Efficient Routing for Overlay Networks in a Smart Grid Context
Lasse Orda
a
, Tue Vissing Jensen
b
, Oliver Gehrke
c
and Henrik W. Bindner
d
Department of Electrical Engineering, Technical University of Denmark, Kongens Lyngby, Denmark
Keywords:
Smart Grid, Overlay Network, Peer-to-Peer (P2P), Distributed Hash Table (DHT), Routing Table, Location-
aware Routing.
Abstract:
In the modern smart grid, prosumers and communities, organized in energy collectives, are showing an in-
creased desire to trade energy directly using different forms of decentralized market models. To support local
autonomy and distributed services, decentralized networking, using peer-to-peer (P2P) networks, can be used
to facilitate dynamic discovery and establish communication between peers. When using a modern overlay
network based on a Distributed Hash Table (DHT), the performance of the overlay network can be improved
by using the physical properties found in the smart grid context. This paper presents an improved network
routing model that takes advantage of these properties, to add a location-aware heuristic to the search algo-
rithms of a standard overlay network. Concepts from complex networks are utilized to improve the average
search path and provide a more efficient design over previous solutions. A proof of concept shows that the
design results in a more efficient routing model, when used in a smart grid context, compared to a standard
uniformly distributed network model.
1 INTRODUCTION
Peer-to-peer networks provides decentralized and dis-
tributed communication that can facilitate the dy-
namic network configuration of distributed energy re-
sources (DER) in a distributed network. Large net-
works such as consumer broadband and the internet
is slow to adapt to changes (Nygren et al., 2010) and
do not provide all of the features to support decentral-
ized communication. Overlay networks are developed
to provide these features, can be rolled out with a fast
cadence, and provides features such as predictable la-
tency (Andersen et al., 2001), scalability, improved
robustness and resilience.
The desire from prosumers and energy collectives
(Moret and Pinson, 2018) to engage in dynamically
changing contract relationships, building micro-grids
and operate fully decentralized, requires a communi-
cation layer that can handle decentralization and the
continuous changes in network topology.An overlay
network can provide the solution and facilitate the
growth of new services and markets (Greer et al.,
2014).
a
https://orcid.org/0000-0002-1787-3559
b
https://orcid.org/0000-0002-6594-5094
c
https://orcid.org/0000-0001-8184-6435
d
https://orcid.org/0000-0003-1545-6994
In a smart grid, DERs connected to the grid, have a
location property. The location can be static as in the
case of stationary DERs or it can be dynamic in the
case of electric vehicles (EV). An overlay network is
generally based on a uniform distribution of nodes in
the network, which ensures robustness and resilience.
However the additional properties introduced by the
smart grid add both requirements (Budka et al., 2014)
to the overlay network as well as the possibility to
optimize the distribution of nodes.
The topic of location aware overlay networks and
multi-dimensional identifiers has been touched upon
by related research, however these works have fo-
cused on their specific goals and interests, e.g. the
work of (Gross et al., 2013) on searching for peers in
a specific geographical location. This paper presents a
design of an overlay network that, in a smart grid con-
text, supports using multiple attributes for routing and
improves performance over previous solutions. The
location property of the smart grid, makes it possible
to add location aware routing to the overlay network
and use a location-based heuristic to calculate the dis-
tance between nodes. To support multi-dimensional
routing, concepts from complex network theory is
used to structure a routing table that improves rout-
ing efficiency.
The overlay network presented in this paper builds
Orda, L., Jensen, T., Gehrke, O. and Bindner, H.
Efficient Routing for Overlay Networks in a Smart Grid Context.
DOI: 10.5220/0007717702510258
In Proceedings of the 8th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2019), pages 251-258
ISBN: 978-989-758-373-5
Copyright
c
2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
251
upon the related work presented in section 2, with the
design of an efficient multi-dimensional routing table
presented in section 3. A proof of concept is described
and tested in section 4 and the results are presented
and evaluated in section 5.
2 RELATED WORK
Modern overlay networks are based on a distributed
hash table (DHT) (Stoica et al., 2001) which contains
nodes with a unique identifier using a uniform dis-
tribution of nodes in the network. The identifier is
used to calculate the distance between nodes, which
is used in the search algorithms. Making overlay net-
works location-aware has seen several suggestions.
