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Flow Allocation in Industrial Intent-based Networks
Barun Kumar Saha
Corporate Research Center
ABB Global Industries and Services Pvt. Ltd.
Bangalore, India
barun.kumarsaha@in.abb.com
Luca Haab
Power Grids, PGGA-P
ABB Schweiz AG
Bern, Switzerland
luca.haab@ch.abb.com
Łukasz Podleski
Power Grids, PGGA-P
ABB Schweiz AG
Bern, Switzerland
lukasz.podleski@ch.abb.com
Abstract—Intent-based Networks (IBNs) are expected to add
various degrees of autonomy and intelligence at different stages
of a network, such as planning and operating. A particular use
case of IBNs relevant to industry is that of end-to-end flow
(service) allocation prior to commissioning such networks, for
example, in power grids. In this context, we investigate the
flow allocation problem for large networks by considering four
schemes. In Shortest Path-based Allocation (SPA), all-pair shortest
paths in a network are computed, which are then used to allocate
the feasible flows. To prevent near-maximal link utilization,
we consider a variation of SPA with usage threshold (SPA-T).
The two other schemes, SPA with probabilistic Hill Climbing
(SPA-HC) and SPA with Simulated Annealing (SPA-SA), also
impose a similar utilization limit on each link. Moreover, SPA-
HC and SPA-SA allocate the flows in a way to improve the
relative fairness. Results of performance evaluation using data
from real-life and synthetically generated networks show that
the proposed schemes can allocate 86%–99% flows when link
utilization threshold is varied from 0.75 to 0.95.
Index Terms—Intent-based Networks, flow allocation, meta-
heuristics, hill climbing, simulated annealing, shortest path
I. INTRODUCTION
IBNs [1]–[4] present the next wave in the evolution of
communication networks. IBNs promise many interesting fea-
tures, such as specification of network operations in high-
level languages [1] and continuous verification of a network’s
operating state. In other words, with IBNs, future networks
will have various degrees of autonomy and intelligence inbuilt
within them.
IBNs offer several industrial use cases [2] targeting different
stages of a network’s lifetime, for example, planning, commis-
sioning, and maintaining operations. A particularly interesting
one is that of planning and commissioning a new industrial
network, for example, in oil and gas fields and power grids.
Before deploying at a customer’s site, extensive planning
is done taking into account the overall network utilization.
Moreover, mission-critical networks typically have networking
devices, such as switches and routers, pre-configured and flows
allocated. In particular, given a set of required network flows
(or services), each (feasible) flow is mapped to an end-to-end
path in the network. Accordingly, relevant rules are installed
in the concerned devices. Moreover, Industry 4.0 is moving
toward Time Sensitive Networks (TSNs) [5]. TSNs need to
schedule flows based on input from field device controllers.
The flow allocation service of IBNs can help TSNs in this
regard. Moreover, operational IBNs can also use this solution
to plan future allocation of additional network flows.
Integral flow allocation (i.e., when no flow is split across
multiple paths) is a combinatorial optimization problem, which
becomes difficult—and costly, in terms of time and skill
needed by network engineers—to solve for large networks.
This is especially true for power grid networks, which often
contain a few hundred densely connected nodes. Motivated by
these challenges, in this paper, we investigate the problem of
flow allocation in large networks with finite link capacities.
We begin by considering a generic scheme, SPA, where
all-pair shortest paths in the network are computed. Subse-
quently, feasible flows, which do not cause violation of link
capacity, are allocated along those shortest paths. However,
such a greedy strategy, can make certain links operate at their
near maximum capacity. As a consequence, any increase in
instantaneous bit rates of one or more flows will potentially
lead to packet loss and delay. To mitigate these issues, we
consider SPA-T, where utilization of each link is limited up
to a threshold θ∈[0,1].
The SPA-HC and SPA-SA schemes are based on metha-
heuristics. In HC, one iteratively keeps choosing a relatively
better solution. However, in probabilistic HC, one also chooses
a worse solution with a small probability. SA [6], [7], on the
other hand, is modeled after the physical process of heating
a metal to a high temperature and then cooling it down very
slowly. Such a process helps in eliminating or reducing defects.
Since HC and SA both are well studied and characterized, we
find them suitable for industrial usage.
