpf ,h)
δ00
i,pf,hϕi,pf ,h = 1 ∀h∈ H
C20:ϕi,m,h ∈(0,1) i∈(Em,h ∪ Mm,h ∪ Ef,h ∪ Mf,h ∪ Ep,h ∪ Mp,h ∪ Epf ,h ∪ Mpf,h )
C21:ϕi,f,h ∈(0,1) i∈(Ef,h ∪ Mf ,h)
C22:ϕi,p,h ∈(0,1) i∈(Ep,h ∪ Mp,h ∪ Epf,h ∪ Mpf,h )
C23:ϕi,pf,h ∈(0,1) i∈(Epf,h ∪ Mpf,h )
The utility of each MVNO is the summation of the utility
(or rate) of the four categories of slice users explained in
Section II (B) and therefore, the network’s sum utility is the
maximisation of the several MVNOs utility which is given
in (19). As shown in (20), the constraints C1, C5, C7and
C9ensure that the minimum achievable data rate for eMBB
slice users is guaranteed in all tiers. In addition, constraints
C2, C4, C6, and C8ensure that the minimum achievable
rate of the latency-aware mMTC slice users is guaranteed in
all tiers. For the URLLC users, constraint C3ensures that
the latency-aware received data rate is above the minimum
threshold. Constraints C10, C11 and C12 impose the slice
user-access point association constraints; a slice user can
only be associated with one access point at a point in time.
Constraint C10 ensures that a category II slice user is either
associated with a femtocell f, or the macrocell m. Besides,
C11 imposes the constraint that a category III slice user is
either associated with a picocell p, or the macrocell m; while
constraint C12 is to ensure that a category IV slice user
is associated with a clustered femtocell pf, or its closest
picocell p, or the macrocell m. Constraints C13-C15 are
the relaxation of constraints C10-C12. From the foregoing,
constraints C16-C19 in general highlight the bandwidth al-
location requirement of the individual slice users in each of
the tiers. The constraints for the bandwidth user-slice ratio
for each user in the different tiers are given in C20-C23. The
user-slice ratio is a fractional allocation indicator which must
be between 0and 1i.e. a positive fractional value.
V. PROPOSED SOLUTION
In this section, we present the detailed description of the
proposed solution to the latency-aware dynamic resource
allocation problem in a multi-tier multi-tenant heterogeneous
network stated in (20). First, we simplify (20) by trans-
forming the objective function into a tractable expression.
The transformed expression is a summation of the utilities
of the MVNOs in the 5G multi-tier network.This is done
by considering each term of the objective function in (20)
and transforming as follows in (21). In order to solve
(21), each term is expressed to fully capture its essence.
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X
h∈H
ϑmϕi,m,h +X
h∈H X
f∈F
ϑfϕi,f,h +X
h∈H X
p∈P
ϑpϕi,p,h +X
h∈H X
p∈P X
pf∈PF
ϑpf ϕi,pf,h (21)
X
h∈H
ϑmϕi,m,h =
net utility from users within monly
z }| {
X
h∈H X
i∈Em,h∪Mm,h ∪Rm,h
log Bβm,h ϕi,m,h γi,m,h+
net utility from users associated with mbut located within f
z }| {
X
h∈H X
f∈F X
i∈E0
f
E0
f={l∈Ef,h∪Mf ,h|δl,m,h =1}
log Bβm,h ϕi,m,h γi,m,h
+
utility from users associated with mbut within p
z}| {
X
h∈H X
p∈P X
i∈E0
p
