2. Merging smart home and software-defined networks

A house is smart when it has installed a series of electronic systems, sensors, and devices, so that any person can easily control it, even from a distance, and the house performs certain actions on their own.

An example of this would be the management of heating and air conditioning, so that our home always has a comfortable temperature, whatever the time of year.

This can be achieved by installing temperature sensors and connecting them to a computer or a dedicated device, which once we have programmed it, deciding which temperature is the best for the residents, sends orders to the heating or airconditioning control devices. This automation is what is called home automation.

In this way, home automation has been around for a long time, as we can link various automations through domestic wiring, sometimes with cable inside the walls. The technological advance has given us wireless connectivity and miniaturization, which have allowed the extension of the concept of home automation to many other aspects, even outside the home.

Currently, and under the definition of the smart home, there are devices that allow to control almost everything imaginable, either automatically or facilitating human control.

Optimizing a Centralized Control Topology of an IoT Network Based on Hilbert Space DOI: http://dx.doi.org/10.5772/intechopen.87206

In this sense, we can say that the smart home is the result of the intersection between architecture, interior design, and the most advanced technology, which allows the automation in an unattended way of certain domestic tasks, but also with the condition that there can be supervision or fixed objectives on the part of the residents.

Thus, a smart home seeks to:

As a network, IoTN behaves as a collective entity which does not depend on a central control or hub. Therefore, it is necessary to design IoTN topologies that are not subject to the performance of a single MCU or node for guarantying the quality of service (QoS) requirements due to an efficient connectivity based on a bandwidth that links each of MCUs with their immediate neighbors at 300 Mbps, in order to ensure that all of them really share their parameters when they are operating. This implies to design networks with shared parameters between their nodes and where the locality is preserved and limited the maximum average distance between the MCUs by using alternative tools, such as space-filling curves. The Hilbert fractal is a continuous space-filling curve whose locality-preserving behavior is better than that of Z-order curves, because the distance between each node in a Hilbert curve does not fluctuate, whereas that distance in a Z-order curve

Internet of Things (IoT) for Automated and Smart Applications

Accordingly, in this chapter an effective and a reliable optimized fractal algorithm (OFA) for extending the range of transmission of a given IoTN in an intelligent, adaptive, and dynamic way is proposed. The OFA finds a path from a source to a target to optimize the links by considering the quality of service constraints such as end-to-end reliability and delay. In this way, with OFA we pretend to achieve the best two MCUs where each smart home of the IoTN can transfer or share its parameters. Finally, through laboratory tests and computer simulations, we demonstrate the effectiveness of our approach by means of a fractal routing in IoTN, using from 16 to 64 smart home devices for real-time monitoring of different parameters, in order to make more efficient the Smart Home Automation by

The further sections of this chapter are organized as follows. First, in Section 2 we explain the relation between smart home devices distributed in networks and the energy efficiency. In Section 3 an explanation of the theoretical definition of the Hilbert space-filling fractal is given. OFA scheme is defined in Section 4, while in Section 5, the simulation and the comparison of the performances are announced, in order to verify the correction and feasibility of the proposal. Finally, the arguments

A house is smart when it has installed a series of electronic systems, sensors, and devices, so that any person can easily control it, even from a distance, and the house

An example of this would be the management of heating and air conditioning, so that our home always has a comfortable temperature, whatever the time of year. This can be achieved by installing temperature sensors and connecting them to a

computer or a dedicated device, which once we have programmed it, deciding which temperature is the best for the residents, sends orders to the heating or airconditioning control devices. This automation is what is called home automation. In this way, home automation has been around for a long time, as we can link various automations through domestic wiring, sometimes with cable inside the walls. The technological advance has given us wireless connectivity and miniaturization, which have allowed the extension of the concept of home automation to

Currently, and under the definition of the smart home, there are devices that allow to control almost everything imaginable, either automatically or facilitating

does fluctuate.

reducing the IoTN energy consumption.

performs certain actions on their own.

many other aspects, even outside the home.

human control.

108

and discussion of this chapter are analyzed in Section 6.

2. Merging smart home and software-defined networks


The latter statement guides us to consider as one of the most important issues the way to save energy among sensors, namely, how efficient is the energy consumption. In this way we identify energy efficiency as the most critical challenges in IoTNs because the nodes or smart home devices in such networks have limited resources. In this way, software-defined networks (SDNs) are a way to approach the creation of networks in which control is detached from the hardware and given to a software application called a controller. So, SDNs, also known as programmable and automated networks, are presented as a proposal that provides greater speed, agile infrastructure, and better costs in cloud IT platforms; it is urgent to respond to the dynamism of the applications required by the user.