Each step of SPA-HC and SPA-SA compares two or more
solutions and selects a relatively better one. The (small) prob-
ability of selecting a bad solution is fixed in SPA-HC, whereas
it varies with iterations in SPA-SA. A “solution” is constructed
by considering the potential allocation of a very few candidate
flows. The value of a solution is a quantitative measure of
fairness in overall flow allocation. When a solution is selected
at the end of an iteration, the corresponding candidate flows
get allocated to the concerned shortest paths.
The scope of this work is limited to wireline networks.
Moreover, the proposed flow allocation strategies are executed
at a logical level; we do not discuss how the routing rules are
actually installed in physical devices.
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A. Contributions
The specific contributions of this work are as follows.
•Proposing greedy and metaheuristics-based algorithms
for efficient flow allocation in large networks.
•Using a threshold, θ, to limit the maximum utilization of
any link and thereby, help them decongest.
•Evaluating the efficiency of the proposed schemes via
simulations using data from real-life and synthetically
generated networks.
B. Organization
The remainder of this paper is organized as follows. Section
II presents a summary of the related works. Section III
presents the system model and discusses the flow allocation
problem. The greedy algorithms SPA and SPA-T are discussed
here. In Section IV, we discuss the proposed metaheuristics-
based algorithms for flow allocation. Experimental set-up
and performance metrics are discussed in Section V. The
corresponding results are presented in Section VI. Finally,
Section VII concludes this paper.
II. RE LATE D WOR K
Optimal flow allocation is a key requirement not only
for communication networks [8]–[11], but also transportation
networks [12]. The large volume of works on flow allocation
and scheduling only underscore how fundamentally important
it is for communication networks.
Hartert et al. [13] developed Declarative and Expressive
Forwarding Optimizer (DEFO) to achieve fast and scalable
routing with low congestion. DEFO partitions the network
graph into smaller “partial graphs,” and labels nodes shared
by any two such graphs as middlepoints. Subsequently, traffic
for a flow is forwarded from one middlepoint to another
until it reaches the concerned partial graph. DEFO, therefore,
reduces the scale of flow allocation problem to selection of
a few middlepoints and routing among them. This, however,
introduces a dependency in the network in order to achieve
inter-middlepoint routing.
Layeghy et al. [14] developed Software-defined Constrained
Optimal Routing (SCOR), a constraint programming (CP)-
based framework for optimal routing in SDNs. CP allows
to specify the desired objective function as well as different
networking constraints in a high-level language. Moreover,
multiple constraints can be combined together as required.
This can potentially simplify operations of a network manager.
In particular, SCOR constructs a binary matrix of links and
flows, and determines which flow should be assigned to which
link based on the given objective function. However, CP, in
general, lacks scalability. Obtaining an optimal solution—or
even a feasible sub-optimal solution—for a large network may
not be practically feasible.
Consideration of fairness is a common aspect in most flow
allocation works. Allybokus et al. [15], for example, used α-
fairness for multi-path flow scheduling, i.e., where flows can
be split across multiple paths. On the other hand, Ito et al.
[10] observed that bandwidth requirements in a network can
change dynamically and lead to bottleneck links and unfair
load distribution. To alleviate this, the authors proposed to
reallocate unused capacity of the links to high-demand traffic
flows. On a similar note, Boley et al. [8] proposed traffic
flow bandwidth reassignment to improve quality of service
of Software-defined Networks (SDNs).
Huang et al. [16] noted that, in practice, a legacy network
may upgrade into an SDN only in steps. Consequently, such
hybrid SDNs would require multi-path traffic to support both
legacy and SDN-enabled devices. The authors, therefore, pro-
pose a utility maximization scheme for bandwidth allocation
in hybrid SDNs.
To synthesize, we see that different methodologies have
been used to allocate network flows, be it during planning or
online operating states. Many of the allocation schemes, for
example SCOR, take an optimization approach. However, such
an approach may lack scalability with the growing size of net-
works. On the other hand, many schemes improve allocation
efficiency by splitting flows. This may not be applicable for all
industrial scenarios, for example, power grid networks, where
communication path symmetry is required. Therefore, in this
paper, we investigate the integral flow allocation problem for
large networks using metaheuristics and greedy strategies.