E0
p={q∈Ep,h∪Mp,h |δ0
q,m,h=1}
log Bβm,h ϕi,m,h γi,m,h+
net utility from users associated with mbut within pf
z }| {
X
h∈H X
p∈P X
pf∈PF X
i∈E0
pf
E0
pf ={r∈Epf,h∪Mpf ,h|δ00
r,m,h=1}
log Bβm,h ϕi,m,h γi,m,h (22)
Herein, P
h∈H
ϑmϕi,m,h denotes the aggregate utility of slice
users associated to the macrocell and is given in (22). The
aggregate utility of slice users associated with the femtocell
is given by:
X
h∈H X
f∈F
ϑfϕi,f,h =
net utility from users associated with fbut only located within f
z }| {
X
h∈H X
f∈F X
i∈E0
f
E0
f={l∈Ef∪Mf|δl,f,h=1}
log Bβf,h ϕi,f,h γi,f ,h
(23)
Likewise from (21), P
h∈H P
p∈F
ϑpϕi,p,h which denotes the
aggregate utility of slice users associated to the picocell is
given as:
X
h∈H X
p∈F
ϑpϕi,p,h =
net utility from users associated with pbut only located within p
z }| {
X
h∈H X
p∈P X
i∈E0
p
E0
p={q∈Ep∪Mp|δ0
q,p,h=1}
log Bβp,h ϕi,p,h γi,p,h
+
net utility from users associated with pbut within pf
z }| {
X
h∈H X
p∈P X
pf∈PF X
i∈E00
p
E00
p={r∈Epf ∪Mpf |δ00
r,p,h=1}
log Bβp,h ϕi,p,h γi,p,h (24)
The net utility from all slice users associated with the clus-
tered femtocells is denoted by P
h∈H P
p∈P P
pf∈PF
ϑpf ϕi,pf,h
and given as:
X
h∈H X
p∈P X
pf∈PF
ϑpf ϕi,pf,h =
net utility from users associated with pf and only within pf
z }| {
X
h∈H X
p∈P X
pf∈PF X
i∈E00
p
E00
p={r∈Epf ∪Mpf |δ00
r,pf,h =1}
log Bβp,h ϕr,pf,h γr,pf ,h (25)
To further transform (22) - (25), the following Lemma is quite
important.
Lemma 1. Given that f=a×b. Hence logz(f) = logz(a×
b). Therefore,
logz(a×b) = logz(a) + logz(b)(26)
By Lemma 1, the logarithmic expression in (22) can be
expressed as:
log Bβm,h ϕi,m,h γi,m,h=
log Bβm,h γi,m,h+ log ϕi,m,h(27)
Similarly by Lemma 1, for (23);
log Bβf,h ϕi,f,h γi,f ,h=
log Bβf,h γi,f,h + log ϕi,f,h (28)
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Likewise for (24),
log Bβp,h ϕi,p,h γi,p,h=
log Bβp,h γi,p,h+ log ϕi,p,h(29)
By Lemma 1, the logarithmic term in (25) can be simplified
as:
log Bβpf,h ϕi,pf,h γi,pf,h=
log Bβpf,h γi,pf,h+ log ϕi,pf ,h(30)
The expression for ϕi,j,h is presented in Appendix B. With
(27) - (30), the optimisation problem in (20) is solved with
βt,h being the decision variable. The hierarchical decompo-
sition method [35] is adapted in solving (20) and the base
station-slice user association is solved first in order to reduce
the complexity of solving (20).
A. THE BASE STATION-SLICE USER ASSOCIATION
In the multi-tier heterogeneous network, the base station-
slice user association is formulated as an integer program-
ming problem [47] [48]. It is given as:
max
δX
h∈H X
j∈J X
i∈I
δi,j,h (31)
subject to
C24 :X
j
δi,j,h ≤1; ∀h, ∀i, j ∈ {f, p, pf }
C25 :δi,j,h ∈ {0,1};∀h, ∀i, j ∈ {f, p, pf }
The base station-slice user association optimisation problem
in (31) is adapted to the respective tiers taking into con-
sideration the index of the association indicator for each
tier. Constraint C24 is to ensure that the slice user can
only be associated with one base station or access point.