When a packet arrives at a switch in a conventional home network, the rules built into the proprietary firmware of the switch tell the switch where to transfer the packet. The switch or router sends each packet to the same destination on the same path and treats all packets in the exact same way. In this proposal, intelligent routers designed with specific MCUs are sophisticated enough to recognize different types of packages and treat them differently, but these router can be only the seed or the begging of the home network. Furthermore, in an SDN, a home network administrator can shape traffic from a centralized control console without having to touch individual smart devices, in this case sensors. The administrator can modify any rule of network switches when necessary—giving or removing priority or even blocking specific types of packets with a very detailed level of control.

This is especially useful in a multi-tenant architecture for cloud computing because it allows the administrator to handle traffic loads flexibly and more efficiently. Essentially, this allows the administrator to use fewer and more intelligent routers and have more control than ever over the flow of all the smart devices of the network traffic. Nowadays, the most popular specification for creating a softwaredefined network is an open standard called OpenFlow. OpenFlow allows network administrators to control routing tables remotely.

In addition, home networks have not changed about 20 years ago; unlike programs, we are facing a paradigm shift to which we must adapt. The development of SDNs began in 1990, where programmable functions are included in the network; in 2001–2007, the control and data planes were improved, improving with this innovation. From 2007 to 2010, it was implemented. The OpenFlow API, is presented as an open interface, presents various ways the separation of the control plane and data to be scalable, practice where virtualization played an important role in this SDN evolution.

There are a variety of factors that will continue to pressure network operators, including the increasing use of public cloud computing, the attack of network traffic created by the Internet of Things, the proliferation of a mobile workforce, and an increasing number of distributed branches. Given this, SDN will play a role

And there is already evidence of this in actual use: Software-Defined Wide Area Network (SD-WAN) is a software management platform to control access to the

In the past, home customers had only one connection to their branches; today SD-WAN allows companies to add several types of network connections to a branch and have a software management platform that allows high availability and auto-

SD-WANs can save a home customer's expense by installing expensive custom

Expects highlight that the SD-WAN will become a market of 6 billion by the

In addition, software-defined IoTNs (SD-IoTNs) can be technically sorted in

1. Security: identifying the malicious user and their activities, namely, global

2. Routing: the network data and information is efficiently transferred.

3.Mobility: due to external forces, any node of the home network can be

4.Reliability: the ability to be, almost always, in an operational state under adverse circumstances, usually after failures. Operating state is understood to be that in which the SDNs are capable of performing a specific operation.

5. Management: maintenance, network configuration, and provisioning.

6.Quality of service: it is a set of service requirements that SDN must accomplish when routing a data flow. It can be implemented in different situations, to manage congestion or to avoid it. It allows to control some significant

characteristics of packet transmission. These characteristics can be specified in quantitative or statistical terms such as bandwidth, latency, jitter, and packet loss in the network, ensuring a pre-established degree of reliability that meets the traffic requirements, depending on the profile and bandwidth for a given

7. Wireless power transfer: energy sensor node can be transmitted to other nodes

8. Localization: many applications of IoTNs need the information of each node.

9.Energy efficiency: sleep scheduling approaches are designed for switching the

• Coverage control: control activates or deactivates the sensor nodes to

nodes into idle state if their functionality is not required. In addition, this classification can be rewritten as follows:

overview of a device's status in the home network.

WAN acceleration hardware allowing them to run a software overlay on less

in configuring the next generation of networks for each of these use cases.

Optimizing a Centralized Control Topology of an IoT Network Based on Hilbert Space

remote offices or branches of an organization.

DOI: http://dx.doi.org/10.5772/intechopen.87206

matically prioritize traffic.

expensive hardware.

nine classifications:

physically moved.

data flow.

111

through an appropriate transmitter.

cover a network region.

year 2020.

The progress and evolution of SDNs underlies because traditional home routers cannot respond to unpredictable traffic patterns much less to peak demand. In addition, there would be two alternatives to climb to a more expensive home network by spending more time in configuration or adapting to a dynamic home network. SDNs are suitable for people that require rapid changes in the short term, which happens in a conventional home where mobile devices are added and disappear arbitrarily over time. Currently a conventional home user uses social networks in many devices, which are in high demand or require sudden changes, for example, not only working on geographic traffic but environmental variables such as temperature or humidity, development of mobile devices, virtualization of network devices and sensors, and cloud services.