One way is to map the multi-dimensional space onto
the one-dimensional space of the identifier (Lopes and
Baquero, 2007), (Nam and Sussman, 2006), (Zahn
et al., 2006), e.g. using space filling curves (Kova
et al., 2007), (Chawathe et al., 2005a), (Knoll and
Weis, 2006), but it has been shown that it is diffi-
cult to do this optimally and it is hard to preserve
the original location (Chawathe et al., 2005b). Other
designs are based on tree structures that are parti-
tioned into a two dimensional space that maps the
two dimensions of a location (Harwood and Tanin,
2003), (Ara
´
ujo and Rodrigues, 2003), (Asaduzzaman
and von Bochmann, 2009), (Heutelbeck and Hemmje,
2006), (Picone et al., 2010). In (Harwood and Tanin,
2003) super-peers are used to control a region and
handle load balancing, but these approaches are sus-
ceptible to dynamic changes in the network. Another
approach is to partition the space into grids (Kantere
et al., 2009), but this suffers from poor performance
during high churn as well as load balancing issues
(Chawathe et al., 2005b).
Kademlia (Maymounkov and Mazieres, 2002) is a
well-known overlay network based on a DHT. The ba-
sic Kademlia routing table is an unbalanced tree with
leafs (known as k-buckets) covering a 160 bit address
space. Each k-bucket covers a part of the range of
the 160 bit space and together all the k-buckets covers
the entire address space in the network. This rout-
ing table provides a segmentation of the network and
fast lookup. However, encoding multiple dimensions
into the 160 bit identifier is not easy without losing
the data needed to calculate the distance metric. Re-
placing the original XOR metric with one based on,
e.g., the Haversine distance (Korn, 2000) presents a
problem as the address space of the identifier is un-
known in a dynamic system. This makes it difficult to
efficiently create a k-bucket range, or would require
continuously restructuring of the k-bucket space, re-
sulting in poor performance.
Geodemlia (Gross et al., 2013) proposes a solution
to this by creating a small range of buckets which first
sorts nodes into buckets depending on their bearing
and then into a number of distance-buckets with expo-
nentially increasing distance. However, the width of
the address space in the k-buckets used in Geodem-
lia is statically defined, which makes it susceptible
to having unbalanced buckets e.g. in the case of
heavily clustered nodes within a small area, resulting
in a longer search path. Geodemlia add new nodes
with a probability inverse proportional to the distance,
meaning that it contains more nodes nearby than far
away. This fulfills the long-range property (Aberer
et al., 2005), but leaves room to optimize the average
path length.
Applying small-world network and scale-free net-
work models can improve network performance
(Amaral et al., 2000), while the average path length
can be reduced by organizing the nodes in a network
using the concepts in a small-world network. Watts-
Strogatz (Watts and Strogatz, 1998) were some of the
first to study small-world networks and describes a
model to produce graphs with small-world properties.
The Barabasi-Albert model describes an algorithm to
generate scale-free network with preferential attach-
ment, which can be used to generate small-world net-
works (Albert and Barab
´
asi, 2002). The Barabasi-
Albert model is interesting because it generates net-
works without the need for a fixed address space. This
makes it especially useful for use in a dynamic net-
work growth scenario.
A smart grid can be a highly dynamic system e.g.
in the case where EV’s move around, resulting in new
locations, while properties of the nodes change de-
pending on the applications and services they provide
and participate in. The overlay network can be im-
proved over previous solutions by using a heuristic
that enables a directed search in the network. Routing
efficiency and load balancing can be improved by ap-
plying concepts from scale-free and small-world net-
works, most importantly local clustering, long-range
property and random hubs, resulting in an overall
shorter average path.
3 ROUTING IN A SMART GRID
The overlay network presented in this section builds
on the Kademlia overlay network and uses its proto-
cols and search algorithms. The routing table in the
underlying network has been replaced to support lo-
cation aware routing and search, but can support any
number of dimensions. The new routing table is de-
SMARTGREENS 2019 - 8th International Conference on Smart Cities and Green ICT Systems
252
(a) A search using uni-
form node distribution rip-
ples out from the starting
position.
(b) Using a location based
heuristic results in directed
search and a shorter average
path.
