Mobile Networks and Applications

, Volume 15, Issue 2, pp 283–297

Randomized 3-D Routing in Fully- and Partially-Covered Sensor Networks

Authors

    • Department of Computing and Information ScienceUniversity of Guelph
  • Nidal Nasser
    • Department of Computing and Information ScienceUniversity of Guelph
Article

DOI: 10.1007/s11036-009-0183-4

Cite this article as:
El Salti, T. & Nasser, N. Mobile Netw Appl (2010) 15: 283. doi:10.1007/s11036-009-0183-4

Abstract

In recent years, sensor network technology has been proposed to improve the detection level of natural disasters (e.g. volcanoes, tornadoes, tsunamis). However, this technology has several design issues that need to be improved. We, therefore in this paper, focus on two main design issues: coverage and routing. For coverage issue, we introduce a new approach for obtaining a fully covered network in \(\boldsymbol{3}\textbf{-}{\boldsymbol D}\) environment such that every single point in a region is fully covered by at least one sensor node. This approach is referred to as the Chipset Coverage Model and Algorithm. This would be accomplished by using a small number of sensor nodes in order to save up some energy. Based on our coverage approach, we address the routing issue by proposing a new position-based routing protocol referred to as the \(\boldsymbol{3}\textbf{-}{\boldsymbol D}\) Randomized Sensing Spheres routing protocol (\(\boldsymbol{3}\textbf{-}{\boldsymbol D}\)\(\boldsymbol{RSS}\)). We show that the \(\boldsymbol{3}\textbf{-}{\boldsymbol D}\)\(\boldsymbol{RSS}\) protocol guarantees packet delivery. Moreover, from our simulation, we demonstrate that the \(\boldsymbol{3}\textbf{-}{\boldsymbol D}\)\(\boldsymbol{RSS}\) has a behaviour close to the behaviour of an existing \(\boldsymbol{3\textbf{-}D}\) progress-based protocol in terms of hop dilation and routing delay, where the delay is defined as Quality of Service (QoS) metric. Furthermore, we demonstrate that the \(\boldsymbol{3}\textbf{-}{\boldsymbol D}\)\(\boldsymbol{RSS}\) protocol outperforms the existing progress-based protocol in terms of Euclidean and power dilations. Thus, the new protocol reduces the energy consumption of the nodes and, therefore, prolongs the lifetime of the sensing nodes. For partially covered networks, we propose a dynamic position-based routing protocol referred to as the \(\boldsymbol{3}\textbf{-}{\boldsymbol D}\) Randomized Sensing Spheres version 1 routing protocol (\(\boldsymbol{3}\textbf{-}{\boldsymbol D}\)\(\boldsymbol{RSSv1}\)). This protocol increases the chances of delivering packets by moving linearly towards the destinations. We demonstrate that the \(\boldsymbol{3}\textbf{-}{\boldsymbol D}\)\(\boldsymbol{RSSv1}\) has a remarkable delivery rate compared to an existing progress-based routing protocol.

Keywords

sensing-covered regions3-D routingpartially-covered networks

1 Introduction

Recently, many natural disasters have occurred (e.g. the 2004 tsunami) which have created massive destruction and displaced thousands of people. These threats continue to occur with no indications of what the main factors are behind those occurrences. For a long time people have been using natural detection methods (e.g. observing animals behavior) moments before the occurrence of a disaster. However, the main drawback of this technique is that it does not give observers sufficient time to evacuate safely.

In response to this drawback, a sensor network technology has been proposed to improve the detection level of some disasters. This type of network integrates systems for processing, sensing and wireless communication without having any fixed infrastructure or centralized control. Each node in this network can communicate with all other nodes within its transmission range [1], which is assumed in this paper to be fixed range for all nodes. However, several nodes may not be within the transmission range of each other. Since the nodes are considered as endsystems (receive, send and process data/packets) and as routers (packet forwarding), multihop routing will be used where intermediate nodes are used to forward packets.