In this way it is important to point out that SDN is an architecture approach, not a specific product, which has traditionally been thought of as the virtualization of data center networks.

This means separating the management of the control plane from the home network devices from the underlying data plane that forwards the home network traffic. The use of a software-defined system to control this disaggregation provides many benefits, including greater network management flexibility and the ability to more easily implement high-precision security policies.

However, Kindness points out that smart home network operators think of SDN with a too narrow focus, although there has been an evolution in the SDN market in recent years, driven by the increase in demands on the network.

To meet these new challenges, the underlying technology that drives SDN has also been applied to other network areas such as the homes with a lot of sensor or smart devices.

SDNs emerged in early 2010 out of mere necessity. Many networks today were designed for client–server applications that run on a non-virtualized infrastructure. The purchase of Nicira by VMware in 2013 was considered a turning point for the SDN industry, as it turned the virtualization giant into a network provider. Today, VMware's NSX SDN product is based on that technology. Cisco Application Centric Infrastructure is the basis of its SDN offer. Many other companies, such as Juniper and Arista, also offer their solutions. IDC estimates that the SDN market has grown from an industry of 406 million dollars in 2013 to over 6600 million dollars in 2017. The consulting firm anticipates that the SDN market will continue to do so at a compound annual growth rate of 25.4%, reaching about 13,800 million dollars in 2021.

A survey conducted in 2017 by the Network World publication among 294 network professionals found that 49% of them are considering or actively piloting an SDN implementation; 18% already have an SDN installed.

Furthermore, IDC has identified a handful of major use cases for SDN today:


Although so far many SDN deployments have focused on the data center network, Kindness, the Forrester analyst, states that the future of SDN will be defined by how this technology is used outside of the data center.

#### Optimizing a Centralized Control Topology of an IoT Network Based on Hilbert Space DOI: http://dx.doi.org/10.5772/intechopen.87206

There are a variety of factors that will continue to pressure network operators, including the increasing use of public cloud computing, the attack of network traffic created by the Internet of Things, the proliferation of a mobile workforce, and an increasing number of distributed branches. Given this, SDN will play a role in configuring the next generation of networks for each of these use cases.

And there is already evidence of this in actual use: Software-Defined Wide Area Network (SD-WAN) is a software management platform to control access to the remote offices or branches of an organization.

In the past, home customers had only one connection to their branches; today SD-WAN allows companies to add several types of network connections to a branch and have a software management platform that allows high availability and automatically prioritize traffic.

SD-WANs can save a home customer's expense by installing expensive custom WAN acceleration hardware allowing them to run a software overlay on less expensive hardware.

Expects highlight that the SD-WAN will become a market of 6 billion by the year 2020.

In addition, software-defined IoTNs (SD-IoTNs) can be technically sorted in nine classifications:


In addition, this classification can be rewritten as follows:

• Coverage control: control activates or deactivates the sensor nodes to cover a network region.

SDNs began in 1990, where programmable functions are included in the network; in 2001–2007, the control and data planes were improved, improving with this innovation. From 2007 to 2010, it was implemented. The OpenFlow API, is presented as an open interface, presents various ways the separation of the control plane and data to be scalable, practice where virtualization played an important role

The progress and evolution of SDNs underlies because traditional home routers

In this way it is important to point out that SDN is an architecture approach, not a specific product, which has traditionally been thought of as the virtualization of

However, Kindness points out that smart home network operators think of SDN with a too narrow focus, although there has been an evolution in the SDN market in

To meet these new challenges, the underlying technology that drives SDN has also been applied to other network areas such as the homes with a lot of sensor

SDNs emerged in early 2010 out of mere necessity. Many networks today were designed for client–server applications that run on a non-virtualized infrastructure. The purchase of Nicira by VMware in 2013 was considered a turning point for the SDN industry, as it turned the virtualization giant into a network provider. Today, VMware's NSX SDN product is based on that technology. Cisco Application Centric Infrastructure is the basis of its SDN offer. Many other companies, such as Juniper and Arista, also offer their solutions. IDC estimates that the SDN market has grown from an industry of 406 million dollars in 2013 to over 6600 million dollars in 2017. The consulting firm anticipates that the SDN market will continue to do so at a compound

annual growth rate of 25.4%, reaching about 13,800 million dollars in 2021.