Constraint C25 is to ensure that the base station-slice user
association indicator is Boolean. In this work, a maximum
SINR matching algorithm is developed to solve the sub-
problem in (31). The many-to-one matching [49] concept is
adapted owing to its practical applications to heterogeneous
wireless networks. Fig. 3 depicts the base station-slice user
matching game for the multi-tier heterogeneous network and
the different categories of the slice users. Consequently, we
develop Algorithm 2to solve (31) following the matching
concept in Fig. 3
B. CONTINUOUS GENETIC ALGORITHM
We solve the transformed dynamic resource allocation prob-
lem in a multi-tenant multi-tier network in network slice
scenario via the Continuous Genetic Algorithm (CGA). We
adapt the Genetic Algorithm (GA) in solving the maximisa-
tion problem (20) owing to its robustness and effectiveness
1Uh,s = (Eh,m ∪ Eh,f ∪ Eh,p ∪ Eh,pf ∪ Mh,m ∪ Mh,f ∪ Mh,p ∪
Mh,pf ∪ Rh,m)
FIGURE 3: Base station-slice user Matching Game
Algorithm 1 Latency-aware Dynamic Resource Allocation
1: for h←1to |H| do
2: for Sh←to {E ∪ M ∪ R} do
3: for i∈ Uh,s1do
4: optimally associate to an access point (Alg. 2)
and (31)
5: determine user cat. using Subsection II-B
6: end for
7: end for
8: for t← {m, F,P,PF } do
9: for k← {m, p, pf, f }do
10: for i∈ Uh,s do
11: determine γi,k,h (2)-(5), (9)
12: determine ϑthres
h(10) - (16)
13: end for
14: determine the cell load characteristics (22)-(25)
15: end for
16: optimally determine βt,h (17)-(19)
17: end for
18: for Sh←to {E ∪ M ∪ R} do
19: for i∈ Uh,s do
20: dynamically allocate radio resources (20), (Alg.
3)
21: end for
22: end for
23: end for
in finding the global optimal solutions compared to most
heuristic algorithms [50]. Consequently, the GA can handle
all kinds of optimisation problems and any constraints, such
as linear and non-linear. In particular, the CGA, widely
acknowledged for its high precision in representing solutions
without extra-long strings of the chromosomes, hence its
low computational complexity, less storage requirement and
faster speeds [51], [52].
It is a stochastic search algorithm which is based on the
principle of natural selection, biological reproduction and
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Algorithm 2 Base Station-Slice User Association
Input: ψj,h,di,j,h
1: if iis under the coverage of a femtocell then
2: if femtocell is clustered then
3: Calculate: γi,m,h,γi,p,h ,γi,pf ,h (2), (4), (5)
4: if γi,pf,h ≥(γi,m,h &γi,p,h)then
δ00
i,pf,h = 1
5: else
6: if γi,p,h ≥(γi,m,h &γi,pf,h)then
δ00
i,p,h = 1
7: else
8: δ00
i,m,h = 1
9: end if
10: end if
11: break;
12: else
13: Calculate γi,m,h,γi,f ,h (2), (3)
14: if γi,f,h ≥γi,m,h then
15: δi,f,h = 1
16: else
17: δi,m,h = 1
18: end if
19: break;
20: end if
21: else
22: Calculate γi,p,h,γi,m,h (4), (5)
23: if γi,p,h ≥γi,m,h then
24: δ0
i,p,h = 1
25: else
26: δ0
i,m,h = 1
27: end if
28: end if
genetics [53], [54]. It starts with an initial randomly gen-
erated set of solutions otherwise called the population. The
population satisfies the boundary conditions of the optimi-
sation at hand. Each individual in the population is called a
chromosome. A chromosome is a standard representation of
solutions, otherwise called genes [55].
The GA determines the fitness of each chromosome in the
population via the objective function in (20). In this work,
the chromosomes with the best fitness values are selected
via the roulette wheel technique, thus creating the different
set of pairs referred to as parents for a crossover which is
significantly governed by the probability of crossover Pc. The
crossover process results in new chromosomes, otherwise
called children. In order to mimic the process of natural
reproduction, the genes of the children are mutated at birth,
giving rise to a new population. The fitness of the new pop-
ulation is evaluated, and by means of elitism a small fraction
of the best individuals from the old population are retained
in the new population, and the others are discarded. This
process is illustrated in Fig. 4 and corresponding parameter
values given in Table 2.
Algorithm 3 CGA-Based Radio Resource Allocation
Input: Pm,Pc,Pe, g, y,t,H
1: number of genes, n=|t| ·|H|
2: Initialise the random population A=y×n
A=
β11 β12 · · · β1n
β21 β22 · · · β2n
.
.
..
.
.....
.
.
βy1βy2· · · βyn
3: while iteration ≤gdo
4: iteration = iteration + 1;
5: Evaluate the fitness Uyof each chromosome in A
U=U1U2· · · Uy
6: Normalise the fitness vector U
ˆ
U=U
kUk
7: Sort
ˆ
Uin descending order
[∼, index] = Sort (
ˆ
U, ‘descend’)
8: Sort the population Aaccording to index
A=A(index:)
9: Select the Chromosome in Awrt. the sorted fitness
ˆ
U
using the roulette wheel section.