In this paper, we present a new approach for covering a 3-D region, which we call the Chipset Coverage Model and Algorithm. Initially, we construct our Chipset Coverage Model, and then our coverage algorithm makes sure that every single point in the Chipset Coverage Model is fully covered by at least one sensing sphere. We also present two new 3-D position-based routing protocols that are based on the Greedy Forwarding protocol (GEDIR) [2]. Moreover, one of these protocols runs on fully covered regions obtained by our Chipset Coverage Model, while the other protocol runs on partially covered networks. For both protocols, we evaluate their performance and compare them to the GEDIR protocol. For the rest of the paper, we assume for simplicity that the sensor nodes are fixed and that they know their 3-D geometric positions via some positioning techniques [3].

The remaining of this paper is organized as follows. In Subsection 1.1, we present the problem background as well as the motivations behind our work. In Subsection 1.2, we list some existing works concerning routing and coverage in 2-D and 3-D environments along with the background needed for our solution. In Section 2, we introduce a new approach for covering a 3-D space. In Section 3, we introduce a new 3-D routing protocol that runs on our 3-D covered model. In Section 4, a new dynamic 3-D routing protocol is proposed that runs on partially covered networks. In Section 5, we explore experimentally the properties of all the proposed routing protocols. In Section 6, we discuss the major findings obtained from our experiments along with their importance. In addition, we illustrate the limitation of our coverage approach, and propose a possible solution that can still obtain fully covered networks. In Section 7, we conclude our work and present some future work.

1.1 Problem background and motivations

Generally, ad hoc networks can process, send/receive, and route packets. However, in addition to these capabilities, sensor networks are required by their sensing applications (e.g., distributed detection [4]) to provide more functionality. One major requirement the sensor networks must provide is the sensing-covering property addressed in the literature [57] in the context of 2-D environments. To the best of our knowledge, most of the existing work has not illustrated clearly how coverage is obtained. In their work, they relied on the assumption that the network is already dense, such that every single point in the area is covered by at least one sensor node (decimation approach). However, in our view, having high density networks does not necessarily mean that every single point in the region is fully covered. Thus, even though the coverage approaches [57] have been proven to be robust techniques, they are flawed due to their high density assumption. Furthermore, unlike 2-D environments, some environments (e.g. oceans) have a third dimension, which makes the existing 2-D approaches inadequate for use in those regions.

Few coverage techniques [8, 9] have been proposed in the context of 3-D environments. The main reason behind the lack of research is that achieving coverage in 3-D environments is much more complex than it is in 2-D environments. We, therefore, define the problem of obtaining coverage in 3-D environments as follows. Assume a region R exists, such that R consists of q points with some coordinates (x, y, z). The problem is how to cover all q points such that every q is covered by at least one sensor node.

Related to this problem is the performance of routing protocols. Several routing protocols have been proposed [10, 11], but we are mainly interested in local position-based routing protocols (a.k.a geographic routing [12]). In position-based routing protocols, a packet is forwarded from the current node based on the location of this node, its neighbours, and the intended destination [11]. However, position-based protocols encounter some challenges within sensor networks. The first challenge is how to route efficiently without the need for permanent infrastructure and with dynamic topological changes which may create partially covered networks, i.e. the network is partially covered by sensor nodes due to some nodes’ failure (e.g. burning out their battery powers). The second challenge is how to optimize the depletion of sensor nodes’ limited resources (i.e. battery power). The Third challenge is how to avoid local minima [13], i.e. a current node, running position-based protocols, can not find a neighbouring node that is closer to the destination than itself. Hence, the packet is dropped. In addition to these challenges, few protocols have been introduced specifically in the context of sensing-covering regions (e.g. 2-D Bounded Voronoi Greedy Forwarding (\(\mbox{\it BVGF}\)) [14]). The use of BVGF, for example requires an additional topology referred to as the Voronoi diagram [15] in order to perform the routing procedure. Therefore, the routing challenges combine to define another major problem in sensor networks: how to construct a position-based protocol that does not need a pre-existing topology and that can efficiently use the network resources while performing its routing task. In the next Subsection, we mention the background used for our solution along with some related work.