• To maximize investments in server virtualization and private cloud

an SDN implementation; 18% already have an SDN installed.

by how this technology is used outside of the data center.

• To enable network programming

A survey conducted in 2017 by the Network World publication among 294 network professionals found that 49% of them are considering or actively piloting

Furthermore, IDC has identified a handful of major use cases for SDN today:

Although so far many SDN deployments have focused on the data center network, Kindness, the Forrester analyst, states that the future of SDN will be defined

This means separating the management of the control plane from the home network devices from the underlying data plane that forwards the home network traffic. The use of a software-defined system to control this disaggregation provides many benefits, including greater network management flexibility and the ability to

cannot respond to unpredictable traffic patterns much less to peak demand. In addition, there would be two alternatives to climb to a more expensive home network by spending more time in configuration or adapting to a dynamic home network. SDNs are suitable for people that require rapid changes in the short term, which happens in a conventional home where mobile devices are added and disappear arbitrarily over time. Currently a conventional home user uses social networks in many devices, which are in high demand or require sudden changes, for example, not only working on geographic traffic but environmental variables such as temperature or humidity, development of mobile devices, virtualization of network

in this SDN evolution.

data center networks.

or smart devices.

110

devices and sensors, and cloud services.

more easily implement high-precision security policies.

Internet of Things (IoT) for Automated and Smart Applications

recent years, driven by the increase in demands on the network.


positive integer n, the interval I is partitioned into 4<sup>n</sup> subintervals of length 4�<sup>n</sup> and the square Q into 4<sup>n</sup> subsquares of side 2�n. A one-to-one correspondence between

constructed: ð Þi adjacent subintervals correspond to adjacent subsquares with an edge in common, adjacency condition, and ð Þ ii if at the n � th partition, the subinterval Ink corresponds to a subsquare Qnk, and then at the ð Þ� n þ 1 st partition, the four subintervals of Ink must correspond to the four subsquares of Qnk, nesting

For each n the 4<sup>n</sup> subintervals are labeled in their natural order from left to right. The correspondence between the intervals and the squares amounts to numbering the squares so that the adjacency and nesting conditions are satisfied. Hilbert's enumeration of the squares is shown in Figure 1 for n ¼ 1; 2; 3. The first square is always in the lower left corner, and the last square is always in the lower right corner. This means that the Hilbert space-filling curve starts at ð Þ ϕð Þ 0 ; ψð Þ 0 at t ¼ 0 and ends at ð Þ ϕð Þ1 ; ψð Þ1 at t ¼ 1. With the first and last squares of each partition determined, there is only one enumeration of the squares that satisfies the adja-

The construction of a Hilbert space-filling curve is presented in Figure 1, in which the dotted square shows the area to be filled by the curve. This square is

On the other hand, many space-filling curves can be produced as the limit of a

The Hilbert fractal can be generated by using specific rewriting rules of the

First four stages in the generation of Hilbert's space-filling curve, axiom = R (see Section 4.3) employed by

sequence of polygonal curves, where the curves are generated via an iterative process, for example, a Lindenmayer system (L-system), in order to visualize such sequences of curves. A small part of the curve at one step of the iteration is close to a corresponding part of the curve at the previous step, and so it is natural to add frames that continuously interpolate between the curves of the iteration.

the subintervals of I and the subsquares of Q subject to two conditions is

Optimizing a Centralized Control Topology of an IoT Network Based on Hilbert Space

condition.

cency and nesting conditions.

DOI: http://dx.doi.org/10.5772/intechopen.87206

divided into four squares.

Lindenmayer systems [5].

Figure 1.

113

Hilbert in [4].

Accordingly to SD-IoTN paradigm, no matter the sort of topology, any sensors inside a smart home network are connected individually to a central router, and they were almost never interconnected among them. Thus, the devices furthest from the router spend more energy than those that are closest to it. In addition, any communication between sensors must necessarily go through a centralized router, even if they are a foot away from each other.

In this sense, the main proposal of this chapter is to communicate with the nearest sensor using a non-centralized, rather a distributed and dynamic, topology that is reorganized according to a fractal function based on the Hilbert scanning.

#### 3. Hilbert space-filling fractal

Mathematician B. Mandelbrot coined the fractal term in his pioneer work The Fractal Geometry of Nature [1], describing a fractal as an irregular or fragmented geometric structure that can be divided into parts: each of which is (or approximately) a smaller-size copy of the whole. He also pointed out that many fractals are found in the nature forming irregularly shaped objects or spatially nonstandardized phenomena in nature that cannot be attributed to Euclidean geometry, such as mountains or blood vessels, with fractional or non-integer dimension. From a mathematical point of view, fractals are a kind of composite geometric shapes which regularly display the property of self-similarity, such that a small segment of it can be reduced as a fractional scale replica of the whole [1].