The probability of a chromosome kbeing selected Pk
is given as
Pk=
ˆ
U
y
X
z=1
ˆ
Uz
10: Carry out crossover using the Pc
11: Mutate the genes of chromosomes with Pm
12: Perform elitism on the initial population wrt. Pe
13: Select population
14: end while
TABLE 2: GA Parameters and Values
Parameter Value
Probability of Elitism (Pe) 0.2
Probability of Crossover (Pc) 0.95
Probability of Mutation (Pm) 0.9
Max. No. of Iteration (g)30
No. of Chromosomes (y)700
The pseudocode of the CGA-based radio resource allocation
algorithm is shown in Algorithm 3. The algorithm follows
the procedure of the GA model in Fig. 4.
C. SPATIAL BRANCH AND BOUND ALGORITHM
A spatial branch and bound (sBB) method [37] is adapted
to solve the maximisation problem in (20) in order to
verify the optimality of the CGA-based results. The sBB
algorithm gives a globally optimal solution, and it is shown
VOLUME 4, 2016 11
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GAParameters
Initialization Population
Selection
(Roulette
Wheel)
CrossOver Mutatation New
Population
Fitness
Evaluation
Elitism
Discard
Fitness
Evaluation
BestFitness
(onMax
Iteration)
FIGURE 4: The GA process.
in Algorithm 4. The sBB is a widely used deterministic
search algorithm to solve the optimisation problem owing
to its exact solutions [56]. The sBB iteratively searches
the solution space of the defined problem. The wide range
of solutions in the search space forms a hierarchical tree
taking into consideration the upper and lower bounds of the
solutions. These sets of feasible solutions are evaluated with
respect to the objective function. If the evaluated solution
does not result in a better solution than the current best
solution, then it is discarded; however, if it is a better solution,
the current best solution is discarded while the evaluated
solution becomes the current best solution. This procedure
is repeated until an optimal solution is discovered [57],
[58]. The pseudo code of the sBB algorithm is illustrated
in Algorithm 4.
VI. COMPLEXITY ANALYSIS
We examine the algorithms discussed in Section V. Herein,
we focus on the time complexity of the algorithms. The
time complexity is employed to determine the worst-case
running time of an algorithm. Furthermore, we employ the
big Omicron (big-O) in our characterisation of the algo-
rithms. The big-Onotation gives a theoretical measure of the
upper bound or worst-case scenario of the growth rate con-
cerning the execution time (or memory) of an algorithm or a
function. A detailed explanation of the big-Ois given in [59],
[60]. First, we examine the time complexity of the CGA and
we further our analysis of the sBB algorithm. Additionally,
we discuss the Latency-aware dynamic resource algorithm
and, finally, the ORA resource allocation algorithm.
A. COMPUTATIONAL COMPLEXITY OF THE CGA
The computational complexity of the GA and other evolu-
tionary meta-heuristics are quite difficult to determine owing
to their stochastic behaviour. However, the big-Onotation of
the CGA adopted in this paper is given by O(g(y·n(t, |H|))),
where gdenotes the number of generation, yrepresents the
Algorithm 4 Spatial BnB-Based Radio Resource Allocation
1: Initialise the upper bound, ωub, of (20)
Set the list of region Gto a single domain
2: Use the least lower bound rule to choose a subregion A ∈
G
3: while G 6=∅do
4: if ωA,lb ≥ωub −πthen
5: Delete Afrom G
6: else
7: if ωA,ub > ωub then
8: Partition A into subregions Aleft and Arig ht
9: else
10: ωub =ωA,ub
11: Delete all subregions in G
12: if ωA,ub −ωA,lb ≤πthen
13: Delete Afrom G
14: end if
15: end if
16: end if
17: end while
18: if ωub =∞then
19: problem is infeasible
20: else
21: ωub is the global optimal of the solution
22: end if
number of chromosomes, and ndenotes the size of the genes
in a chromosome, which in this paper is a function of both
the number of the tiers tin the network and the number of
MVNOs |H|.