1.2 Background and related work

A common model for a position-aware network is a geometric graph, which is a graph embedded in a d-dimensional Euclidean space such that its vertices are points with coordinates and its edges are straight-line segments. The set of n wireless nodes is represented as a point set Q in 3-D, each point possessing a geometric location. For node u, we denote the set of its neighbors by N(u). The number of the neighbors of u is the degree of u. On Q, a graph can be modeled as a weighted (undirected or directed) graph G(Q,E) where E is a subset of the pairs of nodes of Q and the weight of an edge uv between nodes u and v is the 3-D Euclidean distance between the nodes, which we denote as |uv|. The weight of a graph is the sum of its edge weights. Moreover, the path between any pair of nodes has two types: Euclidean length and network length. The former refers to the sum of all the hops’ Euclidean distances in a path. The latter refers to the hop count of a path.

Bounding these paths requires the following definition. A graph Z is a s-spanner [16] if it is a subgraph of G in which the network (or Euclidean) length between any two nodes is bounded by a constant s, where s refers to the spanning ratio or the stretch factor [17], of the network (or Euclidean) length between the two nodes in G. These two nodes are connected in Z as long as they are connected in G. In other words, following the notation of Xing et al. [14], let LG(u,v) refers to the shortest network length between any two nodes, u and v, in the graph G(V,E). Thus, if we have a subgraph Z(V,E′), \(E^{'} \subseteq E\), that is a network t-spanner of graph G(V,E) if ∀u, vV, LZ(u,v)≤ t·LG(u,v). The term t refers to the network stretch factor. Assuming also a graph \(\mbox{\textit{EU}}\)G(u,v) which refers to the shortest Euclidean length between any two nodes, u and v, in the graph G(V,E). Thus, if we have a subgraph Z(V,E′), \(E^{'}\subseteq E\), that is an Euclidean a-spanner of graph G(V,E) if ∀ u,vV, EUZ(u,v) ≤ a.EUG(u,v). The term a refers to the Euclidean stretch factor. Spanner graphs have been heavily studied in computational geometry [17] and mainly provide us with two things: short paths and energy optimal paths.

The stretch factor in general is represented by the dilation with regard to an ultimate wireless network. A network is referred to as an ultimate network if it has a path with network length \(\left\lceil \frac{|uv|}{R_{c}} \right\rceil \) and a path with Euclidean distance |uv| for any pair of nodes u and v. Both of these lengths are feasible for high-density networks. However, if the network is not dense, then the two lengths are obtained by extracting the network/Euclidean shortest paths via well known algorithms (e.g., Dijkstra’s and Bellman-Ford algorithms). For our scope of interest, we adopt two definitions from [14] based on dense networks, and they are as follows:

Definition 1

The network (hop) dilation (Dn) is defined by:
$$D_{n}=max_{u,v \in V } \frac{L_{G}(u,v)}{\left\lceil \frac{|uv|}{R_{C}} \right\rceil}$$

Definition 2

The Euclidean dilation (De) is defined by:
$$D_{e}=max_{u,v \in V } \frac{EU_{G}(u,v)}{|uv|} $$

The dilation in terms of power, proposed by Li et al. [18], is similar to the above definitions. Let π(u,v)=v0v1...vq, where the term π refers to a path between the source u = v0, and the destination v = vq, the term q refers to the total number of nodes, and the term vi (i = 0, 1, ... q) refers to a sensor node. The path π has a consumed total transmission power \(p(\pi)=\sum^{q}_{i=1}||v_{i-1}v_{i}||^{\beta}\), where β is a constant parameter from within the interval \(\left[2,\: 5\right]\). The least energy consumption by all the paths between u and v in G is referred to as pG(u,v). By having Z as a subgraph of G, the power dilation (Dp) of Z can be defined as follows:

Definition 3

$$D_{p}=max_{u,v \in V } \frac{p_{Z}(u,v)}{p_{G}(u,v)} $$

To represent the way nodes communicate, we use a common topological graph in wireless sensor networks. The topology is referred to as the 3-D Unit Disk Graph (3-DUDG). In this graph, two sensor nodes communicate with each other if they are in their transmission range (Rc) of each other. In the next Subsections, we mention the existing routing protocols that are based on the UDG, as well as the existing 3-D coverage models used in sensor networks.