All obtainable fractal objects in nature are generated from non-determined or random steps. Fractals generated by an iterative procedure, produced by consecutive dilations and conversions of a primary set, are deterministic. There are two properties attributed to fractals: self-similarity and space-filling. Self-similarity stands for a piece of the fractal geometry which seems to be like that of the total structure for all time, while the space-filling property means that a fractal outline can be packed in a limited region as the iteration increases without increasing the whole area.

Concerning the space-filling property, there are fractal curves that fill the plane that contains them in a specific order by continually changing direction or passing through each point that is in the defined space [2], such as the Hilbert fractal curve. The Hilbert space-filling curves are in a single layer that do not intersect; each point of them is at a constant distance unique to any other point, and these curves contain only one starting point and one stopping point in a single layer.

In 1878, mathematician G. Cantor demonstrated that there was a one-to-one correspondence between the unit interval 0½ � ; 1 and the unit square (plane) curve. In 1879, Netto showed that any such mapping could not be continuous. In 1887, Jordan defined a (plane) curve as the set of points ð Þ ϕð Þt ; ψð Þt where ϕ and ψ are continuous functions on a closed interval 0½ � ; 1 , t is the time, and the curve is the path of a particle starting at t ¼ 0 and ending at t ¼ 1. In 1890, Peano discovered a space-filling curve. Thus the Peano curve must have multiple points, that is, points which are the images of two or more distinct values of t [3].

In 1891 Hilbert discovered another space-filling curve. Whereas Peano's curve was defined purely analytically, Hilbert's approach was geometric [2].

To construct Hilbert-type space-filling curves, lets denote the unit interval 0½ � ; 1 as I ¼ f g tj0 ≤t≤1 and the unit square as Q ¼ f g ð Þj x; y 0 ≤x≤1; 0≤ y≤1 . For each

#### Optimizing a Centralized Control Topology of an IoT Network Based on Hilbert Space DOI: http://dx.doi.org/10.5772/intechopen.87206

positive integer n, the interval I is partitioned into 4<sup>n</sup> subintervals of length 4�<sup>n</sup> and the square Q into 4<sup>n</sup> subsquares of side 2�n. A one-to-one correspondence between the subintervals of I and the subsquares of Q subject to two conditions is constructed: ð Þi adjacent subintervals correspond to adjacent subsquares with an edge in common, adjacency condition, and ð Þ ii if at the n � th partition, the subinterval Ink corresponds to a subsquare Qnk, and then at the ð Þ� n þ 1 st partition, the four subintervals of Ink must correspond to the four subsquares of Qnk, nesting condition.

For each n the 4<sup>n</sup> subintervals are labeled in their natural order from left to right. The correspondence between the intervals and the squares amounts to numbering the squares so that the adjacency and nesting conditions are satisfied. Hilbert's enumeration of the squares is shown in Figure 1 for n ¼ 1; 2; 3. The first square is always in the lower left corner, and the last square is always in the lower right corner. This means that the Hilbert space-filling curve starts at ð Þ ϕð Þ 0 ; ψð Þ 0 at t ¼ 0 and ends at ð Þ ϕð Þ1 ; ψð Þ1 at t ¼ 1. With the first and last squares of each partition determined, there is only one enumeration of the squares that satisfies the adjacency and nesting conditions.

The construction of a Hilbert space-filling curve is presented in Figure 1, in which the dotted square shows the area to be filled by the curve. This square is divided into four squares.

On the other hand, many space-filling curves can be produced as the limit of a sequence of polygonal curves, where the curves are generated via an iterative process, for example, a Lindenmayer system (L-system), in order to visualize such sequences of curves. A small part of the curve at one step of the iteration is close to a corresponding part of the curve at the previous step, and so it is natural to add frames that continuously interpolate between the curves of the iteration.

The Hilbert fractal can be generated by using specific rewriting rules of the Lindenmayer systems [5].

Figure 1.

First four stages in the generation of Hilbert's space-filling curve, axiom = R (see Section 4.3) employed by Hilbert in [4].

• Clustering: nodes into clusters and a head node for each.

