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Mobile Edge Computing Resources Optimization: a
Geo-clustering Approach
Mathieu Bouet, Vania Conan
To cite this version:
Mathieu Bouet, Vania Conan. Mobile Edge Computing Resources Optimization: a Geo-clustering
Approach. IEEE Transactions on Network and Service Management, IEEE, 2018, 15 (2), pp.787-796.
�10.1109/TNSM.2018.2816263�. �hal-02065474�
1
Mobile Edge Computing Resources Optimization:
a Geo-clustering Approach
Mathieu Bouet, Vania Conan
©2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including
reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or
reuse of any copyrighted component of this work in other works. DOI: <10.1109/TNSM.2018.2816263>
Abstract—Mobile Edge Computing (MEC) is an emerging
technology that aims at pushing applications and content close
to the users (e.g., at base stations, access points, aggregation
networks) to reduce latency, improve quality of experience, and
ensure highly efficient network operation and service delivery.
It principally relies on virtualization-enabled MEC servers with
limited capacity at the edge of the network. One key issue is to
dimension such systems in terms of server size, server number,
and server operation area to meet MEC goals. In this paper, we
formulate this problem as a mixed integer linear program. We
then propose a graph-based algorithm that, taking into account
a maximum MEC server capacity, provides a partition of MEC
clusters, which consolidates as many communications as possible
at the edge. We use a dataset of mobile communications to
extensively evaluate them with real world spatio-temporal human
dynamics. In addition to quantifying macroscopic MEC benefits,
the evaluation shows that our algorithm provides MEC area
partitions that largely offload the core, thus pushing the load
at the edge (e.g., with 10 small MEC servers between 55% and
64% of the traffic stay at the edge), and that are well balanced
through time.
Index Terms—Mobile edge computing, Multi-access edge com-
puting, fog computing, network virtualization, dimensioning,
clustering.
I. INTRODUCTION
M
OBILE Edge Computing (MEC - also know as Multi-
access Edge Computing [1], and similar to fog com-
puting [2]) has emerged as a key enabling technology for
realizing the IoT and 5G visions. It aims at reducing la-
tency and ensuring efficient network operation and service
delivery and pushing content and services close to the users.
Numerous MEC applications are already envisioned and inves-
tigated, for example: chat/video analytics, video acceleration,
augmented/virtual reality, location-based services, connected
vehicles, and IoT gateways [3].
In a MEC deployment MEC servers are positioned in the
infrastructure close to the edge of the network (see Fig. 1): they
are small-scale datacenters with low to moderate resources
collocated with the base stations, access points and/or placed
in the access/aggregation network. They leverage virtualization
to support MEC applications run as virtual machines, con-
tainers, microservices etc. [4]. The purpose of MEC servers
is to host as many applications as possible at the edge to
improve latency and alleviate congestion in the core. MEC
thus performs application and network offloading from the
core data center on to the edge [5], [6].
The central decision in a MEC system design is to decide
which users, applications and share of traffic should be handled
by the MEC servers. To address this key issue we name
MEC cluster the area, and by extension the base stations and
Fig. 1. MEC deployment: tasks and applications (e.g., video chat analytics,
video chat customization) are mainly offloaded onto MEC servers at the edge
of the network to reduce latency and offload the core network. The area is thus
partitioned into MEC clusters, each cluster being served by a MEC server.
Note that it can be an n-level architecture.
the users in the area, served by a MEC server. Indeed the
efficiency of a MEC system heavily depends on such aspects
as the distribution of communications and workloads in time
and space. Its cost depends on server density, capacity, and
interconnection. Imbalanced MEC clusters that handle highly
different traffic volumes would lead to an inefficient use of
resources and to unequal Quality of Experience (QoE). Put in
terms of MEC clustering, the key question is thus: how to have
an efficient partition of MEC areas? From this, a placement
of MEC servers can be derived.
The problem is aggravated by the well documented fact that
mobile traffic is very dependent on time and locality. Indeed
mobile communications are spatially distributed according to
the population density and activity, which vary in time. For
instance, the mobile traffic in the business areas differ from
the mobile traffic in the transport, residential and entertainment
areas [7]–[9]. As it was shown by Qazi et al. [10], in a
MEC perspective, such variations have a direct impact on
the load of the potential MEC servers. In addition, it was
shown by Tastevin et al. [9] that mobile communications in an
urban environment have a high spatial locality - they tend to
follow a power law, which motivates a local consolidation of
applications at MEC servers. Such properties will be amplified
with the realization of the IoT and 5G visions [3].