1.2.1 Routing protocols based on 3-D UDG

Routing research in sensor networks and related ad hoc networks is an active and attractive field. We focus on the unicast approaches for delivering a packet between a single source and a single destination. Several unicast routing protocols have been presented based on 2-D graphs during the past few years, of which we will focus on position-based routing algorithms (also known as online routing [19]). Giordano et al. [11] distinguished several classes of position-based routing protocols including: Basic Distance, Progress, and Direction Based methods class, Power and Cost Aware Routing class, and others. We are interested in the first class, where a node A forwards the packet either based on the Euclidean distance to the destination, projected distance to the destination or the direction to the destination. If we have a source node J and a destination node D, J will select one of its neighbors that has the most positive progress toward the destination. If J selects the node C, then C will repeat the same procedure until reaching, if possible, the node D. The main goal is to always forward the packet toward the destination. We refer to such protocols simply as progress-based routing protocols.

These progress-based routing protocols are locally distributed algorithms, where each node makes a decision to forward a packet to a specific neighbor based on the locations of this node, its neighbors, and the destination [13]. This indicates that these routing protocols do not need to gather the global topology information of the network as a whole. Thus, the bandwidth and limited storage resources can be more efficiently utilized. These characteristics also make the position-routing protocols quick to adapt to network topology changes.

One popular example of position-based routing algorithms is the 3-D Greedy Forwarding routing algorithm (denoted by 3-D GF) [2, 20]. The 3-D GF protocol makes decisions based on neighbor information at most k hops away, where k ≥1 and is fixed. This feature avoids the need of gathering and maintaining the global topology information for the whole network. There are three main types of 3-D GF. One is based on the Euclidean distance to the destination [2, 20, 21] which is referred to as geographic distance routing protocol (GEDIR). Another one is based on the projected distance to the destination1 [20, 22], which is referred to Most Forward within Radius (MFR). The last one is based on the angle between the neighbor and the destination (the angle is measured between the line between the current node and destination node and the line between the current node and the neighbor node) [20, 23], which is referred to Compass Routing (DIR). However, in this paper, we are interested in the GEDIR protocol.

To reduce the effect of the local minima phenomenon, several hybrid position-based protocols are proposed. One work by Alaa et al. in [24] proposes several hybrid routing protocols, and among these, we mention the G-3D_ABLAR(3)-G protocol. This protocol uses the GEDIR protocol as its normal mode. Once the hybrid protocol encounters a local minima phenomenon, it then switches to the 3D_ABLAR(3) [24]. A current node c, running the 3D_ABLAR(3) protocol, chooses a neighbouring node x1, and then constructs a plane p1 that contains c, x1, and the destination node (d). Then the current node c chooses node x2 from above the plane p1, and node x3 from below the plane p1. Afterwards, node c forwards the packet to all the nodes x1, x2, and x3 if node xi is within a predefined cube. Once the 3D_ABLAR(3) finds a node that has neighbours with positive progresses towards the destination, the G-3D_ABLAR(3)-G returns back to the GEDIR normal mode.

Another interesting work done by Haque and Assi in [25] proposes a hybrid protocol referred to as the Optimal Localized Energy Aware Routing (OLEAR) protocol. This protocol uses the GEDIR as its normal mode, and once a local minima phenomenon is encountered, the OLEAR protocol switches to a recovery mode based on a modified version of the Compass protocol. This mode forwards the packet below the line c-d based on Compass protocol. If there is no node below this line, the mode chooses nodes that are above the line c-d based on also Compass protocol. The OLEAR protocol returns back to the GEDIR mode as soon as the hybrid protocol finds a node that has neighbours with positive progresses towards the destination. The drawback of this protocol is that it is based on 2-D environments, and both the OLEAR and the G-3D_ABLAR(3)-G do not guarantee packet delivery. And to the best of our knowledge, most of the existing protocols are not proposed in the context of fully covered regions.

1.2.2 3-D coverage models

Some environments such as ocean, space, etc. present a new challenge for sensor deployments. This is referred to as the 3-D coverage problem in sensor networks. Some sensor applications are developing quite frequently such that in the near future there will be the need for this kind of coverage. An example would be the weather forecasting applications. The level of packets accuracy, acquired by these applications, will have major improvements in the presence of a 3-D coverage approach.