III. THE FL OW ALL OC ATION PRO BL EM
We represent a wireline network as graph G= (V, E ),
where Vis the set of vertices (or nodes) and Eis the set of
(directed) edges (or links). Let Fbe the set of flows that needs
to be allocated in the network G. Moreover, let FA⊆Fbe
the set of allocated flows in the network at any instant. F−FA
denotes the set of elements present in F, but not in FA, i.e.,
the set of unallocated flows. For any edge e∈E, let ceand
re, respectively, be the capacity and residual bandwidth of e;
then xe=ce−redenotes the bandwidth already used by the
edge. Moreover, for any flow f∈F, let dfbe the bandwidth
demand of the flow. We assume that ce>0and df>0for
each e∈Eand f∈F, respectively.
The objective of optimal flow allocation problem is to find a
set of paths (sets of subsets of E) so that traffic corresponding
to the flows in FAcan pass from their respective source
devices to target devices. The definition of “optimal” is highly
contextual. For example, some may want to maximize the
size of FA, whereas others may attempt to improve allocation
fairness. In the following, we discuss SPA and SPA-T, which
attempt to maximize the number of flows allocated.
SPA adopts a greedy strategy to allocate all flows that it
possibly can. In particular, SPA begins with computing all-
pair shortest paths (i.e., from any node to any other node)
for the given network. Subsequently, SPA iterates over all
the flows (F) that need to be installed. At each iteration,
based on the source and target of the concerned flow, SPA
evaluates whether or not the corresponding shortest path has
the minimum capacity to carry the flow. Let PEbe the set
of edges used by any path. Then, the minimum available
capacity of the path is min
e∈PE
re, i.e., the minimum residual
link bandwidth among all edges in PE. If a path is found to
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have minimum capacity available to carry a flow, then SPA
allocates the flow to the links of the concerned path. This
ensures that no link carries traffic more than its designated
capacity. The concerned flow is moved from set Fto FA.
Moreover, residual bandwidths of the links along the path are
reduced by an amount equal to the flow’s bandwidth demand.
Relevant data structures are updated to keep track of which
link carries what flows. When SPA terminates, the set FA
contains all the flows that are allocated for a given network.
SPA-T is exactly similar to SPA, except that maximum
utilization of any link (considering all flows passing through it)
is kept below θ. In other words, the above mentioned minimum
available capacity of the path is evaluated as min{min
e∈PE
re, θ}.
IV. METAHEURISTICS-BASE D FLOW ALLOCATION
The metaheuristics-based SPA-HC and SPA-SA schemes
also rely on pre-computed all-pair shortest paths and restrict
the utilization of each link up to θ. At each step, SPA-HC and
SPA-SA try to improve the overall fairness in link utilization.
We use Jain’s fairness index [17] for this purpose. In particular,
the fairness in bandwidth utilization of links arising out of a
flow allocation scheme is defined as:
J(FA, E) =
(P
e∈E
xe)2
|E|P
e∈E
x2
e
,(1)
where xeis the bandwidth usage of any edge e∈E. Equation
(1) requires that FA6=∅, i.e., at least one flow must be
allocated to compute J(FA, E). In our implementation, SPA-
HC and SPA-SA do an initial allocation of 10 randomly
selected flows using SPA. In both the schemes, the value of a
solution is given by (1), which ranges between 1
|E|and 1.
A. SPA-HC: SPA with Probabilistic Hill Climbing
Algorithm 1 presents the detailed steps of SPA-HC. The
Algorithm runs for a finite number of steps. In each iteration,
SPA-HC creates ηfeasible solutions.1The detailed steps for
creating a solution are depicted in Algorithm 2. The Algo-
rithm essentially selects up to φflows so that the cumulative
bandwidth usage (line number 10)2of the individual links do
not exceed the given threshold θ(line number 12). Note that κ
and φensure that Algorithm 2 terminates after a finite number
of steps.
Once a feasible solution is available, Algorithm 1 com-
putes the updated fairness index value (line number 8)3by
considering link usages based on FAas well as the potential
flows returned by the solution. If the projected fairness value
is better than the previous one, the solution is accepted (line
number 10). Moreover, the consideration of the probability
pbad potentially helps to avoid getting stuck in local optima.
1In classical hill climbing, ηis set to 1.
2To keep the presentation of this Algorithm simple, we skip listing the steps
where link usage from the other flows in the flow s list are also considered.
3In our implementation, we maintain a running sum of xeand x2
eso that
we do not have to repeatedly iterate over Eto compute J.
When a feasible solution is accepted, the sets Fand FA
are updated accordingly; link bandwidth measures are also
updated appropriately.
