IEEE Systems, Man and Cybernetics Magazine - January 2023 - 14

different network functions, and the number of VNFs in
request r is denoted by qri. Therefore, the proposed optimization
model is to allocate the required VNFs for current
service requests. The resource requirements of
VNFi can be described as pi for CPU, oi for memory, and
wi for the network. To illustrate the relationship between
the request and VNFi, we use a binary matrix Fri
j
it as follows:
F = (
ri
j
1
,
,
if VNF is related with request of task ;
others.
i
rj
(1)
We consider the scenario where a task connects to the
source node and requests for R services. The edge nodes
between the source and destination can host the VNFs for
those requests. We use P to denote
the pair of source and destination
for the tasks
And we use t ,rj
Tt ,, ,,tt tj,.
to denote the rth
= " 12 3
f
request of task j. Basically, the
tasks arrive at the industrial edge
system, and each task is composed
of multiple requests. As the
system provider, it is necessary to
consider the cost of allocating
those VNFs to meet the requirements
of these tasks. The links
among the source and destination nodes are denoted as
ll ,,, ,.ll
sd, = "
f
to denote
subject to,,, ,#!6
! =1
tT
j
|||pt FX Pt rn TR E (6)
i rR
i
!
tT
j
|||ot FX Ot rn TR E#!6
! =1
tT
j
i rR
i
!
|||wt IH iX Wt rn TR E#!6n ,, ,, ,
! =1
i rR
i
!
tr TR
j
,,
i
j SD
n
SD
m
ri
n
j
SD
n
SD
m
() (, ), ,,
ri
n
ri
n
= ri
,,
i
j ri
j
ri
n
n
,,
,,
i
j ri
j
ri
n
n
(7)
(8)
| tI Hidm Xd mr tr nT RE (9)#!6
!
|Xq , rR6 !
rR
!
Xt ,, .!!6 rn TR E
ri 01n
{, },
In this article, we
compare three
metrics, including
cost, latency, and
accepted ratio.
nn 123 ml , If VNFi is at node n, the link capacity
associated with this node will be occupied to this block.
The relationship between links and VNFs can be denoted
as follows:
I
SD
n
= (
1
,
,
if link is in the source and destination path;
others.
Hereafter, we use HSD
mi
able of link l is occupied by VNFi
,
,
Hi = *
SD
m
1
m
is a binary variable
X = (
ri
n
1 nr
,
,
i
if VNF is placed at for request ;
others.
(4)
The optimal VNF placement problem can be defined
as the following nonlinear optimization problem where
the objective is the cost of allocating VNFs for the tasks
in the systems:
Min||||ct FX + | |
tT
j
! ==!
i rR
i
!
in
11*
*
,, *
!
j ri
j
ri
n
tt T
j
i rr R
i
! !
ia
ct FX
j ri
j
*
ri
n
*
(5)
14 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE January 2023
(2)
to denote that the binary valuif
link is occupied by VNF
in the source and destination path;
others.
i
(3)
The decision of VNF placement is defined as Xri
n
, which
,,
In the previous problem, c ,in
(11)
is the
cost of allocating VNFi at the edge
node n. Equation (6) is the CPU
resource constraints to place on the
VNFs in the system. Equation (7) is
the memory capacity constraints
to place on a specific VNF, and (8)
represents the network constraints
occupied by allocating VNFs.
Equation (9) enforces each allocated
VNF to meet the delay requirements,
while (10) represents the number of the limitations
of the VNFs. The last constraints (11) are the attribute
parameter x.
The Placement Method
In this section, we propose a cost-driven VNF layout
problem for industrial edge systems. This problem is
challenging because its variables are discrete nonlinear.
The general method to solve this optimization
problem is based on the current distribution of the
VNF and using local scheduling iteration to place the
newly arrived VNF. It is worth noting that the VNFs
placed in the source or target node regions correspondingly
reduce the communication cost. However,
this approach cannot minimize the total cost. Our method
is to treat the industrial edge system as a graph, initially
select the position of the VNF, and then allocate it
according to the reusability. This method can effectively
solve the placement problem, so the VNF layout strategy
is effective.
This problem is an NP-hard problem since it is a nonlinear
problem. Heuristics are therefore the only practical
method for locating competitively viable solutions for realtime
operation. Therefore, a heuristics algorithm named
cost-efficient placement (CEP) is proposed in the description
algorithm that follows. The main logic of the proposed
CEP heuristic is to find a set of original candidate nodes to
place VNFs and apply the reusability VNFs to minimize the
reusable cost.
(10)
IEEE Systems, Man and Cybernetics Magazine - January 2023

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