In this paper, we formally describe the MEC geo-clustering
2
problem and provides a Mixed Integer Linear Programming
(MILP) formulation. However, as the large-scale dimension
of MEC systems and mobile communications makes classic
analytical and simulation-based approaches almost inapplica-
ble, we then investigate a graph-based method. We propose
an algorithm that, based on the spatial distribution of the
communications, finds a MEC partition that favors application
instantiation at the edge instead of at the core. The resulting
clusters correspond to MEC areas. Our algorithm takes into
account the maximum server capacity, that we express as
the maximum number of served communications per unit of
time, but that can be easily expressed in terms of resources
(CPU, storage...) or application instances. We evaluate the
MILP and the clustering algorithm using a dataset of mobile
communications in a city provided by a mobile operator. We
first show that the clustering takes into account the spatial
distribution of the communications and enables to largely
offload the core. In addition, the algorithm provides results that
are close to the MILP results on small-scale problem instances.
Then, we evaluate the clustering algorithm on larger problem
sizes and outline the benefits of MEC even for very small MEC
server sizes. The obtained MEC clusters have well balanced
loads and enable to keep a large portion of the traffic at the
edge. Finally, we evaluate the MEC partition over a week of
communications and show that it largely supports temporal
dynamics. There is almost no server saturation, i.e., traffic
offloaded to the core, while the loads remain balanced.
In summary, this paper makes the following contributions:
1) We formulate the MEC clustering problem and provide
a MILP formulation (Sec. III).
2) We design a MEC clustering algorithm (Sec. IV) that
consolidates as many communications as possible at the
edge.
3) We use a real-world dataset of spatially and temporally
distributed mobile communications (Sec. V-A).
4) We evaluate our proposal and show that, despite the
spatialtemporal dynamics of the traffic, our algorithm
provides well-balanced MEC areas that are close to
optimal on small problem instances (Sec. V-B) and
serve a large part of the communications on real-world
problem instances (Sec. V-C and Sec. V-D).
We discuss related work in Sec. II and conclude in Sec. VI.
In [11] we presented the geo-clustering algorithm and a first
evaluation. In this paper, we introduce a mixed integer linear
programming formulation of the problem and a formalization
of the algorithm. We also evaluate both the MILP and the
algorithm through extensive and detailed simulations.
II. RELATED WORK
In the past few years, in parallel notably to the ETSI MEC
ISG initiative [1] and to the OpenFog Consortium [2], MEC
has emerged as a new promising research area. Very recently,
first surveys have been published to present comprehensive
panoramas of the use cases, architectures and challenges [12]–
[14]. We present in this section challenges and related work
that are linked with the problem of MEC resources dimen-
sioning.
Dimensioning and MEC server placement. The MEC
server placement problem was illustrated by Qazi et al. [10]
who showed that the number and the locations of MEC servers
have a direct impact on the QoE (imbalance loads and high
latencies) and on the operational cost. However, they did
not address the placement problem. They proposed an NFV-
based orchestration for MEC. Note that the server placement
problem is significantly different from the conventional base
station site selection problem since, although both problems
are constrained by the deployment budget, placing edge sites is
coupled with the computational resource provisioning. Ceselli
et al. [15] have proposed a mixed integer linear programming
formulation of the joint problem of base stations allocation to
MEC servers and routing to reduce infrastructure cost. Our
proposal mainly differs on three important aspects. First, they
assume the locations of the LTE 4G base stations are known.
Their analytical formulation does not scale properly. Most of
all, the clusters they obtained are not geo-consistent, meaning
that the base stations associated to a MEC server can be
completely scattered in space.
Control plane design. Recent proposals have addressed
control plane design. They investigate how the current cen-
tralized LTE core architecture, where most of the traffic
converge [16], can be decomposed and split to alleviate con-
gestion and reduce latency [17]. Software-Defined Networking
(SDN) is used to redirect peering traffic in-between the base
stations and the Evolved Packet Core (EPC), thus offloading
the core and improving latency [5]. SDN is also combined
with NFV (Network Functions Virtualization) to propose a
backwards-compatible orchestration architecture where virtual
EPC functions are chained with SDN and instantiated in MEC
servers to efficiently use resources [10].
System approaches. While NFV has gained momentum,
recent proposals have focused on shortening network func-
tions instantiation and reducing their system footprint with
approaches based on unikernels [4]. In particular, it has
been shown that an inexpensive commodity server is able to
concurrently run up to 10,000 specialized virtual machines,
instantiate a VM in as little as 10 milliseconds, and migrate
it in under 100 milliseconds [18]. This technology is very
promising in an MEC context where an application could be
instantiated on the fly at MEC servers for a user or a group
of users and shutdown once the communication is ended.
Progress in this direction complements our deployment work
as it would make it easier to instantiate locally applications at
MEC servers.
