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Dynamic resource control method based onreal world representation with potential ﬁeld
Koudai Kanda1 , Shin’ichi Arakawa1 , Satoshi Imai2 , Toru Katagiri2 , Motoyoshi Sekiya2 , and Masayuki Murata1
1 Graduate School of Information Science and Technology, Osaka University, Yamadaoka 1–5, Suita, Osaka,

565–0871 Japan
2 Fujitsu Laboratories Ltd. Kamikodanaka 4–1–1, Kawasaki, Kanagawa, 211–8588, Japan

Abstract—A real-world sensing application, which senses andanalyzes the situation in the real world via sensor devices,
has attracted increasing attention for providing new services
to mobile users. In this paper, for targeting the application,
we propose a highly adaptive resource control method thatcan control the amount of local computing resources, which isprovided by the Mobile Edge Computing technology and theamount of network resources necessary for service provisioning.
A basic idea is to express various information, such as the amountof sensor information and the amount of user access, into a
simple potential ﬁeld, and then update the potential ﬁeld in ashort cycle in a self-organized manner. Numerical results showthat our resource control method based on the potential ﬁeld is
adaptive for the movement of users.
Index Terms—Real-world Sensing, Mobile Edge Computing(MEC), Resource Virtualization and Control, Potential Field

I. I NTRODUCTION
The real-world sensing that analyzes real-world information around mobile devices is expected to provide more
attractive services to users. Thanks to the development ofmobile devices, various users enjoy network services througha constantly connected network. The recent mobile devices,such as the smartphone, is equipped with various kinds ofsensors, which makes it possible to capture our real-worldinformation. Some service providers acquire and analyze thesesensor values of each user and to provide services such asindoor navigation [1] or crowd navigation [2].
One of important things in the real-world sensing is tounderstand the real world from a large amount of sensor
information. For this purpose, data mining technologies for
extracting real world information are being investigated [3].
However, as a matter of course, computing resources are
required for applying data mining technologies, and it iscurrently considered to analyze and process information by
aggregating the sensor information in data centers.
Recently, Mobile edge computing (MEC: Mobile Edge
Computing) is under investigation in the networking researchﬁeld. As its name indicates, MEC enables computing resources
to be deployed at the edge, i.e., at the mobile-user side of
the mobile network. In MEC, virtual machines are deployedon the mobile edge and they are used for application-speciﬁccomputing resources [4]. MEC aims at reducing delay andimproving immediacy by carrying out data processing at themobile edge, not at the core or the data centers. Some applications such as video analysis and object tracking are alreadyintroduced [5]. Note that MEC architecture fundamentally
follows NFV (Network Function Virtualization) architecture[4]. That is, virtual machines are deployed at the edge, andtherefore applications can use the computing resources in a
ﬂexible manner.
The ﬂexibility of computing resource deployment obtained
by MEC is attractive for the real-world sensing. In the realworld sensing, the sensor information is spatially dependent
data because the sensor information captures the real-worldinformation of an environment. Thus, it is sufﬁcient to analyze
the spatially dependent data at the mobile edge rather than at
the data center. Without MEC, the sensor information frommobile devices is sent to the data center (DC) via the edge
router and the Internet. The sensor information is processedby using computing resources at the DC, and the processing
result is sent back to the mobile devices. With this case, ananalysis of the environment which surrounds mobile devices isperformed by the data center that is usually located far fromthe mobile devices. The information exchange between themobile devices and data centers degrades a delay characteristicof users response. Furthermore, because of the progress ofcloud services and an increase of sensor devices, upstream
information sent from users to DC is increasing, and it has
been pointed out that unacceptable delays occur due to theaggregation of information in data centers [6], [7]. More
importantly, the amount of sensor information is not constant,it always ﬂuctuates depending on the user’s movement andthe events occurring around the mobile device. Therefore,
it is desirable to deploy computing resources quickly basedon the amount of the sensor information and to deploy
network resources ﬂexibly based on the value of the real-worldinformation, i.e., amount of access requests to the results ofdata mining.
In this paper, we develop a dynamic resource control methodthat adjusts the amount of computing resources and network
resource in conjunction with the change of events occurring in
the real world. Speciﬁcally, the amount of sensor informationin the real world and the amount of user access to thisinformation are expressed as potential ﬁelds. The value of thepotential is updated quickly in a self-organized manner, andthen computing and network resources are placed based on thevalue of potential. With our potential expression and spatiotemporal interaction of potential, we achieve highly adaptive
resource control against the change of the event occurring in2

the real world.
This paper is organized as follows. Section 2 describes a
network resource control method based on real world expression using a potential ﬁeld. In Section 3, we will examine
the behavior of the potential ﬁeld against the movement of
the user and the behavior of the potential ﬁeld under resource
constraints. A conclusion of this paper and future work aredescribed in Section 4.
II. A DYNAMIC RESOURCE CONTROL METHOD BASED ON
REAL WORLD REPRESENTATION WITH POTENTIAL FIELD