Figure 1: Using a heuristic to optimize the search path.
signed to support a multi-dimensional metric and dis-
tance calculation.
A standard DHT based overlay network uses a
uniform distribution of nodes that provides global re-
silience, load-balancing, good support for churn and
many other features. When location is introduced,
the distribution becomes clustered around the nodes
physical location, this improves local resilience, per-
formance and efficiency, but at the cost of global ro-
bustness. To improve global performance, the model
and properties of small-world networks is used to im-
prove both local and global performance.
As the underlying routing and iterative search al-
gorithm is based on uniformly distributed nodes, the
result is that the search will spread out in all directions
as shown on figure 1a. With the additional properties
in the smart grid, the search performance is improved
by using the location in the heuristic for the distance
calculation. The heuristic is based on the geograph-
ical distance between the nodes and by directing the
search towards the target node, shown on figure 1b,
the search path length is reduced.
3.1 Improved Routing Table
In a small-world network most of the nodes are not
neighbors, but there likely exists a connection be-
tween the neighbour of a given node and other nodes.
A property of small-world networks is that most
nodes can be reached with a small number of steps.
Another property of small-world network is robust-
ness as the shortest paths between nodes flow through
hubs, and if a peripheral node is deleted it is unlikely
to interfere with connection between other periph-
eral nodes. As the amount of peripheral nodes in a
small world network is much larger than the amount
of hubs, the probability of deleting an important hub
node is low.
These properties of the small-world network pro-
vides good average performance both when querying
(a) Local neighbors. (b) Random neighbors.
(c) Random hubs.
Figure 2: Network model concepts used to improve routing
efficiency.
local clustered nodes as well as nodes in remote clus-
ters. In a standard overlay network, the identifier as-
signed to each node is a simple hash value. To provide
support for multiple dimensions, a complex identifier
is required to contain multiple dimensions, such as
a unique id, and coordinates. Because the identifier
of the node consist of multiple dimensions, the un-
derlying DHT design with k-buckets cannot be used.
Instead the design must handle multiple dimensions
and do it in a dynamic way, such that the grouping of
nodes does not causes hot-spots. Previous solutions
uses fixed ranges for the buckets or require continuous
recalculation. Preferably the design should adapt to
changes in the network by adjusting the bucket ranges
over time and in a way that does not require recalcu-
lation.
The local nodes in figure 2a ensures detailed
knowledge of nearby nodes. This is the most ba-
sic bucket of nodes, but needs a dynamic approach
that adapts the probability of nodes being added so
that it can adjust to different networks automatically.
The random neighbors in figure 2b provides the long-
range property, which compliments the local nodes by
providing access to random remote nodes. The in-
clusion of random nodes results in a shorter path on
average. The random hubs in figure 2c is an addi-
tional improvement, where hubs in the network fur-
ther cut down the average path. A hub is known by
many nodes and know many nodes, which compared
to random nodes results in fewer network hops. The
routing table uses dynamic ranges, such that as the
network grows, the routing table dynamically adapts.
Efficient Routing for Overlay Networks in a Smart Grid Context
253
Figure 3: Probability curves for d
avg
= 1. ϕ affects the prob-
ability of nodes being added to A, such that more remote
nodes can be allowed or disallowed into A.
The design of the routing table consists of three
classes of buckets: A, a dynamic range based bucket
of local nodes; B, a bucket containing random nodes;
and C, a bucket of network hubs.
The local nodes bucket A, holds the local neigh-
bor nodes and creates a cluster with neighboring
nodes such that local nodes have good connectivity.
This provides very fast local communication and fast
lookup when queried by a remote node.
P
a
(d) = e
(d/d
avg
)
ϕ
(1)
A has a max size A
max
of suitable proportions such
as 1.000. Nodes are added to A with a probability P
a
,
shown in equation 1, such that the chance of nodes
being added to routing table A decreases exponen-
tially as the distance grows. d denotes the distance
to the node, d
avg
is the average distance of the nodes
currently in A and ϕ describes the slope of the curve,
whether it should include more nodes with long dis-
tance or with a short distance.