Algorithm 1: Flow allocation using SPA-HC
Input:
•F: Set of flows to allocate
•FA: (Very small) set of already allocated flows
•P: Set of all-pair shortest paths
•θ: Link utilization threshold
•η: Number of solutions to consider in an iteration
•φ: Maximum number of flows in a solution
•pbad: Probability of selecting a bad solution
Output: FA: Set of allocated flows
1max steps =|F−FA|
2istep = 0
3best value =Compute J(FA, E )using (1)
4while istep < max steps and |F−FA|> η do
// Solutions generated in this iteration
5S= [ ]
6for j∈1. . . η do
7s=create solution(F−FA, P, θ , φ, S)
// s.flows indicate the flows selected by
solution s
8v=Compute J(FA∪ {s.flows}, E )using (1)
9r=Uniform random number between 0and 1
10 if v > best value or r < pbad then
11 best value =v
12 best solution =s
13 end
14 end
15 flows =best solution.f lows
16 paths =best solution.paths
17 foreach (f, p)∈(f lows, paths)do
18 F=F− {f}
19 FA=FA∪ {f}
20 foreach e∈pdo
// Initially, re=xe,∀e∈E
21 re=re−df
22 xe=xe+df
23 end
24 end
25 istep =istep + 1
26 end
B. SPA-SA: SPA with Simulated Annealing
The SPA-SA scheme bears close resemblance to SPA-HC,
except the fact that, in each iteration, only one feasible solution
is evaluated. Algorithm 3 presents the detailed steps of SPA-
SA. The initial temperature Tis set to a high value, which
is scaled down by a factor 0< γ < 1(usually close to
0.99) in each iteration until Tgoes below ε(a very small
positive fraction) or the upper limit on number of iterations is
exceeded, whichever is earlier. Line numbers 8–10 represent
the heart of SA. Given a solution, we define cost as the
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Algorithm 2: Feasible solution creation
Input:
•FU: Set of unallocated flows
•P: Set of all-pair shortest paths
•θ: Link utilization threshold
•φ: Maximum number of flows in a solution
•κ: Maximum number of attempts
Output: A set of up to φfeasible flows and their
corresponding paths
1istep = 0
2flows = [ ]
3paths = [ ]
4while istep < κ do
5for j∈1. . . κ do
6f= Randomly selected flow from F−FA
7p= Shortest path from Pindexed by f’s
source and target
8flag =True
9foreach e∈pdo
// Potential new usage of edge e
along the path p
10 x0
e=xe+df
11 θe=x0
e/ce
12 if θe> θ then
13 flag =False
14 break
15 end
16 end
17 if flag is True then
18 Append fto flows and pto paths
19 foreach e∈pdo
20 re=re−df
21 xe=xe+df
22 end
23 end
24 if |flows|=φthen
25 break
26 istep =κ// Exit the outer loop
27 end
28 end
29 istep =istep + 1
30 end
31 return (f lows, paths)
reciprocal of its value. The difference in cost between the
current solution and a previous one is stored in ∆. Based on
this, the acceptance probability Ais defined, which depends
both on the contemporary temperature and the cost difference.
New solution that provides a lower cost is definitely accepted;
otherwise it is chosen with probability A.
V. PERFORMANCE EVAL UATIO N
In this Section, we discuss the experimental setup and the
metrics used to evaluate the proposed flow allocation schemes.
Algorithm 3: Flow allocation using SPA-SA
Input:
•F: Set of flows to allocate
•FA: (Very small) set of already allocated flows
•P: Set of all-pair shortest paths
•T: Initial temperature
•γ: Cooling coefficient
•ε: Zero temperature
•θ: Link utilization threshold
•φ: Maximum number of flows in a solution
Output: FA: Set of allocated flows
1max steps =|F−FA|
2istep = 0
3best value =Jain’s index based on FAand E
4while T > ε and istep < max steps do
5s=create solution(F−FA, P, θ , φ)
6v=Compute J(FA∪ {s.flows}, E )using (1)
7∆ = 1
v−1
best value
8A= exp(−∆
T)
9r=Uniform random number between 0and 1
10 if ∆≤0or r < A then
11 best value =v
12 best solution =s
13 flows =best solution.f lows
14 paths =best solution.paths
15 foreach (f, p)∈(f lows, paths)do
16 F=F− {f}
17 FA=FA∪ {f}
18 foreach e∈pdo
19 re=re−df
20 xe=xe+df
21 end
22 end
23 end
24 T=γT
25 istep =istep + 1
26 end
A. Experimental Setup
We implemented the proposed algorithms using Python 2.7
in a Linux system with Intel(R) Core(TM) i5-4570S 2.90 GHz
CPU and 8 GB RAM. The “networkx” library of Python was
used to compute the all-pair shortest paths.