A. Application scenario
We suppose following application scenario with the MEC
architecture. Users have a mobile device, and sensor information of the real-world surrounding the mobile device is sentfrom the mobile device to the closest router. The router isthe mobile edge and has computing resources for analyzing
the sensor information. Hereafter, we call the router as theedge router. Using the computing resources of the edge router,sensor information is processed and analyzed at the edge
router, and the result is stored at the edge router. For example,
with the occurrence of a trafﬁc accident, the sensor information
around the point of the trafﬁc accident is aggregated andanalyzed at an edge router, and the result, e.g., the signiﬁcanceof the accident and/or degree of trafﬁc congestion, is stored at
the edge router. The results may be accessed by users which
are close to the point of the trafﬁc accident and by users
spatially separated from the edge router through a network
between the edge routers.
Thus, the computing resources of edge routers around thepoint of the trafﬁc accident as well as network resource
around the point of the trafﬁc accident should be increased.
More generally, the computing resource should be increased as
the amount of sensor information increases, and the network
resource should also be increased as the computing resource
increases because the increase of sensor information will leadto giving more chance of accessing the information and/or
retrieval of the information. This is why we consider threelayer potential ﬁeld, which will be explained in the next
section, to handle the real-world information.
B. Real world expression using potential ﬁeld
A potential ﬁeld is one of the approaches to express astate of control or control information itself. In the case of
potential routing [8] which is used for controlling the routeof information in the mobile ad-hoc and sensor network, thepotential ﬁeld expresses a distance to a sink node to which all
the sensor node send their data. Each sensor node updates its
potential in a self-organizing manner, and the potential of allnodes forms the potential ﬁeld.
In this paper, we use the potential for expressing the amountof computing resources and network resources necessary inconjunction with the events occurring in the real world. With
the simple expression by the potential, we realize a spatiotemporal resource control by updating and exchanging only thepotential values without grasping details of real-world eventsand information accesses occurring in the real world.

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Our method introduces three layers; ENV layer (Environmental layer), IR layer (Information Retrieval layer), and
VoI layer (Value of Information layer). Each of three layers
expresses some real-world information as potential and forms
a potential ﬁeld.
ENV layer expresses the amount of sensor information
processed by each edge router, and IR layer expresses theamount of information retrieval offering access to the result of
the information processing. VoI layer is most important layer
in our method because it is designed such that a potential of
VoI layer represents a potential access to an information. We
will explain the detail of each layer in following.
1) ENV layer: A potential of ENV layer is deﬁned as
the number of users connected to an edge router or more
directly the amount of sensor information at the edge router.
Figure 1 illustrates an example of the potential ﬁeld in ENV
layer. In the ﬁgure, we suppose that some event such asa trafﬁc accident occurs at the coordinate (x, y) = (50, 50)
on the two-dimensional space, and the amount of sensor
information increases around the coordinate (50, 50). Notethat the increase of sensor information is not restricted tothe coordinate (50, 50), but may spread around the coordinate(50, 50) due to the increase of a number of users caused by a
trafﬁc jam.
The potential of ENV layer is useful for preparing computing resource at the edge because more computing resource isnecessary as more increase of the potential, i.e., the amountof sensor information. The actual computing resource should
be determined by converting the potential of ENV layer with
an appropriate function.
2) IR layer: A potential of IR layer is deﬁned as the numberof access requests to the information stored at an edge router.
The potential represents the user’s demand for the informationand takes high value when the value of information of theedge router is high. When the value of information of theedge router is low, the potential takes low value.
3) VoI layer: A potential of VoI layer is deﬁned as an
amount of potential access to the information stored at an edge
router. However, it is difﬁcult to formally deﬁne the amountof potential access because the amount depends on the valueof information and we do not have a formal method to deﬁne

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Fig. 3: Image of the potential ﬁeld diffused in VoI layer
TABLE I: Explanation of each constant and parameter

