Two Approaches to Resource Allocation in Hybrid Fog and Cloud

Systems

Dariusz Gasior

Faculty of Computer Science and Management, Wroclaw University of Science and Technology, Wroclaw, Poland

Keywords:

Cloud, Fog, Resources, Optimization, Game-theory.

Abstract:

In this paper, two approaches to the hybrid fog and cloud computing environment are presented. The ﬁrst is

based on the assumption of centralized management performed by cloud, while the latter takes utilization of

self-managing concept enabling distributed resource allocation carried by fogs. The appropriate mathematical

models are introduced and the optimization problems are formulated. While the ﬁrst concept turned out to be

the mixed nonlinear programming, the second may be interpreted as the noncooperative game. The ideas of

the possible solutions are brieﬂy suggested.

1 INTRODUCTION

Recently fog computing and similar concepts at-

tracted much attention. It turned out that the comput-

ing resources which are around us (e.g. smartphones,

tablets, etc.) has very high computing power in total.

Moreover, it may be possible to use it instead of cloud

to perform some computing tasks. This, in turn, leads

to a reduction in the use of network connections and

cloud resources.

In this paper, we introduce to concepts of resource

and task allocation in the hybrid fog and cloud com-

puting environment. We assume that the computa-

tional task may be divided into the operations. Each

operation may be performed either locally - in the fog

or globally - in the cloud.

2 STATE OF THE ART

The concept of fog computing was ﬁrst proposed by

Cisco in 2011 (Bonomi, 2011) and its basic assump-

tions can be found in (Cisco, 2015). The computa-

tional fog is to provide cloud computing functional-

ity with the use of devices and network infrastruc-

ture located near terminal devices instead of data cen-

ters (Bonomi et al., 2012). It has been noticed that

a large number of devices with even relatively small

unit computing powers such as mobile devices, termi-

nal network devices or other embedded systems pro-

https://orcid.org/0000-0001-6425-1691

vide sufﬁcient resources to perform at least part of

the tasks that were originally directed to the cloud.

The fog approach, on the one hand, makes it possi-

ble to limit the use of cloud computing resources and

network communication resources and, on the other

hand, allows reducing the delivery times of the data

processing results.

In (Varghese et al., 2017) it was demonstrated that

in some applications the use of fog instead of the

cloud allows to reduce the use of network resources

needed to perform computational tasks by up to 90%

while providing results in time 20% shorter. The au-

thors of the work (Hassan et al., 2015) reduced the

waiting time for the results of the face recognition al-

gorithm by 50% using a computational fog instead of

a cloud.

In recent times, solutions have been sought to

make the best use of the advantages of fog and cloud

computing when both approaches are used within a

single hybrid system. The research led to the de-

velopment of the F2C (fog-to-cloud) (Masip-Bruin

et al., 2016) paradigm and the Foud model (Tao et al.,

2017). These efforts made possible to design sys-

tems that can use both fog and cloud resources si-

multanously. However, such hybrid systems can op-

erate on the basis of different architectures, which

should be chosen depending on practical applications.

Sample proposals of structures of fog-cloud systems,

which correspond to various potential applications,

can be found e.g. in (Bierzynski et al., 2017) or (Skar-

lat et al., 2017).

At the same time, one of the most important re-

Gasior, D.

Two Approaches to Resource Allocation in Hybrid Fog and Cloud Systems.

DOI: 10.5220/0008168700990105

In Proceedings of the 9th International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS 2019), pages 99-105

ISBN: 978-989-758-385-8

search areas in the ﬁeld of fog-cloud systems has be-

come the problems of managing their resources. The

effective use of limited local resources of comput-

ing fogs and their proper complementation with cloud

computing resources is now a key issue. At the same

time, the authors of many articles on this topic point

out that work in this area is still in the initial phases.

In (Souza et al., 2016a), the authors propose algo-

rithms that allow for the allocation of tasks. They as-

sume that tasks can be divided into operations (called

atomic services). Each of the fog nodes can perform

only the indicated operations, while in the cloud all

of them can be performed. The resources of com-

puting nodes are treated in an abstract way (they rep-

resent computational possibilities) and are discrete -

they are represented by the so-called slots. Each op-

eration has speciﬁc requirements on the number of

resources (slots) needed for its implementation. The

problem is to assign operations to nodes so as not to

exceed the number of available resources and to min-

imize three criteria simultaneously: delays in delivery

of results, node load and energy consumption.

