IEEE Systems, Man and Cybernetics Magazine - January 2023 - 15

As mentioned in step 1, CEP
chooses the target node in E. In
CEP, searching for the minimum
cost involves the node-choosing
process. Hence, the searching
phase of the node set and choosing
cost phase are appl ied in
this algorithm. As a result, the
computat ional complexity is
() ()
OO 2
log
+
nn k , where n de -
notes the number of nodes and k
denotes the number of requests.
Here, let OPT be the results of
the optimal solution. The complexity
of searching the minimum cost
in all nodes is O(logn). There are n
nodes in this system, and m nodes
are on the paths of the user and destination. It can be said
that the cost of the ith node # OPT/ni 1-+
rithm 1 chooses the most cost-effective solution for each
step, the cost of the ith node
denotes the nodes not allocated in this algorithm), while
the value of E − A equals ni 1-+ .
The of all nodes
cost
#
#
#
a
OPTOPT
2
1
OPT
OPT*
a1
logn.
Numerical Results
In this section, we show the performance of our proposed
placement strategy CEP. Our simulations are run in
MATLAB on an Intel i7-12700F 2.1-GHz machine with
32 GB of RAM. We consider this scenario in the industry
system; the number of industrial edge nodes is random
from 20 to 50. The kind of the VNF number is five, and the
job requires randomized VNFs among the nodes [1], [5].
The number of requests is 50-100. We assume that a total
of 100 requests are generated and required to allocate
VNFs in the system. From the perspective of the physical
resources of the nodes in the system, we assume that
each node has 8-16 GB of memory capacity and 16
Algorithm 1. CEP Algorithm.
1: For any request r, find the destination dD! and the
source sS! and the links L among the SD pair.
2: In the set of links L, select the minimum cost to allocate
desired VNFs and find all candidate nodes by E.
3: Choose the minimum cost nodes for request r to host
VNF ,ir
.
4: Based on the first-round placement, for other requests r,
find the minimum reusable cost to serve the request and
host the VNFs until running out of resources.
5: Repeat steps 3 and 4 until all VNFs of request r are
hosted.
++ +
++ +
11
g
OPT
2 g n k
n k
Our proposed CEP
method effectively
slows down the
increasing speed of
cost for the feature
of VNF reusability,
which reduces the
installation cost to
some degree.
virtual CPU cores. The virtual memory
requirement is 50-200 MB and
takes 0.2-0.5 cores. For the network
constraints, we assume that
the link capacity is 1 Gb/s and
that each VNF uses 1-10 Mb/s.
The detailed parameters are shown
in Table 1.
The CEP method is based on a
CEP heuristic method. We evaluate
our CEP compared to VNF Placement
Edge (VPE) [21] based on the
minimum cut graph method and
cost-efficient VPS scheme (CE-VPS)
method, and we model their throughput
as a function of the available
computing resources [8]. The VPE
^h. Since Algo#
OPT/EA-^h (here, E − A
method focuses on minimizing cost from communication
and energy consumption in a mobile edge system, while
the CE-VPS method works in public cloud networks to
trade off computing resource consumption and latency
guarantees. In this article, we compare three metrics,
including cost, latency, and accepted ratio. The detailed
performance is shown in Figure 2.
In Figure 2(a), we investigate the total cost with the
increasing number of edge nodes. With the increasing number
of nodes, the available resources allocated to VNFs get
increased, so the overall cost gets lower as the number gets
larger. The cost of the CE-VPS method gets larger because
it considers reducing the costs by placing VNFs at a small
Table 1. The simulation parameters.
Parameter
Number of nodes
VNF-type number
VNFs in one request
Number of requests
Memory required per VNF
CPU required per VNF
Link required per VNF
Delay requirement
Memory capacity
Capacity per link
CPU capacity
Link delay
Reusability of the VNF
Cost per node to host the VNF
Value
20-50
5
1-5
50-100
50-200 MB
0.2-0.5
1-10 Mb/s
1-3
8-16 GB
1 Gb/s
16
[0.2, 0.4]
1-2
1-5
January 2023 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 15

IEEE Systems, Man and Cybernetics Magazine - January 2023

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