Fig. 2: Interactions among three layers

the value of information. Thus, we try to design a behavior of
the potential such that the potential reﬂects potential access tothe information.
Deﬁnitions of potentials of ENV layer and IR layer suggestthat the potential of VoI layer should be increased (decreased)
as the potential of ENV layer becomes high (low). That is,
the potential of VoI layer should be determined based on theinteractions between the potential of ENV layer/IR layer. Thisis because an increase of the amount of sensor information,that is, an increase of the potential of ENV layer reﬂects theoccurrence of some event and leads to a potential access tothe information. The potential of VoI layer should be also
increased as the potential of IR layer increases because moreaccess to the information reﬂects the value of information.
Figure 2 illustrates the factors that affect the potential of VoI
layer.
In addition to the interactions between ENV layer/IR layer,
we should consider the spatio-temporal interactions of potentials at VoI layer when applications such as real-world sensing
are targeted. Let us suppose that the potentials of ENV layer
and IR layer are high at the edge router z at time t. A potentialof VoI layer at z becomes high based on the interactions
between ENV layer/IR layer. As for the spatio interaction,
the potential of VoI layer should increase more because theinformation will be accessed not only from users connected toz but also from users connected to edge routers close to z. As
for the temporal interaction, the value of information at time t
is not lost immediately at time t + 1 even when the amount of
information access is lost and is decayed as the time passed.
Such spatio-temporal interactions of the potential ﬁeld are
expressed by exchange and diffusion of potential values withneighboring edge routers, and its speciﬁc behavior of updatingx, yt
p(t, x, y)C(t, x, y)I(t, x, y)
Du
Dt
Dv
n
G
Pf
Ai

Coordinate
Numbers of steps
Amount of sensor information at step t at coordinate(x, y)Internal variable in VoI layer
Potential in VoI layer
Diffusion coefﬁcient of C(t, x, y)
The time constant of potential for C(t, x, y)
Diffusion coefﬁcient of I (t, x, y)
Fixed decrease value of I (t, x, y)
Reduction coefﬁcient of C(t, x, y)Positive inﬂuence from ENV layer/IR layer
A set of adjacent nodes of node i

the potential is introduced at Section II-C. Figure 3 illustrates
a potential ﬁeld of VoI layer after when our equations of
updating potential are applied for the potential ﬁeld of ENV
layer given in Figure 1. Compared with the potential ﬁeld of
ENV layer, we can see that the potential of VoI layer spreads
widely because of a diffusion of the potential ﬁeld.

C. Update potential
In this section, we explain the potential of VoI layer andequations with spatio-temporal interactions. Table I summarizes constants and variables used in the equations. I(t, x, y),which is the potential of VoI layer located at (x, y) at time t,
is calculated by the following equation,∂I(t, x, y) ∂I(t, x, y)∂I(t, x, y)= Dv (
+
)
∂t
∂2 x
∂2 y
+P f −n+Dc(1)

The ﬁrst term on the right side of equation 1 is the potential
to be diffused from the adjacent edge routers. Hereafter, wecall an edge router as a node for simplicity. The diffusion
is based on the second derivative of the potential in eachdirection. This implies that we consider the differences ofdensities of potentials: the potential diffuses quickly when
the density difference is large, or the potential diffuses slowly
when the density difference is small. P f is the inﬂuence fromIR layer and n is a decay parameter. The last term, Dc is the4