B. COMPUTATIONAL COMPLEXITY OF THE SBB
The time complexity of the sBB method depends on the size
of the search tree. However, it is pertinent to note that the
time complexity does not include the time for executing the
branching rule or inserting nodes in the queue. sBB decom-
poses non-linear or non-convex objective functions symboli-
cally and recursively into simple operations by applying sim-
12 VOLUME 4, 2016
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ple operations [61] such as linear over- and underestimators
given in [62]. Furthermore, an integer linear programming
is NP-hard, hence optimal solutions would mostly require
exponential upper bound (i.e. worst case) run time in tandem
with input size [63], [64]. Therefore, the time complexity of
the sBB is given by O(2t·|H|).
C. COMPUTATIONAL COMPLEXITY OF THE
LATENCY-AWARE DYNAMIC RESOURCE ALLOCATION
Furthermore, we examine the time complexity of the latency-
aware dynamic resource allocation in a multi-tier multi-
tenant network. It is given by O(|H|· t· |Sh|). The time com-
plexity of the ORA is given in [38] as O(KM log( 1
)+ M3),
where Mis the number of slice users and we have adapted
Kto be 1 to fit into the multi-tier multi-tenant slice network.
VII. NUMERICAL RESULTS
In this section, the performance of the proposed genetic
algorithm (GA) intelligent latency-aware resource allocation
scheme (GI-LARE) is evaluated via Monte Carlo based com-
puter simulations in a Matlab environment. We considered
a multi-tier multi-tenant network of MVNOs operating in an
area of interest of 950m radius. The macro station was placed
at the centre and surrounded with femtocells and picocells,
which had a coverage radius of 50m and 250m, respectively.
The multi-tier network consisted of 7femtocells, 4picocells
and 5clustered femtocells per picocells. Furthermore, the
transmit powers budget of 15dBm,30dBm,36.9dBm, and
40dBm for V2V transmit mode, femtocells, picocells and the
macrocell was considered. The different categories of slice
users were randomly distributed across the different access
points in all the tiers with a data packet arrival rate of 5
packet/s,20 packet/s, and 20 packet/sfor mMTC, eMBB
and URLLC slice use cases with packet size of 1000bits,
9000bits, and 500bits, respectively. In addition, for URLLC
slice users, we assumed the vehicles were moving at a ve-
locity of 60Km/hr on a 4-lane highway with a lane width
of 4m. For each simulation, 10000 iterations were generated
and then averaged to obtain a numerical result.
A. IMPACT OF THE SLICE USER DENSITY
First, we evaluate the performance of the proposed algorithm
with different network parameters. With an assumed maxi-
mum delay bound of 100ms and a maximum delay bound
violation of 0.001, we investigate the impact of varying the
slice user density on the network slice ratio per tier for each
MVNO respectively and also its impact on the total network
utility. In Fig. (5), the impact of the slice user density on
the network slice ratio, βh,t is studied. We consider the
different densities of slice users in the range of 4to 7for
the respective slice categories in the different tiers for the 3
MVNOs. The proposed GI-LARE is compared with a Static
resource scheme and also an exact solution from the sBB
scheme. In Fig. 5(a), Fig. 5(b) and Fig. 5(c), we investigate
the performance of the algorithms with a slice user density
of 4. Fig. 5(d) to Fig. 5(f) show the results of the GI-
LARE, sBB-based and SS Schemes for a user density of
5. Similarly, Fig. 5(g) to Fig. 5(i) show the results of the
respective schemes when the user density is set to 6. Finally,
Fig. 5(j) to Fig. 5(l) show the results of the GI-LARE, sBB-
based and SS schemes with user density of 7. We observe
that unlike the SS scheme, the GI-LARE and the sBB-based
schemes dynamically respond to the variation of the user
density in the respective tiers and MVNOs. The dynamic
scheme ensures fairness in the different tiers while at the
same time maximising the network utility.
From the foregoing, we investigate the impact of the user
density on the network utility. Fig. 6 shows the impact of the
user density on the total network utility. Similar to Fig. 5, the
user density is set between 3and 10 slice users. It is observed
that as the user density increases, the total network utility
increases owing to the increase in the utilisation of network
resources. The GI-LARE scheme outperforms the SS (Static
scheme) by an average of 25%, however its performance
is almost the same as sBB-based scheme which gives a
global optimum. Besides, the GI-LARE scheme outperforms
the ORA when adopted to the multi-tier multi-tenant slice
network.