Application/task and content offloading. Application of-
floading, both from the device to the edge and from the core
to the edge, has been extensively studied. It notably includes
task decomposition and packaging [19], assignment, and mi-
gration [6], server scheduling and selection, content caching
and pre-fetching [20]. Some of the proposals are similar to
those addressed in Mobile Cloud Computing (MCC), which
addresses distributed clouds [21], [22].
III. MEC RESOURCES CLUSTERING
In this section, we formulate the MEC resource geo-
clustering problem that we address and we present the cor-
3
responding mathematical optimization model.
A. Problem formulation
From a network system standpoint we consider a MEC
deployment as presented in Fig. 1. All users belong to a
MEC cluster, a geographic area whose traffic can be han-
dled by a MEC server, that is a small-scale datacenter with
low to moderate compute and storage resources. All user
communications and applications, for instance ephemeral per-
communication unikernel-based video analytics applications,
are either handled by the local MEC server (e.g., the blue plain
line in Fig. 1) or by a highly capacitated core data center (e.g.,
the black dotted line in Fig. 1), which can be farther in terms
of latency.
We argue that one of the key design issues in a MEC system
is to efficiently dimension MEC areas (or clusters). Such a
MEC geo-partitioning must have the following properties:
1) MEC servers, as any compute, storage and network
node, have a maximum capacity (e.g., in terms of CPU,
storage resources or application hosting capabilities) that
we considered as known a priori in our problem.
2) MEC server loads should be balanced both spatially
and temporally to improve user experience and system
expenditures.
3) The traffic between the MEC servers and the core should
be minimized, in particular by consolidating applications
at the MEC server level, such that the global latency is
reduced.
This problem turns out to be both theoretically and com-
putationally hard. It generalizes the graph cut based image
segmentation problem with connectivity constraints, which is
NP-hard [23], and introduces capacitated components.
In the following, we formulate the mathematical optimiza-
tion formulation of the MEC geo-clustering problem and intro-
duce alternative connectedness constraints that are restrictive
but allow reducing the number of constraints.
Note that the following problem formulation focuses on
edge-to-edge communications to be consolidated at the MEC
servers. However, it could be easily extended to address edge-
to-core communications.
B. Model
Input (problem data).
We assume that the considered area has been discretized in
N cells. Let note G the set of the N cells. For example, if the
discretization has been done according to a grid of length n,
then G = {0, ..., n
2
−1}. For a clearer constraint formulation, let
note Neigh(i) the cells that are spatially neighbors of the cell
i. In a grid, a cell that is not on a boarder has 8 neighbor cells.
t
i, j
corresponds to the amount of traffic or communications per
unit of time from the cell i ∈ G to the cell j ∈ G. The goal is
to cluster the area cells. We note C the set of clusters. C is a
partition of the set G. By default, C is equal to G, which means
that the discretized parts are all in a unique cluster. The aim
being to cluster cells, a solution of the program might result in
a number of empty clusters. A cluster has a maximum capacity,
Input (problem data)
N Number of cells after area discretization
G Set of N cells
N eigh(i) The set of the cells that are spatially neighbors of the cell i
C Set of clusters (clustered cells)
M Maximum cluster capacity
t
i, j
Amount of traffic or communications per unit of time from
the cell i and to the cell j
x
i
, y
i
Integer variable, define the x and y coordinates of the cell i
in a grid
Output (decision variables)
a
i, c
Binary variable, equal to 1 iff the cell i belongs to the cluster
c
b
i, j, c
Binary variable, equal to 1 iff the cell i and the cell j are in
the same cluster c
f
sr c, dst
i, j, c
Float variable in [0, 1], define the fraction of flow between
the cell i and the j for a cluster c when the cell src
and the cell dst are the source and destination of the flow
respectively
TABLE I
PROBLEM DATA AND DECISION VARIABLES.
in terms of traffic or communications per unit of time that can
be processed at its MEC server, noted M.
Output (decision variables).
We introduce two sets of binary variables. The first one
corresponds to cell-cluster attachment variables: a
i, c
take value
1 if the cell i ∈ G is in cluster c ∈ C. The second one is a set
of intermediary variables: b
i, j, c
take value 1 if the cell i ∈ G
and the cell j ∈ G are in the same cluster c ∈ C. Finally,
since we want clusters that are geo-consistent, meaning that all
their cells are connected, we introduce a set of float variables,
noted F, for the commodity flow formulation that will ensure
connectivity: f
sr c, dst
i, j, c
∈ [0, 1] define the fraction of flow
between i ∈ G and j ∈ G for cluster c ∈ C when src ∈ G and
dst ∈ G are the source and destination of the flow respectively.
Objective function.
Maximize
Õ
i ∈G
Õ
j ∈G
Õ
c ∈C
t
i, j
b
i, j, c
(1)
Constraints.