The 3-D coverage techniques are much less compared to 2-D techniques [57] due to the complexity of the space-filling problem in the 3-D environment. Such work by Huang et al. [26] presents a solution for 3-D coverage problem which is based on the 2-D approach presented in [5]. Their approach simply works as follows. To check whether a network is being covered, each sensor node checks if its sensing spherical surface is covered by some constant k. This term is referred to as the least number of sensor nodes that must cover the surface of one node’s sensing sphere. The drawback of this approach is that it is a decision-based approach that checks whether a network is sufficiently covered by k. In other words, it does not make sure to cover every single point in the 3-D space. Another work by Alam and Haas [8] proposes a technique for placing nodes in a 3-D region resulting a fully covered region. This technique is based on truncated octahedron cells constructed from the Voronoi tessellation of a 3-D space. Although the authors show that other shapes, such as hexagonal prism and rhombic dodecahedron placing techniques, can solve the space filling problem, it was shown that the truncated octahedron placing approach uses the least number of nodes. In the next Section, we introduce our approach for obtaining fully covered 3-D regions.

2 Description of Chipset Coverage Model and Algorithm

In this section, we, first, illustrate the Chipset Coverage Model used. Secondly, we introduce the Chipset Coverage Algorithm, which is based on the Chipset Coverage Model for obtaining fully covered regions.

2.1 Chipset Coverage Model

This Chipset design, consisting of 3-D columns or pins, is only created once for a region with equal dimensions, i.e the width and the length of the model’s base, where the base is virtual and it holds some pins, are alike and equal to the height of the pins (See Fig. 1). This model gives an impression that we deal with a cube in a 3-D region. Fortunately, since the region is in 3-D, our approach is applicable in any kind of 3-D environments (e.g. Ocean, space, and atmosphere).
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig1_HTML.gif
Fig. 1

The underlying Chipset Coverage Model

2.2 Chipset Coverage Algorithm

Our main purpose is to show that we can have a fully covered 3-D sensor network. This would mainly depend on covering every single point in a region by at least one sensing sphere. To achieve this goal, we introduce a new algorithm which is referred to as the Chipset Coverage Algorithm, where the Chipset model is the base for this algorithm (See Fig. 2).
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig2_HTML.gif
Fig. 2

The procedure of filling up the Chipset Coverage Model

The Chipset Coverage Algorithm works as follows. Based on the Chipset model, the algorithm starts placing sensing spheres one at a time. If a newly placed sensing sphere covers some uncovered pins, then it would become active; otherwise it would discarded. The algorithm keeps placing spheres until obtaining full coverage for all the pins. This procedure leads to resolve the power saving issue. The reason is that we are only placing the necessary sensing spheres at the Chipset model.

Such coverage is not enough, since we might have spaces between these pins. We resolve this issue as follows. After filling out all the points on all the pins by a set of sensing spheres, the algorithm increases the sensing range (Rs) by r = \(S / \sqrt{2}\), where S is the spacing between these pins. This is illustrated in Fig. 3. Filling up all these spaces as well as the points on the pins would lead to a full coverage. Obtaining this coverage would imply high connectivity. This would be achieved based on the assumption that Rc for the nodes, is equal to w*Rs, where w ≥ 2 [14].
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig3_HTML.gif
Fig. 3

The top view of the Chipset Coverage Model where the black points represent the pins

This algorithm performs in O(l), where l is the number of sensor nodes. The reason is that once a sensing sphere is placed at a random position within the Chipset model, the algorithm checks which pins are intersecting the sensing sphere. This would be done based on the node’s position as well as its sensing range. In the next section, we propose a 3-D position-based protocol that runs on the proposed Chipset Coverage Model.

3 Proposed 3-D position-based routing protocol on fully covered networks

Upon having a fully covered 3-D region, we introduce in this section, a novel 3-D position-based routing protocol. This new protocol is referred to as the 3-D Randomized Sensing Spheres routing protocol (3-DRSS). This protocol makes a forwarding decision based on the operational definition of the GEDIR routing protocol. We choose this protocol since it guarantees that the packet is always delivered to the destination. This is illustrated through the following theorem.

Theorem 1

In a sensing-covering network with Rc = w*Rs, where w is a constant and w ≥ 2, the 3-D GEDIR routing protocol always guarantees the packet delivery.