We used two real-life network topologies (labeled as “NR1”
and “NR2,” respectively) and a synthetic topology (labeled as
“NS1”) from the data set made available by Hartert et al. [13].
These network topologies and the corresponding flow demands
are summarized in Table I.
We conducted several experiments to investigate the flow
allocation schemes. First, we executed SPA, SPA-T, SPA-HC,
and SPA-SA with the aforementioned three networks of differ-
ent sizes as input. This helped us to collect various data, such
as the number of flows allocated, average path length, number
of hot links, and execution time. Next, keeping all other
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TABLE I: Network topologies and flow demands
NR1 [13] NR2 [13] NS1 [13]
Nodes 79 87 199
Links 294 322 522
Flows 6162 7527 37881
Min. link bandwidth (bps) 2400000
Max. link bandwidth (bps) 10000000
Min. flow demand (bps) 1 11 11
Max. flow demand (bps) 499374 396931 118476
parameters constant, we varied the value of θto investigate
how utilization threshold affected the flow allocation. We also
performed sensitivity analysis of the algorithms’ parameters.
We varied the value of pbad from 0.002 to 0.012 to understand
how selecting a bad solutions affected SPA-HC.
At the beginning of each experiment, the network and
corresponding flow details were read from an external file.
Based on these, a networkx directed graph data structure
was created, which was then used to compute the all-pair
shortest paths. Each experiment was repeated for five times,
based on which the mean and 95% confidence interval were
computed. Unless otherwise specified, we assumed θ= 0.85,
T= 100000.0,γ= 0.999,ε= 10−5,pbad = 0.01,η= 10,
and φ= 5.
We considered the following metrics to measure the perfor-
mance of SPA, SPA-HC, and SPA-SA.
•Percentage of flows allocated (|FA|
|F|) by each scheme
•Fairness of flow allocation across the network measured
by Jin (1)
•Utilizations of the links breaching threshold θ(only in
case of SPA)
•Processing time of the proposed schemes
The final metric, processing time of a scheme, indicates
the time spent in reading the network data file, constructing a
graph data structure from it, computing the all-pairs shortest
path, performing algorithm-specific operations, and finally,
verifying the allocations.
VI. RE SU LTS
Figure 1a shows the percentage of flows allocated by SPA,
SPA-T, SPA-HC, and SPA-SA in the three networks. Note
that as we move from NR1 to NR2 and NS3, both the size
of the network and number of flows to allocate increase. In
general, SPA allocated more than 90% flows in all the three
networks. SPA-HC, on the other hand, was found to allocate
more flows than SPA in the networks NR1 and NR2. This
can be accounted to the comparison of multiple solutions
at each step of SPA-HC. However, for larger networks, the
maximum limit on the number of steps executed by SPA-HC
potentially disallowed consideration of enough candidate solu-
tions. This largely explains why SPA-HC allocated marginally
less number of flows than SPA in case of NS1. On the other
hand, since SPA-SA evaluates only one potential solution in
each iteration, enough alternative flow allocations may not
have been considered by SPA-SA. This possibly resulted in
relatively less number of flow allocations by SPA-SA in the
three networks. Finally, SPA-T allocated fewer flows than SPA
because of the additional link utilization threshold constraint.
Figure 1b plots the Jain’s fairness index obtained with
respect to flow allocation. In general, SPA-HC resulted in
a relatively more fair flow allocation than its peers. This is
because SPA-HC, by considering ηsolutions, had a better view
of the global solution space. On the other hand, even SPA-T
was found to be fair than SPA, because the former did not
indiscriminately allocate flows to links.
Figure 1c shows the total time taken by the algorithms to
complete their execution. SPA and SPA-T were found to be the
fastest schemes, which took less than or up to a second. SPA-
HC and SPA-SA, in contrast, took several minutes to complete
execution. In particular, SPA-HC takes about 40 minutes, on
average, to allocate the flows in NS1. This is largely due to the
several solutions (combinations of multiple flows) that SPA-
HC generate and evaluate in each iteration. SPA only evaluates
whether or not a given path can meet requirements of a flow.