B. IMPACT OF THE NETWORK BANDWIDTH
Fig. 7 and Fig. 8 present the effect of the total bandwidth of
the network on network utility. In Fig. 7, we vary the total
network bandwidth from 200MHz to 700MHz and set the
user density at 5users and the delay bound at 1ms. From
Fig. 7, we can observe that the network utility increases as the
total bandwidth of the network increases. This is owing to the
fact that the utility increases as more resources are available
to the network slice users. Similarly, in Fig. 8, the delay
bound is set at 10ms and a user density of 5users. Similar
to Fig. 7, we observe that the network utility increases as the
total bandwidth of the network increases. However, with a
relax delay bound constraint of 10ms, the network utility is
quite higher than that of the 1ms but with a compromise on
the QoE. In both Fig. 7 and Fig. 8, the GI-LARE outperforms
the SS and ORA schemes.
C. IMPACT OF THE DELAY BOUND
In Fig. 9 and Fig. 10, we show the impact of the delay bound
on the network utility and effective bandwidth. With a user
density of 2users and a network bandwidth of 100MHz,
in Fig. 9, we present the impact of the delay bound on the
network utility. Similar to Fig. 7 and Fig. 8, there is a rapid
increase in network utility for a delay bound relaxation from
1ms to 10ms; however, with a limited network resource,
the utility remains constant despite the increase in the delay
bound. Fig. 10 shows the effect of the delay bound on the
effective bandwidth. As seen in constraints C2, C3, C5and
C6, the effective bandwidth greatly affects the received rate
of the mMTC and URLLC slice users. We observe that as
the maximum delay bound increases, the threshold decreases
which is in tandem with (16).
VOLUME 4, 2016 13
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(a) GI-LARE scheme with a user density of 4 (b) sBB-based scheme with a user density of 4 (c) SS with a user density of 4
(d) GI-LARE scheme with a user density of 5 (e) sBB-based scheme with a user density of 5 (f) SS with a user density of 5
(g) GI-LARE scheme with a user density of 6 (h) sBB-based scheme with a user density of 6 (i) SS with a user density of 6
(j) GI-LARE scheme with a user density of 7 (k) sBB-based scheme with a user density of 7 (l) SS with a user density of 7
FIGURE 5: Impact of the slice user density on the Network
Slicing ratio βt,h
14 VOLUME 4, 2016
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D. IMPACT OF THE PACKET SIZE
Fig. 11 and Fig. 12 present the impact of the eMBB data
packet size on the network utility. In Fig. 11, with a delay
bound of 1ms, a user density of 5users and a total network
bandwidth of 200MHz, it can be observed that as the packet
size increases, the net utility increases to about 2000 bits and
then a dip occurs in the net utility. This can be ascribed to
the bandwidth and power limitation of the network. However,
the GI-LARE scheme outperforms the SS and ORA resource
allocation schemes. Similar to Fig. 11, in Fig. 12, we further
study the impact of the packet size on the network utility with
delay bound and user density parameters set at 100ms and 5
users and follows the same trend with Fig. 11. However, the
network utility fared better at a delay bound of 100ms than at
a delay bound of 10ms.
E. IMPACT OF THE PACKET LOSS PROBABILITY
Fig. 13 shows the impact of the packet loss probability on the
network utility. Typically, the packet loss includes loss due
to errors in the network, buffer overflows and late arrivals of
packets. We vary the packet loss probability range from 10−5
to 10−1, with a user density of 5users; a delay bound of
10ms; and a bandwidth of 200MHz. Although the network
utility increases with lower packet loss probability, the GI-
LARE outperforms the SS and ORA resource allocation
schemes. The lower the packet loss probability, the higher
the probability that the packets are received. Consequently,
we observe from Fig. 13 that the performance of the network
can be improved by ensuring the packet loss probability value
is low. Moreover, we observe that at a packet loss probability
value of greater than 1, the network revenue and ultimately
the performance of the network significantly degrades.
F. IMPACT OF THE COVERAGE RADIUS
Fig. 14 and Fig. 15 present the impact of the coverage radius
of the femtocells and picocells on the network utility. We
vary the coverage radius range from 10m to 100m and set
the delay bound at 10ms, with a network bandwidth of
100MHz. We observe that the network utility increases when
the coverage radius reduces. This is owing to better channel
conditions of the respective slice users. Similar to Fig. 14, in
Fig. 15, we examine the impact of the coverage radius of the 4
picocells on the network utility. We vary the coverage radius
range from 200m to 300m and set the delay bound of 10ms.