Internet of Things (IoT) for Automated and Smart Applications

reorganized according to a fractal function based on the Hilbert scanning.

it can be reduced as a fractional scale replica of the whole [1].

region as the iteration increases without increasing the whole area.

only one starting point and one stopping point in a single layer.

which are the images of two or more distinct values of t [3].

112

was defined purely analytically, Hilbert's approach was geometric [2].

of time.

even if they are a foot away from each other.

3. Hilbert space-filling fractal

• Lifetime: possibility to utilize the node capabilities for a longer period

Accordingly to SD-IoTN paradigm, no matter the sort of topology, any sensors inside a smart home network are connected individually to a central router, and they were almost never interconnected among them. Thus, the devices furthest from the router spend more energy than those that are closest to it. In addition, any communication between sensors must necessarily go through a centralized router,

In this sense, the main proposal of this chapter is to communicate with the nearest sensor using a non-centralized, rather a distributed and dynamic, topology that is

Mathematician B. Mandelbrot coined the fractal term in his pioneer work The Fractal Geometry of Nature [1], describing a fractal as an irregular or fragmented geometric structure that can be divided into parts: each of which is (or approximately) a smaller-size copy of the whole. He also pointed out that many fractals are found in the nature forming irregularly shaped objects or spatially nonstandardized phenomena in nature that cannot be attributed to Euclidean geometry, such as mountains or blood vessels, with fractional or non-integer dimension. From a mathematical point of view, fractals are a kind of composite geometric shapes which regularly display the property of self-similarity, such that a small segment of

All obtainable fractal objects in nature are generated from non-determined or random steps. Fractals generated by an iterative procedure, produced by consecutive dilations and conversions of a primary set, are deterministic. There are two properties attributed to fractals: self-similarity and space-filling. Self-similarity stands for a piece of the fractal geometry which seems to be like that of the total structure for all time, while the space-filling property means that a fractal outline can be packed in a limited

Concerning the space-filling property, there are fractal curves that fill the plane that contains them in a specific order by continually changing direction or passing through each point that is in the defined space [2], such as the Hilbert fractal curve. The Hilbert space-filling curves are in a single layer that do not intersect; each point of them is at a constant distance unique to any other point, and these curves contain

In 1878, mathematician G. Cantor demonstrated that there was a one-to-one correspondence between the unit interval 0½ � ; 1 and the unit square (plane) curve. In 1879, Netto showed that any such mapping could not be continuous. In 1887, Jordan defined a (plane) curve as the set of points ð Þ ϕð Þt ; ψð Þt where ϕ and ψ are continuous functions on a closed interval 0½ � ; 1 , t is the time, and the curve is the path of a particle starting at t ¼ 0 and ending at t ¼ 1. In 1890, Peano discovered a space-filling curve. Thus the Peano curve must have multiple points, that is, points

In 1891 Hilbert discovered another space-filling curve. Whereas Peano's curve

To construct Hilbert-type space-filling curves, lets denote the unit interval 0½ � ; 1 as I ¼ f g tj0 ≤t≤1 and the unit square as Q ¼ f g ð Þj x; y 0 ≤x≤1; 0≤ y≤1 . For each

The L-systems, developed by Lindenmayer in 1968, emerged as a way to discreetly describe the development and growth of multicellular organisms [6]. An L-system is a string rewriting system. We have an alphabet of symbols V; a string of symbols ω defining the start of the system, or axiom; and a set of production rules P determining how we produce a new string from an old string. The L-system grammar is the collection of these three parts, G ¼ ð Þ V;ω; P . This generates a sequence of strings by repeatedly applying the rules P, starting with the axiom ω.

• Hilbert fractal scanning

DOI: http://dx.doi.org/10.5772/intechopen.87206

It is also important to consider the general parts of the environment of the proposal, so any configuration of IoTNs consists of a wireless access point (WAP) and a β number of IoTN nodes which can be increased or decreased in its amount. In this case β embedded systems or MCUs that composed the IoTN, which shares parameters among sensors inside a given room or floor plan; β ranges dynamically

Optimizing a Centralized Control Topology of an IoT Network Based on Hilbert Space

, i.e., a specific period of time ð Þ<sup>t</sup> when the IoTN is defined as a set

of MCUi with at least one member up to 4<sup>n</sup> members. Whereas n is the Hilbert fractal level needed to go from the first to the last MCUi and it is expressed by n ¼ d e log <sup>4</sup>ð Þ β , here i represents the index inside the IoTN ð Þt of a given MCU,