inﬂuence from ENV layer which reﬂects the amount of sensor
information and is deﬁned as,( ∂C(t,x,y)≥ 0)
Dt ∂C(t,x,y)
∂t
∂t
(2)
Dc =
∂C(t, x,y)tanh G · I(t, x, y) ( ∂C(t,x,y)
<
0),
Dt ∂t
∂t
where
C(t + 1, x, y)=(1 − Du )p(t, x, y) +1
Du| Ai |AiC j . (3)jC(t, x, y) is an internal variable in VoI layer and is calculated
based on sensor information amount p. C(t, x, y) reﬂects thechange of amount of the sensor information not only at thenode (x, y) but also the adjacent nodes (x±1, y), (x, y±1). Whenthe diffusion coefﬁcient Du is large, the amount of sensor
information at adjacent nodes is reﬂected more.
In equation 2, when the derivative of C(t, x, y) is negative,
it is multiplied by tanh G · I(t, x, y). This is to prevent I(t, x, y)from becoming negative values when the value of I(t, x, y) is
close to 0.
D. Resource control based on a potential update formulaconsidering resource constraints
In the previous section, we have designed the potentialof VoI layer such that it reﬂects the potential access to an
information stored at (x, y) through inﬂuences from ENV
layer/IR layer and spatio-temporal interactions in VoI layer.
Since the potential of VoI layer expresses the potential accessto the information, the amount of the network resources should
be prepared based on the potential ﬁeld of VoI layer. However,since an amount of network resources are ﬁnite in general, it
is necessary to modify equations for updating a potential withconsideration of resource constraints.
Here, we suppose that network resources cannot be added
anymore against the increase of information access to a nodedue to the resource constraints. In this case, the information
access to the node should be relaxed by accommodating
the part of the access at the other nodes. Considering theapplication such as real world sensing and MEC applications,
it is desirable to compensate for the insufﬁcient resource at anode by increasing the resource allocation at adjacent nodes
which are spatially close to the node. Given a threshold of thepotential value which corresponds to the limit of resources,
the diffusion coefﬁcient of the potential, Dv , is modiﬁed to,
D1 (W hen I(t,x,y)< the threshold value)(4)Dv =D2 (W hen I(t,x,y) the threshold value).
D1 is the diffusion coefﬁcient under the condition that thepotential is less than the threshold value and we do not haveto deal with resource constraints, D2 is used for the situationthat the resource constraints are crucial. When a potential of anode reaches or exceeds the threshold value, diffusion of thepotential should be accelerated. We, therefore, use D2 which isgreater than D1 as the diffusion coefﬁcient under the resource
constraints. With the diffusion coefﬁcient D2 , the potentialof the node decrease more and the potential of the adjacentnodes increases more. After updating the potential considering

TABLE II: Parameter conﬁguration
Du
Dt
n
G

0.6
0.6
0.0001
0.6

resource constraints based on the above-mentioned equation,
resource allocation is performed based on the potential of eachnode.
In the case where there is a large discrepancy between thepotential value of VoI layer and the amount of resources that
can actually be allocated, it is necessary to reduce the amountof sensor information. For this purpose, the potential of VoI
layer should be used as an inﬂuence to control the potential of
ENV layer and/or IR layer. The mutual interactions between
layers must be considered, but this is our future subject.
III. S IMULATIONIn this section, we examine the behavior of the potential
ﬁeld of VoI layer by updating the potential with equations in
Section II-C. The purpose of simulations is to conﬁrm that thepotential ﬁeld of VoI layer can follow the ﬂuctuation of thepotential ﬁeld of ENV layer and that the potential of nodes
reﬂects the limitation of network resources. Thus, inﬂuence
from the potential ﬁeld of IR layer, P f is set to 0 and is
not considered hereafter. The values of the parameters usedin our simulation are summarized in Table II. We examined
two network scenario. At the ﬁrst scenario, we consider thesquare lattice network where edge routers are placed at thebond of the lattice and they are connected through links. At
the second scenario, we use the actual trafﬁc data from PeMS
system. Edge routers are assumed to be placed at measurement
points of the PeMS system for the second scenario.
A. Results of the ﬁrst scenario
We use a network where edge routers are connected in agrid of 100 × 100. Edge routers are equally spaced and eachedge router exchanges information of its own potential value
and diffusion coefﬁcient Dv (D1 or D2 ) with four neighboringedge routers at each step. The potential ﬁeld of ENV layer is
supposed to reﬂect the amount of sensor information generated
by mobile devices, and the potential ﬁeld will be changed
based on the movement of users. As for the model of the user
movement, we consider a simple model in which a group ofusers moves along either x-axis or y-axis with ﬁxed velocity,which we suppose an orthogonal transport network of Osaka inJapan. More speciﬁcally, the potential of ENV layer p(t, x, y)of node (x, y) at a step t is set to,p(t, x, y) =(y − 50)2tx) sin(
β1 + )
γ1100
10(x − 30)2ty) sin(+ α2 exp(
β2 + )
γ2
100
10
(5)
+ α1 + α2 .

α1 exp(−With this equation, the group of users that moves along thex axis and the group of users that moves along the y axis
direction are moves with a ﬁxed velocity, and these two groups