Cluster attachment unicity:
Õ
c ∈C
a
i, c
= 1, ∀i ∈ G (2)
Intermediate variable: the cells i and j belong to the same
cluster c
0 ≤ a
i, c
+ a
j, c
− 2 b
i, j, c
≤ 1,
∀i ∈ G, j ∈ G, c ∈ C
(3)
Maximum cluster capacity (intra cluster communications):
Õ
i ∈G
Õ
j ∈G
t
i, j
b
i, j, c
≤ M, ∀c ∈ C (4)
Commodity flow constraints to ensure that a cluster c is
connected (geo-consistent):
(i) For a cluster c , a flow between i and j exists if and only
if i and j are in the same cluster c:
f
sr c, dst
i, j, c
≤ b
i, j, c
,
∀ src ∈ G, dst ∈ G, i ∈ G, j ∈ G, c ∈ C
(5)
4
Fig. 2. Visualization of the steps of our graph-based algorithm. The area where are distributed the MEC communications is discretized into nodes which form
MEC clusters. Each pass is made of two phases: one where the pair of neighbor nodes (i.e., clusters) that interact the most, while respecting the maximum
cluster capacity, are selected; one where the two selected nodes (i.e., clusters) are merged to build a new/updated graph with an increased self-loop weight
meaning that more communications or traffic are in the same cluster. The passes are repeated iteratively until no pair of neighbor nodes (i.e., clusters) can be
merged because of the maximum MEC server capacity (self-loop weights). The result corresponds to a spatial partition of MEC clusters.
(ii) Flow conservation on transit cells:
Õ
l ∈N eigh(k)
f
i, j
k, l, c
−
Õ
l ∈N eigh(k)
f
i, j
l, k, c
= 0, when i = src, j = d st
∀i ∈ G, j ∈ G, k ∈ G \ {i, j }, c ∈ C
(6)
(iii) Flow conservation at source and destination cells:
Õ
l ∈N eigh(i)
f
sr c, dst
i,l, c
−
Õ
l ∈N eigh(j)
f
sr c, dst
l,i, c
=
(
b
i, j, c
if i = src
−b
i, j, c
if j = dst, i , j
∀ src ∈ G, dst ∈ G, i ∈ G, j ∈ G, c ∈ C
(7)
Alternative connectedness constraints.
The number of constraints explodes very rapidly with the
number of cells generated by the discretization of the space.
We thus define alternative connectedness constraints that can
be substituted for the flow commodity formulation to reduce
the number of constraints when the space discretization struc-
ture is a grid and thus manage larger problem instances.
On a grid, the cells i and j, whose coordinates are (x
i
, y
i
)
and (x
j
, y
j
) respectively, are connected within the cluster c if
it exists at least |x
i
− x
j
| + |y
i
− y
j
| + 1 cells of the same cluster
in the rectangle they form on the grid:
(|x
i
− x
j
| + |y
i
− y
j
| + 1) b
i, j, c
≤
Õ
k ∈[min(x
i
, x
j
), max(x
i
, x
j
)]
l ∈[min(y
i
, y
j
), max(y
i
, y
j
)]
b
i, j, c
if i , j
∀i ∈ G, j ∈ G, c ∈ C
(8)
These constraints can be seen as working recursively. Two
cells are connected in a cluster if and only if at least they each
have one of their neighbor cells that are connected in the same
cluster.
Note that these connectedness constraints are more restric-
tive than the commodity flow constraints since they impose
that the path between two cells is strictly inside the rectangular
they define on a grid.
IV. GRAPH-BASED GEO-CLUSTERING ALGORITHM
In this section, we present our graph-based algorithm for
MEC area-geo-clustering. We first explain how it works and
then present its formal description.
Given a maximum MEC server capacity, the algorithm finds
MEC clusters (also referred to as MEC areas) which tend to
maximize the traffic handled inside the clusters (i.e. at the edge
by the MEC servers) and thus reduce the traffic that goes up
to the core data center.
It is divided in two phases that are repeated iteratively.
Assume that we start with two graphs that have the same
set of nodes (see Fig. 2). These nodes correspond to the
discretization of the area where the MEC communications
demands are distributed into clusters. We note it C. The first
graph G
a
= (C, E
a
) represents the adjacencies of the nodes
on the area. For instance, in a square grid, a node (a grid
cell) has up to 8 adjacent nodes (grid cells). The second
graph G
int
= (C, E
int
) represents the interactions (i.e., the
communications or the traffic) between the nodes. The weight
w
i, j
∈ R of the edge e
i, j
∈ E
int
represents the amount of
interaction (e.g., the number of communications or traffic)
between node i and node j. Note that a node i can have
interaction with itself, leading to a self-loop e
i,i
- this is
actually desired as it corresponds to communications that
are inside the corresponding MEC cluster. So, in this initial
partition there are as many MEC clusters as there are nodes.