It is important to emphasize that the IoTN has β MCUs in the time frame tj

but it can have up to 4<sup>n</sup> � 1 devices. If <sup>β</sup> <sup>≥</sup>4<sup>n</sup>, the value of <sup>n</sup> is recalculated, and a new topology is reconfigured; otherwise the algorithm just adds a new node in the network, with the purpose that each node of the same network is linked or indexed by the curves that make up the Hilbert fractal. Subsequently, the effectiveness of the methodology exchange parameter throughout the network is measured. Finally,

the point-to-point algorithms of Wi-Fi (P2P) and SoftAP are configured.

a certain floor plan which forms a matrix <sup>γ</sup> with 2<sup>n</sup> � <sup>2</sup><sup>n</sup> dimension. Namely, our proposal estimates a certain topology according to the β devices in the room in a certain period of time tj. Then, the main WAP or hub is placed in the center of the main room, although it can be placed anywhere within the room, to have connections at any direction. That is, every connection to the WAP will be the mainstream star topology. In this first generation of MNIs, a consecutive number will be assigned according to the speed of its link with the WAP. Thus, certain MCUi has the best link so this device is labeled as i ¼ 1 or MCU1. Any floor plan had some walls, which attenuate the signal; that is why certain devices with shorter linear distance have a

slower maximum speed than others that are further away from the WAP.

MCUi¼<sup>1</sup>ð Þt is identified as the main node in the IoTN. In this way, all the embedded systems both IoTNe tð Þ and MCU1ð Þt , enable Wi-Fi Direct mode and a full table with the bandwidth of the nodes are next to them, in order to generate a list of reliable nodes in a certain period of time t (LRNið Þt ). Every MCU generates a particular LRNið Þ<sup>t</sup> ; then the proposed IoTN can generate 4<sup>n</sup> LNRs at the instant <sup>t</sup>. In addition, every LRNið Þt contains the bandwidth of all MCUið Þt with which it establishes connection. In order to belong to the wireless sensor network, every MCUið Þt must connect to at least one link to another MCUið Þt . All LRNs are shared, and

<sup>i</sup>¼<sup>1</sup>MCUið Þ<sup>t</sup> knows the way to any node in the network, namely, everyone knows the topology of the network. In this way it is important to estimate the LRNið Þt , but not all of these nodes are significant to be considered as the best option to establish a link, in which manner we define LSNið Þt as the list of significant nodes

namely, MCU<sup>1</sup> is the first MCU, MCU<sup>2</sup> the second one, and so on.

<sup>i</sup> <sup>≥</sup><sup>1</sup>MCUið Þt , where

IoTN devices are randomly distributed along

,

are 1≥β>4n. In this way, we also define IoTNNðÞ¼ <sup>t</sup> <sup>∑</sup><sup>β</sup>

• Initial topology

t ¼ t0; t1; t2; …tj

4.1 Hub MCU

4.2 LRNið Þt and LSNið Þt

∑<sup>4</sup><sup>n</sup>

115

It is important to establish that β tj

To construct the Hilbert space-filling curve, we proposed the following L-system grammar:

$$G\_{Hilbert} = (\{F, -, +\}, R, \{R \to +RF - LFL - FR + \})$$

Then the output of the L-system is the following sequence of strings for the first three steps:


Given the L-system for the Hilbert space-filling curve, it is possible to view the produced strings as instructions for building these curves in a turtle graphic fashion [7]. That is, we start somewhere on the plane, with a specified forward-facing direction. We read the input string from left to right and interpret the symbols as actions to be performed. For the L-system for the Hilbert space-filling curve, we make the following interpretations:


In this chapter it is proposed to use the symbols L and R to represent a kind of small deviation from a forward step (starts with a left turn) and to represent a small detour in the other direction (starts with a right turn), respectively.

#### 4. Methodology

The proposed methodology in this chapter is defined by the following passes:


Optimizing a Centralized Control Topology of an IoT Network Based on Hilbert Space DOI: http://dx.doi.org/10.5772/intechopen.87206


The L-systems, developed by Lindenmayer in 1968, emerged as a way to discreetly describe the development and growth of multicellular organisms [6]. An L-system is a string rewriting system. We have an alphabet of symbols V; a string of symbols ω defining the start of the system, or axiom; and a set of production rules P determining how we produce a new string from an old string. The L-system grammar is the collection of these three parts, G ¼ ð Þ V;ω; P . This generates a sequence of strings by repeatedly applying the rules P, starting with the axiom ω. To construct the Hilbert space-filling curve, we proposed the following L-system