Figure 3 shows the characteristics of probability
with changes to ϕ. The probability curve is dynami-
cally updated as d
avg
changes with time, as the net-
work grows and the overlay network learns about
other nodes. When there are many nearby nodes,
the curve will prefer nodes that are even closer and
nodes far away have less probability for being added.
When there are less nearby neighbors, the algorithm
allows for nodes further away to be added. This is an
improvement over previous solutions that uses fixed
sizes for sub-buckets, which can lead to unbalanced
buckets.
Removal of nodes, happens using a FIFO queue,
though with a preference for nodes which are inac-
tive, described in equation 2 and 3. When a node
becomes inactive e.g. because it is unresponsive or
returns bad results, it is placed in a passive queue. As
nodes are removed from a bucket, the passive nodes
are removed first, and then active nodes are removed,
both in FIFO order.
n =
(
L
i
[0] if L
i
Q =
/
0
(L
i
Q)[0] otherwise
(2)
(L,Q) =
(
(L \ {n}, Q{n}) if n Q
(L \ {n}, Q) otherwise
(3)
L denotes the node bucket to remove a node n
from, i.e A, B or C, and Q is the queue of passive
node.
The random neighbor bucket B, contains nodes
which exhibit the long-range property of small-world
networks and the distribution is completely random.
Nodes with any distance can be added, as statistically,
the larger portion of nodes in the network are further
away from a given node, than its nearby neighbors
and as such, there is no need to cut-off nodes with a
short distance. The long-range property is important
to provide connectivity to nodes far away and thereby
reduce the path length for non-local queries.
rate = r ·
1
t
last
+ (1 r) · prev rate (4)
P
b
=
rate
target rate
1
(5)
Nodes are added to and removed randomly from
B, operating on a passive modus. I.e. whenever other
nodes makes contact, they are added to B. The ran-
dom property of B is important to keep the robust-
ness of the network, but to avoid excessive rotation
of nodes and mitigate abuse or bad behavior, the in-
clusion of nodes is rate limited. The rate, in equation
4, continually adjusts to reach a target rate. The tar-
get rate can be some constant e.g. add max 10 nodes
per second or it can be dynamically updated based on
network performance or user preference. The rate is
based on the previous rate and to help dampen fluctu-
ations, a smoothing factor r is added to the rate. P
b
is
then calculated based on the rate and the target rate, in
equation 5, to provide a probability for adding a new
node to the bucket.
The random hubs bucket C, consists of nodes that
are estimated to be hubs. As the network grows, some
nodes becomes known to many nodes and as such,
over time, they become a hub in the network. A node
is acquired on an active modus, by actively querying
random known nodes for a single random node. This
action is scheduled to happen periodically, e.g. on the
underlying maintenance loop. New nodes are simply
added with no restrictions, as the discovery of new
nodes happens in a controlled loop.
When a search is initiated or a query is received
from the network, the standard procedure is to com-
pute and return k nodes from the routing table by
calculating the distance with a given identifier. In
Kademlia the standard specifies that k is 20. Here,
using A, B and C a mix of nodes from each is returned
SMARTGREENS 2019 - 8th International Conference on Smart Cities and Green ICT Systems
254
Table 1: Nodes in test networks.
Test network Number of nodes
European test feeder 900
8500 entity test feeder 2.500
NetworkX geometric network 2.000
to fulfill the properties of a small-world network to
form the search set S:
S = A{m} B{n} C{n},k = m + n + n, (6)
where the notation A{m} indicates that m random
nodes are selected from A.
A smaller range from B and C e.g. n = 5 is re-
turned and a larger range from A e.g. m = 10 is re-
turned. A larger portion of nodes from A is used to in-
crease the probability of returning a local node which
may be relevant for the request and to support the un-
derlying algorithm, which has several functions that
requires the nearest neighbours of a node. S in equa-
tion 6, is sorted according to the distance to the given
target node defined in the query and returned to the
network query or to the underlying routing algorithm.
4 PROOF OF CONCEPT
To evaluate the efficiency of the routing table, it was
tested in 3 different scenarios. The scenarios consists
of networks based on the IEEE European Low Volt-
age Test Feeder, the IEEE 8500 Entity Test Feeder
(Dugan et al., 2009) and a generated geometric scale
free network created with the Python library Net-
workX (Hagberg et al., 2008).