A similar problem was considered in (Souza et al.,

2016b), but in this article, the authors considered a

system in which only two types of tasks exist and

the criterion of its operation was expressed in a total

delay in providing all results. In the article (Szydlo

et al., 2017), the authors focused on the problem of

the separation of operations (performed as part of the

task) between the fog and the cloud. Based on the

distributed data dissection paradigm, they proposed

a method of transforming the task into an operation

graph, based on which the assignment of operations

to be performed in the cloud or in the fog is to be

made. The authors do not address aspects related to

the availability of resources. As in previous cases, the

problem is solved for a deterministic and static case.

The issue related to system adaptation is also over-

looked.

In (Hassan et al., 2015), the authors also deal with

the problem of separating calculations between fog

and cloud. The tasks are represented in the form of an

operation graph. As a consequence, the problem itself

is reduced to the classical task of splitting the graph.

However, the authors consider aspects related to the

existence of various computational resources (proces-

sor, RAM memory) and network resources (band-

width). In addition, they point to the importance of

the variability of resource availability in making deci-

sions on the allocation of tasks.

In (Taneja and Davy, 2017) the problem was con-

sidered, in which not only should the task operations

be divided between the fog and the computational

cloud, but also assign the execution of individual op-

erations to the fog nodes. Both computing resources

in the form of processor power and RAM as well as

network resources in the form of connection band-

width were taken into account. Importantly, it was

taken into account that the allowable assignment of

operations to nodes must take into account the lim-

ited availability of resources.

The authors of the article (Aazam and Huh, 2015)

take into account the uncertainty associated with the

parameters describing the task. To make a proper

reservation of resources, they use predictive models

to determine what the task requirements for comput-

ing resources (CPU, RAM, mass storage) and net-

work (connection capacity) will be. Reservation of

resources is performed independently for each task at

the moment of its appearance in the system. It is as-

sumed that the task is indivisible and the manner of

its implementation can not be changed. The alloca-

tion of resources is carried out in a static manner for a

given system state and remains unchanged. A similar

approach was also proposed in (da Silva and da Fon-

seca, 2018).

In (Shah-Mansouri and Wong, 2018), it is as-

sumed that decisions on the allocation of tasks are

made by local nodes of the computing fog in a dis-

tributed way. It is assumed that each task can be di-

vided in any way between nodes of fog and cloud. In

addition, the processing of individual parts of the task

takes place in a parallel manner and they do not affect

each other. The authors evaluate the operation of the

system by the function of perceived quality (Quality

of Experience - QoE) taking into account energy con-

sumption and waiting time for the result of the opera-

tion. The allocation of tasks is determined only for the

current moment, assuming constant and deterministic

values of the parameters describing the system. The

aspect of resource allocation, the ability to change the

methods of performing tasks and system adaptation

are omitted. Only a limited amount of computing re-

sources are included, network resources are not con-

sidered.

The article (Liu et al., 2017) deals with the prob-

lem of allocating tasks for a stochastic case. It is as-

sumed that services in the system consist of streams

of indivisible tasks. It is taken into account that these

streams have a stochastic character (tasks appear in

random times and have a random size). Using queu-

ing models, the authors propose a method for deter-

mining the probabilities of redirection of entire tasks

to other nodes. The goal is to minimize delays, en-

ergy consumption and costs, taking into account con-

straints related to the availability of computing and

communication resources. The decisions are, how-

ever, determined for the average values of the param-

PECCS 2019 - 9th International Conference on Pervasive and Embedded Computing and Communication Systems

100

eters describing the tasks and for the deterministic

amounts of available resources. In addition, the so-

lution found only for the current moment (statically)

assuming the consistency of the way the tasks are car-

ried out.

A similar approach to allocation of tasks in foggy

cloud systems can be found in (Yu et al., 2017). It

is assumed, however, that computational tasks can be

divided in any way between fog nodes and cloud, and

processing takes place in parallel. Despite taking into

account the stochastic nature of the appearance of

tasks, the decisions are determined only for the cur-

rent moment and only on the basis of average values.

The possibility of adapting the system during its oper-

ation and the tasks are always carried out in the same

way.

In (Pham and Huh, 2016), it was assumed that the

tasks can be represented in the form of an operation

graph. Each operation has a deﬁned size (number of

instructions to be executed) and a volume of result

data. Both computing resources (processor capaci-

ties) and network resources (bandwidth connections)

are included. The system is modeled in the form of

a graph whose vertices correspond to computational

nodes and edges of communication resources. The

problem is considered as a classic task of scheduling

tasks on machines (computing nodes). The ranking is

found only for the current moment and the system’s

volatility and uncertainty are not taken into account.