Consequently, SPA takes much lower execution time compared
to its counterparts.
We also look at the links whose utilization crossed θunder
SPA. In particular, SPA created six, ten, and seven such links
in NR1, NR2, and NS1, respectively. Figure 2 shows that most
of those links were very close to 100% utilization. As noted
earlier, this can lead to potential network disruptions in the
near future.
Figure 3 shows how pbad, the relative frequency of choosing
a bad solution, affected the performance of SPA-HC. The plots
with solid lines show that, as pbad increased, more flows were
allocated in the networks NR1 and NR2. However, at the
same time, the overall fairness of flow allocation measured
by (1) consistently decreased (dotted lines, y-axis on the right
side). In particular, beyond pbad = 0.01, the increase in flow
allocation was almost negligible. The plots indicate that the
value of pbad should typically range between 0.005 and 0.01.
Figure 4 shows how the performance of SPA-HC, SPA-
SA, and SPA-T varied with the link utilization threshold. As
expected, when θincreased, all the schemes allocated more
flows (plotted with solid lines), because capacity of links to
accommodate new flows increased. At the same time, fairness
in link utilization (plotted with dotted lines) decreased with
increase in θ. Interestingly, the percentage of flows allocated
did not seem to have a steep increase with θ. In other words,
setting link utilization threshold to say, more than 90%, may
not be of much practical use.
VII. CONCLUSION
The rise of industrial IBNs would witness various forms
of automation both in-network and to other/external networks.
One such service is the flow allocation for large networks.
In this paper, we investigated four schemes in this regard.
All these algorithms rely upon pre-computed all-pair shortest
paths for a network. SPA-T, SPA-HC, and SPA-SA tend to
maximize the number of flows allocated while also limiting
per-link bandwidth usage and thereby, improving the alloca-
tion fairness. SPA-HC fares better than the others because it
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80
85
90
95
100
NR1 NR2 NS1
Flows allocated [%]
Network
SPA
SPA-HC
SPA-SA
SPA-T
(a) Total flows allocated.
0
0.1
0.2
0.3
0.4
0.5
NR1 NR2 NS1
Jain’s fairness index
Network
SPA
SPA-HC SPA-SA
SPA-T
(b) Flow allocation fairness.
10-1
100
101
102
103
104
NR1 NR2 NS1
Processing time [s]
Network
SPA
SPA-HC SPA-SA
SPA-T
(c) Processing times (y-axis in
log-scale).
Fig. 1: Comparative performance of the SPA, SPA-T, SPA-HC, and SPA-SA.
86
88
90
92
94
96
98
100
Link utilization [%]
NS1NR2NR1
Fig. 2: Highly utilized links
under SPA (θ= 85%).
60
65
70
75
80
85
90
95
100
0.002 0.004 0.006 0.008 0.01 0.012 0.3
0.4
0.5
0.6
0.7
Flows allocated [%]
Jain’s fairness index
Probability
NR1
NR1
NR2
NR2
Fig. 3: Effects of pbad on
SPA-HC.
93
94
95
96
97
98
99
100
0.75 0.8 0.85 0.9 0.95 0.35
0.36
0.37
0.38
0.39
0.4
0.41
Flows allocated [%]
Jain’s fairness index
Link utilization threshold
NR1
NR1 NR2
NR2
(a) SPA-HC.
88
90
92
94
96
98
100
0.75 0.8 0.85 0.9 0.95 0.35
0.36
0.37
0.38
0.39
0.4
0.41
Flows allocated [%]
Jain’s fairness index
Link utilization threshold
NR1
NR1
NR2
NR2
(b) SPA-SA.
86
88
90
92
94
96
98
0.75 0.8 0.85 0.9 0.95 0.34
0.35
0.36
0.37
0.38
Flows allocated [%]
Jain’s fairness index
Link utilization threshold
NR1
NR1 NR2
NR2
(c) SPA-T.
Fig. 4: Effects of utilization threshold θon the different schemes.
takes a more detailed look at the feasible solutions space. On
the downside, it takes a longer time to run.
The results presented here offer various insights and di-
rections that can be investigated in the future. In particular,
speeding up SPA-HC while retaining its performance would
be a very interesting task. Moreover, other local and global
search techniques can be explored in quest of better solutions.
Additional constraints for flow allocation, for example, latency
and jitter, can also be considered, which, in turn, would make
the problem still more difficult.
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