The routing table design has been implemented
in a prototype overlay network along with an imple-
mentation of the default Kademlia specification. The
two implementations utilizes the same underlying al-
gorithms described by Kademlia.
The IEEE Test Feeder networks, shown in figure
4, provides realistic test cases for testing the location
aspect of the heuristic and routing. The test feeders
are used both to provide the location data as well as
the initialization of the DHT state of the communica-
tion links between the nodes in the overlay network.
Using the test feeder as a model for a computer net-
work, where every node is more or less chain-linked
to only one or two other nodes, results in an unnatural
state on initialization for the overlay network. It does
however provide a good initialization state for com-
paring how efficient the routing is able to find its way
through the network and to analyze how the routing
table is built as it interacts with the network.
Tests are performed using multiple iterations, each
with a randomized start point and end points in the
(a) 900 node test feeder lay-
out.
(b) 2.500 node test feeder
layout.
Figure 4: IEEE Test Feeders.
network. Each iteration has multiple sub-iterations
using the same starting node for the iteration, but with
randomized end nodes. This ensures that the network
is subjected to queries across more than 90% of the
network.
As each search in the network results in a path
that has a different length and because the nodes are
randomly chosen, the results cannot be directly com-
pared and needs to be normalized with the shortest
path. The shortest path is obtained by utilizing Di-
jkstra’s shortest path algorithm on the full network
model, which is used to initialize the network. The
resulting efficiency factor ω can be used to compare
the tests:
ω =
query path length
shortest path
, (7)
where the query path length is the total path tra-
versed in the query including the path count of the
sub-queries sent as parallel queries in the algorithm.
Note, that ω may be less than 1, as the query path may
be shorter than the initial path length after routing ta-
ble updates.
To simulate an active network, where every node
is alive, each node should randomly do some work to
exercise its routing table, this will help build the con-
nections between the nodes. To achieve this, a random
amount of nodes performs a search in the network for
each sub-iteration of the reference node.
4.1 Test Configuration
The test feeder networks are tested with the standard
bucket size k = 20 and k = 10 for the default overlay
network and with a range of sizes, noted in table 2,
for the multi-dimensional routing table. The purpose
is to explore the impact of various bucket sizes. Since
a bucket size of 3.000 would equate to a DHT that can
contain every node in the European test feeder and
about half of the nodes in the 8500 entity test feeder
network, it is necessary to test the network using a
smaller bucket size to simulate a network where the
Efficient Routing for Overlay Networks in a Smart Grid Context
255
DHT can only know a portion of the total nodes. This
will make the efficiency of the routing table have an
effect as the nodes learns about the network.
Table 2: DHT bucket sizes used for testing.
Overlay network Bucket sizes (k)
Kademlia 3.200 (k = 20)
1.600 (k = 10)
Multi-Dimensional 3.000
300
150
60
The size of each bucket: A, B and C in the multi-
dimensional routing table is 1/3 of the number in table
2, which means that e.g. A has a size of 1.000.
The NetworkX generated network uses a geomet-
ric network model with small-world network proper-
ties, to provide an initialization that is similar to a
real computer network. This provides a more real-
istic starting point for testing albeit less realistic with
regards to the location aspect.
5 RESULTS
5.1 Efficiency of Routing Tables
The figures 5a, 5b and 5c show the results of running
the test on the three different network models. On
figure 5 and 6, md references the multi-dimensional
routing table and kd references the standard Kadem-
lia routing table. The dotted lines are the results of
the default overlay routing based on Kademlia with
standard bucket size and also k = 10. The other lines
shows the multi-dimensional routing table using the
four different bucket sizes. The curve is very steep in
the first few iterations, as the overlay networks learn
about the nodes in the network. Because the nodes are
initialized with a very simple state, the first queries in
the network will fill up the routing tables quickly. The
results on figure 6 show the average bucket size across
the entire network for each iteration. The connection
between the efficiency on figure 5 and the bucket size
shows that, as the buckets are filled, the efficiency im-
proves. Generally the standard routing table is filled
faster than the multi-dimensional routing table, this
is partly because the standard routing table performs
more queries in the network and partly because of the
configuration of the probability curves for the multi-
dimensional routing table. A continuous increase in
performance on figure 5 can be seen from the graphs
as the properties from small-world networks begins to
have an effect. The Kademlia curve reaches a plateau,
where it doesn’t really improve any further with the
given network. But the multi-dimensional routing ta-
ble continually improves its efficiency as it is able to
bring down the average path length by taking advan-
tage of the long-range and random hub properties.