Tasks can be implemented only one way. In (Skarlat

et al., 2017) the problem of task allocation is consid-

ered. Tasks (identiﬁed with applications) are divided

into operations (services). It is necessary to choose on

which fog node or cloud computing the particular op-

erations will be carried out. It takes into account the

existence of many limited computational resources

(such as CPU, RAM memory, mass storage), but com-

munication resources are omitted. It’s assumed only

that the data transfer takes a certain time. At the same

time, it was noted that these parameters are variable

over time and it is proposed to use a simple predictive

mechanism (in the form of a weighted average). It is

assumed that decisions are made cyclically, at regular

intervals, taking into account the current state of the

system.

The review of the literature leads to a conclusion

that works in the ﬁeld of fog and hybrid systems are

still at a preliminary stage. In particular, no attempt

has been made to solve the allocation problems for

the distributed case, i.e. when the resource and task

allocation problem is solved by each computational

fog independently.

3 SYSTEM MODEL

In this section we describe the hybrid fog-cloud sys-

tem under consideration.

3.1 System Description

Taking into account the indicated principles of the

system’s functioning, it can be stated that its structure

should be layered and correspond to the one shown

in Fig. 1. Such a system can be described as a hy-

brid fog-cloud system, and its individual layers can

be characterized as follows:

1. Sensor layer - consists of devices collecting data,

2. Fog layer - consists of devices (usually mobile),

which are responsible for redirecting data to the

cloud but also able to perform part of the com-

putational tasks needed to provide the service. It

consists of:

• at least one permanent node acting as a de-

vice managing the computational fog and en-

abling the implementation of certain computa-

tional tasks,

• additional nodes providing computational re-

sources, the number of which can change over

time,

• infrastructure of the local network performing

data transmissions within the calculation fog

(e.g. between local calculation nodes).

3. Transmission layer - responsible for transmitting

data from the fog to the cloud.

4. Cloud layer - performing a computational task

needed to complete the services and responsible

for storing data for all users of the system.

Figure 1: Layered architecture of the considered hybrid fog-

cloud system.

Two Approaches to Resource Allocation in Hybrid Fog and Cloud Systems

101

In this paper, we also assume that each fog is iso-

lated from the others (it is not possible to use com-

putational resources for the needs of another fog).

In contrast, the cloud computing provides a common

computing and archiving space for all fogs. In simpli-

ﬁed form, it can be illustrated in Fig. 2. The results

of computation for the services must be sent to the

cloud.

Figure 2: Connection structure of the considered hybrid

fog-cloud system.

3.2 Services

We assume that all computational tasks are performed

to provide particular services. Each task may be per-

formed at any fog node (but only one) or in the cloud.

All tasks may be interrupted at any time of process-

ing. The calculations may be started in the fog and

completed in the cloud. WE assume that services gen-

erates constant streams of tasks.

As an example, one may consider a video image

acquisition and processing system. The basic services

of the system under consideration are: a. streaming -

the service consists in transferring data from IP cam-

eras (sensor layer) to the cloud in order to provide

the currently recorded image and its archiving. Im-

age quality and the amount of data sent to the cloud

depend primarily on: number of frames per second

(frame per second - fps), frame compression rate.

Once the camera may capture video in higher qual-

ity than user requires, some image processing tasks

may be done - e.g. changing fps or increasing degree

of compression. These tasks may be performed either

in the fog or in the cloud. If they are carried out lo-

cally, the less data is to be send. But even performing

them in the cloud is still proﬁtable since it saves the

disk space.

3.3 Resources

The resources of the considered system that can be

allocated for the needs of individual services can be

divided into computational and network (communi-

cation). Among computing resources, the most im-

partant are: CPU, RAM memory and storage. In turn,

among network resources, the capacity of links is crit-

ical (ie the maximum possible data transfer speed be-

tween two network nodes).

The characteristics of the resources of the consid-

ered system that can be used in the implementation of

speciﬁc computational tasks from the perspective of

individual layers is as follows:

1. Sensor layer - resources that could be subject to

allocation are not considered here. stream.