GHilbert¼ð Þ f g F; �; þ ; R; f g R ! þRF � LFL � FRþ

RFR þ FL � F � LF þ RFR þ FL � þ F þ RF � LFL � FR þ � Step 3: �þ�LF þ RFR þ FL � F � þRF � LFL � FR þ F þ RF � LFL�

Then the output of the L-system is the following sequence of strings for the first

FR þ �F � LF þ RFR þ FL � þF + - + RF-LFL-FR + F + - LF þ RFR þ FL � F � LF þ RFR þ FL � þF þ RF � LFL � FR þ � F � þRF � LFL � FR þ F þ �LF þ RFR þ FL � F � LFþ RFR þ FL � þF þ RF � LFL � FR þ �F þ �RL þ RFR þ FL�

Given the L-system for the Hilbert space-filling curve, it is possible to view the produced strings as instructions for building these curves in a turtle graphic fashion [7]. That is, we start somewhere on the plane, with a specified forward-facing direction. We read the input string from left to right and interpret the symbols as actions to be performed. For the L-system for the Hilbert space-filling curve, we

In this chapter it is proposed to use the symbols L and R to represent a kind of small deviation from a forward step (starts with a left turn) and to represent a small

The proposed methodology in this chapter is defined by the following passes:

detour in the other direction (starts with a right turn), respectively.

F � þFR � LFL � FR þ F þ RF � LFL � FR þ �F � LF þ RFR þ FL � þ�

grammar:

three steps:

Step 1: �LF þ RFR þ FL�

make the following interpretations:

1. F, move forward one unit

3.�, turn right (clockwise) 90<sup>o</sup>

4. Methodology

• Hub MCU

114

• LRNið Þt and LSNið Þt

2. +, turn left (counterclockwise) 90<sup>o</sup>

Step 2: � þ RF � LFL � FR þ F þ �LFþ

Internet of Things (IoT) for Automated and Smart Applications

It is also important to consider the general parts of the environment of the proposal, so any configuration of IoTNs consists of a wireless access point (WAP) and a β number of IoTN nodes which can be increased or decreased in its amount. In this case β embedded systems or MCUs that composed the IoTN, which shares parameters among sensors inside a given room or floor plan; β ranges dynamically are 1≥β>4n. In this way, we also define IoTNNðÞ¼ <sup>t</sup> <sup>∑</sup><sup>β</sup> <sup>i</sup> <sup>≥</sup><sup>1</sup>MCUið Þt , where t ¼ t0; t1; t2; …tj , i.e., a specific period of time ð Þ<sup>t</sup> when the IoTN is defined as a set of MCUi with at least one member up to 4<sup>n</sup> members. Whereas n is the Hilbert fractal level needed to go from the first to the last MCUi and it is expressed by n ¼ d e log <sup>4</sup>ð Þ β , here i represents the index inside the IoTN ð Þt of a given MCU, namely, MCU<sup>1</sup> is the first MCU, MCU<sup>2</sup> the second one, and so on.

It is important to emphasize that the IoTN has β MCUs in the time frame tj , but it can have up to 4<sup>n</sup> � 1 devices. If <sup>β</sup> <sup>≥</sup>4<sup>n</sup>, the value of <sup>n</sup> is recalculated, and a new topology is reconfigured; otherwise the algorithm just adds a new node in the network, with the purpose that each node of the same network is linked or indexed by the curves that make up the Hilbert fractal. Subsequently, the effectiveness of the methodology exchange parameter throughout the network is measured. Finally, the point-to-point algorithms of Wi-Fi (P2P) and SoftAP are configured.

#### 4.1 Hub MCU

It is important to establish that β tj IoTN devices are randomly distributed along a certain floor plan which forms a matrix <sup>γ</sup> with 2<sup>n</sup> � <sup>2</sup><sup>n</sup> dimension. Namely, our proposal estimates a certain topology according to the β devices in the room in a certain period of time tj. Then, the main WAP or hub is placed in the center of the main room, although it can be placed anywhere within the room, to have connections at any direction. That is, every connection to the WAP will be the mainstream star topology. In this first generation of MNIs, a consecutive number will be assigned according to the speed of its link with the WAP. Thus, certain MCUi has the best link so this device is labeled as i ¼ 1 or MCU1. Any floor plan had some walls, which attenuate the signal; that is why certain devices with shorter linear distance have a slower maximum speed than others that are further away from the WAP.