Proof

For simplicity, the proof is illustrated in 2-D which also applies to 3-D as well. This can be proved by contradiction as follows, see Fig. 4a. Assume that any node C on the field has only neighbours (Nei(C), where Nei(C)= 1, 2, ..., h) with progresses αNei(C) ≤ αC. This would apply to the node A which is the current node, as well as the source node, and the node B which is the destination node. Based on this assumption and the fact that the region is fully covered, there should be sensor nodes that cover the area between A and B, respectively, see Fig. 4b. Therefore, node A will have Nei(i) with progresses αNei(C) ≥ αA toward the destination. This contradicts the fact that the 3-D GEDIR does not always guarantee packet delivery. □
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig4_HTML.gif
Fig. 4

The proof for Theorem 1, where the circles refer to the nodes’ sensing areas (a, b)

After proving that the 3-D GEDIR guarantees packet delivery based on the Chipset Coverage Model, we present in the following Subsection, the 3-DRSS protocol including its main heuristics.

3.1 3-D randomized sensing spheres routing protocol

The 3-D Randomized Sensing Spheres Protocol (3-DRSS) has three main heuristics. The first heuristic, referred to as Heuristic a, checks if the neighbours’ sensing spheres of a current node intersect the line segment between the source and the destination. After having this set of nodes, the current node chooses the closest neighbouring node to the destination, see Fig. 5.2 This heuristic keeps running on each chosen node until reaching the intended destination.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig5_HTML.gif
Fig. 5

Heuristic a

Although the underlying region is fully covered, Heuristic a may fail in packet delivery (See the counter-example illustrated in Fig. 6). For simplicity, the figure is illustrated in 2-D which also applies to 3-D as well. In this figure, the neighbour’s sensing circle (with non-continuous pattern) that do intersect the line between the source and the destination, has a negative progress toward the destination. The other neighbours either they have positive progresses toward the destination but their sensing circles do not intersect the line or their sensing circles do intersect the line but with negative progresses toward the destination.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig6_HTML.gif
Fig. 6

A counter-example for Heuristic a. The line refers to the line joining the source and the destination, and it is pointing toward the destination. The black sensing circle is the sensing circle for the current node

Because of this fact, we need to present other heuristics that can be used as recovery modes for Heuristic a. The recovery heuristics, which are referred to as Heuristic b, and c, respectively, are chosen randomly, hence the word “Randomized” characterizes the 3-DRSS. When using Heuristic b (See Fig. 7), a current node chooses the neighbouring node whose angle to the line between the source and the destination is the smallest possible. This neighbour should also has positive progress toward the destination. The angle for one neighbour is between the line between this neighbour and the source node, and the line between the source and the destination. The angle might not be the smallest angle since this heuristic chooses the neighbor that has the smallest angle among all the neighbours that have positive progresses toward the destination. Hence, there might be a neighbour that has the smallest angle but it has a negative progress and thus, this heuristic will ignore this neighbor. Therefore, this heuristic always stays as close as possible to the line between the source and the destination, and at the same time it goes in a positive direction toward the destination. Heuristic b guarantees packet delivery which is illustrated in the following Theorem.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig7_HTML.gif
Fig. 7

Heuristic b

Theorem 2

In a sensing-covering network with Rc = w*Rs, where w ≥ 2, Heuristic b always guarantees packet delivery.

Proof

The proof is similar to the proof of Theorem 1, presented in Section 3, with an additional criterion that the chosen node should have the smallest angle among the other neighbours that have positive progresses toward the destination. □

When Heuristic c is chosen, a current node chooses one neighbouring node that has the best positive progress, and another neighbouring node that has the second best positive progress after the first chosen node. Afterwards, the current node chooses one of these two nodes such that the chosen node has the shortest projection line that is perpendicular with the line between the source and the destination, see Fig. 8. In this figure, the term dis A represents the length of the projection line that is perpendicular to the line between the source and destination. The same applies to dis B. As can be seen from the figure, node A is chosen, since even though it has the second best positive progress, its dis A is shorter than dis B. Heuristic c is repeated until reaching the destination. Therefore, this heuristic guarantees packet delivery which is illustrated in the following Theorem.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig8_HTML.gif
Fig. 8

Heuristic c

Theorem 3

In a sensing-covering network with Rc = w*Rs, where w ≥ 2, Heuristic c always guarantees packet delivery.