2. Fog layer:

• Calculation resources - are located in fog

nodes, which most often are mobile devices

(tablets, smartphones) or - potentially - other

equipment that can share its processor and

memory and its appropriate software is possi-

ble. The computational resources of the system

fog node can be characterized as follows: CPU

- mobile processors with relatively low unit ef-

ﬁciency, the amount of RAM and storage are

relatively small.

• Network resources - communication between

devices constituting nodes of the computational

fog and IP cameras takes place within the local

network, usually based mainly on the so-called

Wi-Fi routers operating in accordance with the

IEEE 802.11 b / g / n / ac standards in the

2.4Ghz and 5Ghz band. Fog nodes are most

often equipped with wireless interfaces (WiFi).

The amount of network resources of the fog

may be characterized as follows. Links’ capac-

ities are relatively high (especially when net-

work devices use the latest wireless communi-

cation standards and technologies) and not sub-

ject to signiﬁcant changes in time (unless the

user uses a local network for other applications

- then the resources can be signiﬁcantly lim-

ited or strongly variable), the capacity of lo-

cal calls may become critical when the number

of recording devices and computational cloud

nodes increases signiﬁcantly.

3. Transmission layer:

• Calculation resources - computational re-

sources are not considered in this layer, as it

is only used to transmit data from the fog to the

cloud.

• Network resources - in this case, the key re-

sources concern the access connection between

the calculation fog and the Internet, allowing

data to be sent to the cloud. These resources

can be described as follows. The link capacities

may be undoubtedly bottlenecks. They are usu-

ally very limited in comparison to the requests.

especially when the user uses the mobile net-

work.

PECCS 2019 - 9th International Conference on Pervasive and Embedded Computing and Communication Systems

102

4. Cloud layer:

• Calculation resources - relatively large, but it

involves certain costs.

• Network resources - similar to computing re-

sources and these are easily scalable.

The amount of resources allocated to the perfor-

mance of individual operations affects primarily the

time of their implementation, and consequently deter-

mines the time of completion of the task as part of the

service. In addition, there may be requirements re-

lated to the minimum amount of resources needed to

perform a speciﬁc service (especially RAM and mass

memory). In this paper we make the following as-

sumptions in the context of resources:

• The amounts of available resources within the

calculation nodes and network resources can be

treated as approximate values.

• From the point of view of system operation, only

the resources listed above are relevant.

3.4 Objective

The performance of the system may be measured by

the average time of completing tasks. The time of

completing particular task is a sum of fog’s process-

ing time and cloud’s processing time. The processing

time depends on the load of the computational node

(as well in fogs as in the cloud). The higher is load,

the longer is potential processing time.

3.5 Notation

3.5.1 System Parameters

The following notation is used to describe system’s

parameters:

- set of tasks indexes related to the kth fog,

- the amount of CPU needed to perform ith task,

- amount of RAM needed while ith task is pro-

cessed,

start,i

- the data volume related to ith task at the be-

gining of processing

stop,i

- the data volume related to ith task when the

processing is ﬁnished, we assume that the volume of

data linearly decrease during processing, i.e. the data

volume while the ith task is ﬁnished in nth percent is

given as S

= n/100 ∗ (S

start,i

− S

stop,i

) + S

stop,i

- number of kth fog’s nodes (for convenience we

use k = 0 to denote a cloud and we assume J

= 1).

CPU

- the amount of CPU resources of the jth node

of kth fog,

RAM

- the amount of RAM resources of the jth

node of kth fog,

HDD

- the amount of storage of the jth node of kth

fog,

CAP

- the link capacity between the kth fog and the

cloud,

CPU

CLOUD

- the amount of CPU resources of the

cloud (it is assumed that it is enough to perform all

tasks in the cloud, i.e.

∑

≤ CPU

(CLOUD)

Q - the objective function (e.g. the quality of the sys-

tem).

3.5.2 Decision Variables

The decision variable are as follows:

- the fraction of ith task performed in the fog,

x = [x

ijk

∈ {0, 1} - indicated if ith task is assigned to

jth node of kth fog, y = [y

ijk

- the link’s capacity allocated to transmit ith task

from the fog to the cloud, c = [c

3.5.3 Objective Function

Let us assume that the processing time of ith task in

the kth fog may be calculated as follows:

∑

ijk

and in the cloud:

∑

(1− x

. The queing delay of the kth fog node for ith task

may be estimated as follows:

∑

ijk

CPU

−

∑

qvk

and the queing delay of the cloud:

CPU

CLOUD

−

∑

(1− x

The transmission delay of ith task between fog and

cloud we estimate as:

F2C

= (x

/100)((S

start,i

− S

stop,i

) + S

stop,i

)/c

The total delay of processing ith task is:

= t

+ t

+ d

+ t

F2C

The performance of the system may be measured

as a average total delay of all tasks:

Q(x,y,c) =

∑

Two Approaches to Resource Allocation in Hybrid Fog and Cloud Systems

103

4 PROBLEM FORMULATIONS

4.1 Cloud-based Central Resource

Management

For the centralized resource allocation problem, we

may give the following formal formulation:

Given: system parameters

Find:

(x,y,c) = arg max

(x,y,c)

Q(x,y,c)

subject to the following constraints:

∀

i∈I

∑

j∈J

ijk

≤ 1 (1)

∀

j∈J

∑

i∈I

ijk

≤ CPU

(2)

∀

j∈J

∑

i∈I

ijk

≤ RAM

(3)

∀

j∈J

∑

i∈I

ijk

start,i

≤ HDD

(4)

∀

∑

i∈I

≤ CAP

(5)

∀

≥ 0 (6)

∀

0 ≤ y

ijk

≤ 1 (7)

∀

∈ {0,1} (8)

The constraint (1) guarantees that each task is per-

formed by no more than one fog node. The con-

straints (2) - (4) means that computational resources

are not overloaded(according to the assumptions only

fog resource must be taken into consideration). The

network resources are not exceeded while (5) is pre-

served (it is assumed that only transmission layer net-

work resources must be considered). The constraints

(6) - (8) deﬁne the variables domains.

4.2 Fog-based Distributed Resource

Management

Let us introduce auxiliary variables x

(k)

which con-

sist of only these x

for which i ∈ I

. Simirarly we

deﬁne c

(k)

. Let us also denote y

(k)

= [y

ijk

]. For con-

venience, let x

(−k)

means the vector of variables x

for

which i 6∈ I

and y

(−k)

= [y

ijl

]

l6=k

. For simiplicity let

us denote x =< x

(k)

(−k)

>, c =< c

(k)

(−k)

> and

y =< y

(k)

(−k)

Finally, for the distributed resource allocation prob-

lem, we may give the following formal formulation:

Each fog solves the following problem: Given: sys-

tem parameters

Find:

(k)

)) =

= arg max

(k)

)

Q(< x

(k)

(−k)

< y

(k)

(−k)

>,< c

(k)

(−k)

subject to the following constraints:

∀

i∈I

∑

j∈J

ijk

≤ 1 (9)

∀

j∈J

∑

i∈I

ijk

≤ CPU

(10)

∀

j∈J

∑

i∈I

ijk

≤ RAM

(11)

∀

j∈J

∑

i∈I

ijk

start,i

≤ HDD

(12)

∑

i∈I

/100)(S

start,i

− S

stop,i

) + S

stop,i

≤ CAP

(13)

∀

≥ 0 (14)

∀

0 ≤ y

ijk

≤ 1 (15)

∀

∈ {0,1} (16)

The constraints (9) - (13) corresponds to the ap-

propriate constraints (1) - (5), but only for particular

fog.

This is a set of optimization problems and the so-

lution of one affects the others. Such deﬁned prob-

lem is called a game and may be considered from the

Game Theory perspective. The fogs are the players.

The x

(k)

and y

(k)

constitutes a strategy. The feasible

strategies are deﬁned by the constraints. The objec-

tive is the payoff.

5 SOLUTION

Assuming that Q is the concave function, one may

notice, that the cloud-based central resource manage-

ment problem is the mixed integer nonlinear program-

ming and to solve it, the appropriate optimization

methods may be applied - e.g. the Bender’s decom-

position.

On the other hand, fog-based distributed resource

management problem is the game, since each fog

solves their own optimization problem simultanously

and these solutions affects the objective (so-called

PECCS 2019 - 9th International Conference on Pervasive and Embedded Computing and Communication Systems

104

payoff) of other fogs. In this case, the solution is per-

ceived as an equilibrium. The most common is ap-

plication of a Nash equilibrium since it is a solution

that once obtained, no one is going to change their

decision independently.

6 FINAL REMARKS

In this paper, we described the proposition of hybrid

fog and cloud system. We discussed which resources

are critical for the system’s performance. We also for-

mulate the allocation problems for the case of cen-

tral and distributed resource management in the in-

troducted systems and brieﬂy discussed the possible

solution method.

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