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Fig. 4: The example of the potential ﬁeld in ENV layer of
equation 5
Fig. 5: The example of ﬂow obtained from PeMS
intersect at the coordinates (x, y) = (30, 50). Note that α, β andγ are parameters that adjust the maximum value of potential
in each axis direction and degree of changes of number ofusers. In this paper, we set α1 = α2 = 20, β1 = 1, β2 = 0.4,
γ1 = γ2 = 200. Fig.4 shows an initial settings of the potential
ﬁeld of ENV layer.
We examined the behavior of potential I(t, x, y) underresource constraints. The diffusion coefﬁcient deﬁned in Equation 4 is used for this simulation. Fig.6 shows the potential
I(t, 30, 50) and the potential I(t, 30, 51), where D1 is 0.01 andD2 is 0.025. The threshold value of the potential is set to50. Each ﬁgure of Fig.6 shows the potentials p(t, 30, 50) andp(t, 30, 51) of ENV layer, and the potential without a potential
constraint is depicted as I (non-constraint) for reference purpose. Looking around step 2200 of Fig.6, when the potential
reaches the upper limit at coordinates (x, y) = (30, 50),I(t, 30, 50) is not exceed the threshold value. This is because
the potential diffuses to the adjacent nodes, and we actuallyobserve that the potential I(t, 30, 51) is larger than the potential
with no resource constraint.
B. Results of the second scenario
The second scenario uses the data collected by Performanceand Measurement System (PeMS) which is a system thatgathers trafﬁc information of freeway in California. In PeMS,
stations are installed at various points on the freeway, andeach station is assigned an ID as an identiﬁer. In addition,
information such as amount of trafﬁc ﬂow is collected fromeach station every 30 seconds. In this paper, we regard
these stations as edge routers, and calculate the potential foreach station. The data from PeMS system includes metadata
indicating station ID, longitude, latitude, and freeway number,and a RAW data showing station ID and amount of trafﬁc
ﬂow. Thus, a time-series data of amount of trafﬁc ﬂow at eachcoordinate can be obtained. Figure 5 shows the integration of
the ﬂow graph obtained from the stations around San Jose. An
geographical map is also inserted in the ﬁgure. The distance
between actual stations is also calculated and we set 200 m asa unit of distance in the ﬁgure. Note that when the distance
between stations is less than 1 unit, a data from either ofstations is ignored. Also, adjacent stations on the same freeway
are assumed to be connected though the actual connectivity ofstations may be different. Each station exchanges informationof its own potential value and diffusion coefﬁcient Dv (D1, D2 )with the adjacent station every ﬁxed step and one step is set
to 30 seconds.
Using the actual data obtained from PeMS, we examine
the behavior of the potential under resource constraints. There
are many stations in PeMS, so we select three stations thatare placed in the same freeway. Their ID is 401948, 401937,
401936, and denote three stations as A, B and C respectively.
Station A is located in between stations B and C. Figure 7
shows the amount of ﬂow of the vehicle and the potential
when there is resource constraint and nothing where D1 is
0.01 and D2 is 0.2. The threshold value of the potential atstation A is set to 40, and there is no resource restriction
at station B and C. Looking at step 800 in this ﬁgure, we
observe that the increase in potential of station A is suppressednear the threshold value as a result of setting higher diffusion
coefﬁcient. We also observe that the potentials are increased
at stations B and C, and the ascending value of station B
is much larger than station C. This is because the distance
between station A and station B is smaller than the distance
between station A and station C. For updating the potential,
we change the amount of diffusion dependent on the distance
between nodes; the smaller the distance between the nodes is,
the larger the amount of diffusion is set in this paper. Whena network topology in which distances between stations are
remarkably different, there is a possibility that the ﬂuctuationof the potential may not match the ﬂuctuation of the realworld. Modiﬁcations of equations may necessary to handle thedistance between stations, but it is left for our future work.
From the above, we conﬁrm that the potential of VoI
layer is changed immediately when the amount of the sensor
information are changed. We also conﬁrmed that under the
resource constraint, the potential of adjacent nodes is further
increased.
IV. C ONCLUSION
From a viewpoint to improve the quality of experience, it
is important to adjust computing resources and network resources in accordance with changes in the real world situationin applications requiring information processing. In this paper,

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ACKNOWLEDGMENT
Apart of this work was supported by No.19104 of National
Institute of Information and Communications Technology(NICT) in Japan.
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2500(b) station B(ID=401937)

Fig. 6: Transition of I(t, x, y):where D1 = 0.01, D2 = 0.02560Flow/Potential

we propose a dynamic resource control method that expresses
the amount of sensor information and user access to realworld information as a potential ﬁeld, and allocates a resource
amount according to the potential value. The proposed method
instantly reﬂects changes in events occurring in the real world.
Furthermore, by incorporating self-organizing spatiotemporal
diffusion of potential, we allocate resources to prepare for
event ﬂuctuations and potential information access.
In this paper, we conﬁrmed that the potential ﬁeld formation
and resource constraint are considered by using computer
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