In the same trend with the femtocells, we observe that the
network utility increases when the coverage radius reduces.
However, it is not as significant that of the femtocells, as a
result of the closeness of the femtocells to the slice users.
3456789
Slice Users Average Arrival Rate
0.5
1
1.5
2
2.5
3
Total Utility of the Network
104
sBB
GI-LARE
SS
ORA
FIGURE 6: Effect of the slice user density on the total utility
of the network
200 250 300 350 400 450 500 550 600 650 700
Total Bandwidth of the Network (MHz)
0.95
1
1.05
1.1
1.15
1.2
1.25
Total Utility of the Network
104
sBB
GI-LARE
SS
ORA
FIGURE 7: Impact of the total bandwidth on the total utility of
the network at 1ms delay bound
200 250 300 350 400 450 500 550 600 650 700
Total Bandwidth of the Network (MHz)
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
Total Utility of the Network
104
sBB
GI-LARE
SS
ORA
500 550 600
1.72
1.725
1.73
1.735
1.74
104
FIGURE 8: Impact of the total bandwidth on the total utility of
the network at 10ms delay bound
VOLUME 4, 2016 15
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0 10 20 30 40 50 60 70 80 90 100
Maximum Delay Bound (ms)
7100
7200
7300
7400
7500
7600
7700
7800
7900
8000
Total Utility of the Network
sBB
GI-LARE
SS
ORA
1 2 3 4 5
7300
7400
7500
7600
7700
7800
7900
8000
FIGURE 9: Effect of the delay bound on the total utility of the
network
100 120 140 160 180 200 220 240 260 280 300
Maximum Delay Bound, D (s)
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Effective Bandwidth threshold, (bits/s)
104
FIGURE 10: Effect of the maximum delay bound on the
effective bandwidth threshold
0 1000 2000 3000 4000 5000 6000 7000
eMBB Packet Size (bits)
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
Total Utility of the Network
104
sBB
GI-LARE
SS
ORA
FIGURE 11: Impact of the eMBB data packet size on the total
network utility at 1ms delay bound
0 1000 2000 3000 4000 5000 6000 7000
eMBB Packet Size (bits)
1.46
1.48
1.5
1.52
1.54
1.56
1.58
1.6
1.62
1.64
Total Utility of the Network
104
sBB
GI-LARE
SS
ORA
5400 5600 5800 6000
1.58
1.59
1.6 104
FIGURE 12: Impact of the eMBB data packet size on the total
network utility at 100ms delay bound
10-5 10-4 10-3 10-2 10 -1 100
Packet Loss Probability
1.4
1.45
1.5
1.55
1.6
1.65
Total Utility of the Network
104
sBB
GI-LARE
SS
ORA
FIGURE 13: Impact of the Packet loss probability on the total
network utility
0 10 20 30 40 50 60 70 80 90 100
Coverage radius of the femtocells (m)
7000
7200
7400
7600
7800
8000
8200
8400
Total Utility of the Network
sBB
GI-LARE
SS
ORA
80 90 100
7600
7650
7700
7750
FIGURE 14: Effect of the Coverage radius of the femtocells
on the network utility
16 VOLUME 4, 2016
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200 210 220 230 240 250 260 270 280 290 300
Coverage radius of the Picocells (m)
7550
7600
7650
7700
7750
7800
7850
7900
7950
8000
Total Utility of the Network
sBB
GI-LARE
SS
ORA
FIGURE 15: Effect of the Coverage radius of the picocells on
the network utility
VIII. CONCLUSION
In this paper, we have proposed a genetic algorithm (GA)
intelligent latency-aware resource allocation scheme (GI-
LARE) that explicitly considered the latency and data rate
constraints slices in a multi-tenant, multi-tier heterogeneous
network. The optimisation problem was transformed and
solved via the hierarchical decomposition method. Slice
users were associated with base stations in different tiers
by the concept of matching game theory, and the latency-
aware dynamic resource allocation problem is solved using
GI-LARE. Using the Monte Carlo simulation, GI-LARE was
compared with the sBB-based, static slicing resource allo-
cation (SS) and optimal resource allocation (ORA) schemes
under different scenarios. Our dynamic GI-LARE scheme is
shown to have outperformed the SS approach.