Proof

The proof is similar to the proof of Theorem 1, presented in Section 3, with an additional criterion that the chosen node, among the two neighbouring nodes, should have the shortest projection line that is perpendicular with the source-destination line. □

For completeness, we include the formal algorithm for the 3-DRSS (See Algorithm 1). In the next Section, we present the modified version of the 3-DRSS protocol when encountering partially covered networks. This type of networks appears when there exist some node failures (e.g. some of the sensors’ batteries are completely burned out).

Algorithm 1   3-DRSS(u, N(u), αu, s, d) routing algorithm

    Input:uis the current/source node,N(u) is the list of neighbors ofu,αuis the progress ofu,sis the source node, anddis the destination node.

    Output:A neighbour ofu,NewNode, that satisfies either Heuristicaor one of the Heuristicsborc.

    Let NewNode := 0

    for allz ∈ N(u) such that αz is the maximum and z’s sensing sphere intersects s-d line do

        NewNode := z

    end for

    if (NewNode != 0)

      return NewNode

    else /*Execute either Heuristic b or c*/

    /*Heuristic b*/

    for allz ∈ N(u) such that αz is the maximum and z’s angle with the s-d line is minimized do

        NewNode := z

    end for

    return NewNode

    /*Heuristic c*/

    for allz ∈ N(u) such that αz is the maximum do

        FirstNode := z

    end for

    for allz ∈ N(u) such that αz is the maximum and αz < αFirstNodedo

        SecondNode := z

    end for

    if (projectionLengthFirstNode  < projectionLengthSecondNode)

        NewNode := FirstNode

        return NewNode

    else

        NewNode := SecondNode

        return NewNode

4 Proposed 3-D position-based routing protocol on partially covered networks

Sensor nodes perform many operations (e.g. sensing the surroundings and sending/receiving packets), leading some nodes to become out of service, i.e. the sensors’ batteries are completely burned out. As a result, the network may no longer be covered, which creates partially covered network. To deal with these networks, we propose a new version of the 3-D Randomized Sensing Spheres Protocol (3-DRSS) presented in Section 3.1, where the new version reduces the chances of dropping too many packets; especially when dealing with local minima. This new version is referred to as the 3-D Randomized Sensing Spheres version 1 routing protocol (3-DRSSv1).

The 3-DRSSv1 protocol works as follows (See Fig. 9a, and b, respectively). Each time a node wants to forward a packet, it relies on the operational definition of the 3-DRSS protocol. However, if a current node can not forward a packet due to a hole on the way towards the destination, then the 3-DRSSv1 protocol constructs a line between the current and the destination nodes. Afterwards, the node3 moves according to α value, where α represents the position of the current node along the line between the current and destination nodes (0 < α ≤ 1). Displacing the current node based on α, increases the chances to deliver the packet to the destination. For the 3-DRSSv1, we demonstrate experimentally that it outperforms an existing progress-based routing protocol in terms of delivery rate either when varying the nodes’ transmission range or varying the density of the deployed nodes. In the next Section, we evaluate the proposed routing protocols, and compare them to an existing progress-based routing protocol based on fully and partially covered networks.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig9_HTML.gif
Fig. 9

3-DRSSv1 protocol. a A case where a current node encounters a hole. b A current node is displaced with an α value towards the destination

5 Performance evaluation

In this section, we perform our experiments based on two cases. The first case is based on fully covered networks, while the second case is based on partially covered networks.

5.1 Fully covered networks

We begin with the fully covered sensor networks. In particular, we mention the simulation model used, performance metrics, and the simulation results for the 3-D Randomized Sensing Sphere (3-DRSS) routing protocol compared to the existing 3-D Geographic Distance (3-D GEDIR) routing protocol.

5.1.1 Simulation model

Our Chipset Coverage Model is based on a stochastic approach. This model covers a specific part of an ocean region with the following dimensions: 100 m×100 m×100 m. The spacing between the pins is denoted by d which is equal to two. We also assume to have an Rs equal to 10 m. We increase the Rs value by \(d/\sqrt{2}\), which become 11.4142 m, in order to eliminate the possibility of having spaces between the pins (See Section 2). Also, as mentioned in the same section, our network is based on the fact that Rc = w*Rs, where w ≥ 2. This would lead to have different values for Rc. We use w with the following values: 2, 4, 6, 8, 10 which would lead to have Rc with the following values: 22.8284 m, 45.6568 m, 68.4852 m, 91.3136 m, 114.142 m, respectively.