The difference in efficiency, using different bucket
sizes becomes visible in two different ways: first the
initial learning curve lands on different levels, where
the size of the bucket dictates the efficiency level, a
larger bucket can hold more nodes giving a larger
knowledge space. The second way is less obvious,
in the test feeder networks, the smaller buckets actu-
ally converges to about the same efficiency, but still
with an improving trend. However, using too small a
bucket size hinders increase in efficiency as the bucket
will start forgetting nodes. The overall efficiency in-
crease across all three networks is about a factor 10.
A good solution has both a small ω and a small bucket
size. The less space used, the more optimal the solu-
tion is.
5.2 Discussion
In the presented routing table, an issue arises, when
the algorithm has to move in a direction that goes
against the heuristic. Since the heuristic prefers to
move towards the target node location, it tends to ex-
amine the nodes in that direction first, but if the only
connection to the node is through a node that lies fur-
ther away than the given start node, it will prefer to
not take that route. This is where the random neighbor
and random hubs are important, as they allow the al-
gorithm to try a search starting from a different point
in the network. This not only allows the search to
succeed, it also improves the average path length.
To improve network stability and to provide
some protection against attacks like denial of service
(Douceur, 2002), additional properties may be tied to
the nodes to affect whether a node should be kept in
the routing table or removed. These properties could
range from long-lived nodes, query round-trip time,
bandwidth, load-balancing indicator etc. Adding a la-
tency property to the routing would enable the algo-
rithm to find the path with the lowest congestion.
Churn, i.e. nodes entering and leaving the over-
lay network, is an inherent and significant property
of overlay networks (Stutzbach and Rejaie, 2006). In
our work, it was not necessary to test churn, as the
focus was on location based heuristics and establish-
ing an efficient routing table. The simulated systems
were based on power grids, where the unit state, based
on location, updates rarely. Applying the small-world
network model is something that can improve routing
during churn, e.g. if a node leaving has blocked the
path to a target node, the small-world network is able
SMARTGREENS 2019 - 8th International Conference on Smart Cities and Green ICT Systems
256
(a) ω: 900 node test feeder. (b) ω: 2.500 node test feeder. (c) ω: NetworkX geometric generated
network.
Figure 5: Routing efficiency results for IEEE test feeders and NetworkX generated network.
(a) Bucket size: 900 node test feeder. (b) Bucket size: 2.500 node test feeder. (c) Bucket size: NetworkX geometric
generated network.
Figure 6: Average bucket size calculated from every node in the network on each iteration.
to find a new route with a shorter search path on aver-
age, than the underlying routing, which may have to
start a search that fans out in every direction again.
Using a complex identifier comes with a cost.
Most importantly the computing cost goes up as more
properties are added to the identifier. The distance
calculation is performed multiple times for each node
in the routing algorithm. When another property is
added, that increases the cost and more so if the cal-
culation is complex. The cost of the distance calcu-
lation for the Pythagorean location is very small and
the increased efficiency of the heuristic far outweighs
the cost in the scenarios tested here.
6 CONCLUSIONS
With the desire of prosumers and energy collectives
to trade energy directly and increasing autonomy at
the local level, overlay networks can provide the
required decentralized communication. The multi-
dimensional overlay network presented in this pa-
per was shown to utilize the properties in the smart
grid to provide a heuristic based on location that im-
proved routing efficiency and using the concepts from
complex networks both averted the inherent problems
with robustness in a clustered node distribution and
improved the average path length when searching in
the network. The results showed a increase in perfor-
mance over the standard Kademlia overlay network in
the context of a smart grid.
In future work, churn is going to an interest-
ing parameter to test when the unit state is based
on system dynamics that changes rapidly. The de-
fault storage algorithm causes hot-spots with clus-
tered nodes and load-balancing needs to handled and
measured. Both the small-world properties and the
location based heuristic improved efficiency, however
testing the small-world properties with the heuristic
enabled and disabled would provide additional valu-
able insight.
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