With the successes in the field of machine learning (ML) and,
by extension, deep learning (DL) and generative adversarial
network (GAN), together with the increasing influence of big
data in mobile networks, the challenge of latency-aware dy-
namic resource allocation in a multi-tenant multi-tier network
could be approached from the ML perspective. Our future
work would address the dynamic resource allocation problem
in a multi-tier, multi-tenant network slicing by adopting the
concept of GAN.
APPENDIX A
Combining (14) and (15), we have:
e−θi,hλi,h Dmax ≤µ(32)
Taking the logarithms of both sides of (32), this yields:
−θi,hλi,h Dmax = logeµ(33)
where λi,h can also be said to be the minimum achievable
rate in packet/s of slice i(i.e. Mm,h,Mp,h ,Mf,h ,Mpf,h ,
Rm,h). From (33), we express λi,h as:
λi,h =−logeµ
θi,hDmax
(34)
Based on the effective bandwidth theory, the delay-bound
violation probability threshold can be guaranteed if and only
if the effective bandwidth is equal to the minimum achievable
rate. Therefore, from (13) and (34), we have:
−logeµ
θi,hDmax
=λi,h
θi,h eθi,h −1(35)
Therefore, eθi,h can be expressed as:
eθi,h = 1 −logeµ
λi,hDmax
(36)
Consequently from (36), θi,h is given as:
θi,h = loge1−logeµ
λi,hDmax (37)
Note the unit of λi,h in (34) is packet/s and it can be
transformed to bit/s by multiplying (34) by the packet size
Li,h. From the foregoing, by substituting (37) into (34), we
now have the minimum achievable rate bounded by the delay
violation probability, ϑthres
h, for a user which is given as:
ϑthres
h=−Li,h log(µ)
Dmax loge(1 −log(µ)
Dmaxλi,h )(38)
APPENDIX B
The slice user ratio is a function of the aggregate number
of slice users associated to an access point in a tier. Taking
a holistic look at (22), constraints C16, and C20,ϕi,m,h is
given as:
ϕi,m,h =
1
Em,h+Mm,h +Rm,h+P
f∈F P
l∈Ef,h∪Mf ,h
δl,m,h
+P
p∈P P
q∈Ep,h∪Mp,h
δ0
q,m,h
+P
p∈P P
pf∈PF P
r∈Epf,h∪Mpf ,h
δ00
r,m,h
(39)
For ϕi,f,h, taking into consideration (23), C17 and C21, it
can be expressed as:
ϕi,f,h =1
"X
f∈F X
l∈Ef,h∪Mf ,h
δl,f,h #(40)
VOLUME 4, 2016 17
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Similarly, for ϕi,p,h, taking into consideration (24), C18 and
C22, it can be expressed as:
ϕi,p,h =
1
"X
p∈P X
q∈Ep,h∪Mp,h
δ0
q,p,h +X
p∈P X
pf∈PF X
r∈Epf,h∪Mpf ,h
δ00
r,p,h#
(41)
The user slice ratio in the clustered femtocells, ϕi,pf,h look-
ing at (25), C19 and C23, is expressed as:
ϕi,pf,h =1
"X
p∈P X
pf∈PF X
r∈Epf,h∪Mpf ,h
δ00
r,f,h#(42)
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SUNDAY OLADAYO OLADEJO received the
B.Eng degree in electrical and electronic engineer-
ing from the Federal University of Technology,
Akure, Nigeria, in 2004 and the M.Eng degree in
communication engineering from the Federal Uni-
versity of Technology, Minna, Nigeria, in 2016.
He is currently pursuing a PhD degree in electrical
engineering at the University of Cape Town, South
Africa.
From 2007 to 2017, he was Senior Core Net-
work Engineer with Glo-Mobile, Nigeria. His research interest includes
radio resource management in wireless networks, and artificial intelligence.
OLABISI EMMANUEL FALOWO received his
PhD in electrical engineering at the University of
Cape Town, South Africa, in 2008. He is currently
an Associate Professor in the same department.
He has published over 100 technical papers in
peer-reviewed conference proceedings and jour-
nals. His primary research interest is in radio
resource management in heterogeneous wireless
networks. Olabisi Falowo is a senior member of
the IEEE.
VOLUME 4, 2016 19