Each time the Chipset model is covered, we would have around 1000 sensor nodes covering a region. We repeat this for ten times ending up with the following numbers: 833, 851, 821, 854, 858, 823, 866, 873, 829, 811, where each number of these represents the number of nodes in one experimental network. In addition, in each of these networks, we would have a strongly connected network since Rc = w*Rs, where w ≥ 2. The more we increase the value of w, the more the number of edges are established for each sensor node. This implies that the network will become stronger in its connectivity.

For each experimental network, every node sends a packet to every other node (except itself). For example, in the first experimental network, where the number of nodes obtained is 833, there will be 833*832=693,056 packets reaching the last experimental network, where the number of nodes obtained is 811, which would have 811*810=656,910 packets.

5.1.2 Performance evaluation metrics

Sending and receiving packets would depend on the 3-DRSS and the 3-D GEDIR routing protocols. Thus, we evaluate them in terms of: 1) network dilation, 2) Euclidean dilation, 3) power dilation, and 4) routing delay. The network (hop) dilation is the maximum ratio between any pair of nodes u, v, uv, of the hop count of the route path from u to v returned by the routing protocol to \(\left\lceil |uv|/R_{c} \right\rceil\), where Rc is the transmission range of each sensor node. For the Euclidean dilation, we look up for the maximum ratio between any pair of nodes u, v, uv, of the Euclidean length of the route path from u to v returned by the routing protocol to |uv|.

For the power dilation, we look up for the maximum ratio between any pair of nodes u, v, uv, of the power consumed via the sensor nodes along the routing path from u to v returned by the routing protocol to |uv|β, where β is a constant parameter from within the interval [2, 5]. Lastly, the routing delay, which is a Quality of Service (QoS) metric, is defined as the accumulated delays for the routing process on the paths between all pair of nodes for each experimental network. For all the routing protocols used based on our Chipset Coverage Model, we found that all of them achieve 100% delivery rate. This applies for all the ten experimental networks, which therefore validates our theoretical analysis.

5.1.3 Simulation results

According to Fig. 10, even though the 3-D GEDIR protocol has much better network dilation compared to 3-DRSS when Rc/Rs = 2, the difference between them is relatively small. As the ratio Rc/Rs increases, both dilations become close to each other and converge to one. From all these observations, we can see that when the ratio Rc/Rs = 2, the 3-D GEDIR outperforms the 3-DRSS. This is due to the execution of the recovery modes. However, as this ratio increases, the 3-DRSS would more depend on heuristic a, which traverses a number of hops that is close to these traversed by the 3-D GEDIR. This is because heuristic a depends on the operational definition for the 3-D GEDIR.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig10_HTML.gif
Fig. 10

The hop dilation for the two position-based routing protocols

From Fig. 11, the 3-DRSS routing protocol outperforms the 3-D GEDIR protocol in terms of the Euclidean dilation. This is due to the fact that the 3-DRSS always tries to be as close as possible to the line between the source and destination by running Heuristic a. This heuristic chooses the neighbouring node whose sensing sphere intersects the source-destination line. If this heuristic fails, especially when the ratio Rc/Rs = 2, then either Heuristic b or c is chosen. Both of these heuristics tries to be as close as possible to the line between the source and the destination, since Heuristic b chooses the neighbouring node that has the smallest angle with the source-destination line. In addition, Heuristic c chooses the neighbouring node that has the shortest projection line which is perpendicular with the source-destination line. However, it seems that both Heuristics b and c do not get close enough to the source-destination line, which explains why the 3-DRSS is still higher than the 3-D GEDIR in terms of the Euclidean dilation. But as the ratio Rc/Rs increases, Heuristic a dominates the 3-DRSS’s main performance and outperforms the 3-D GEDIR. This is due to the fact that although Heuristic a is based on the 3-D GEDIR’s operational definition, Heuristic a always tries to be as close as possible to the source-destination line by checking the intersection of the neighbours’ sensing spheres with this line. In addition, the region is fully covered. This makes the 3-DRSS to better approximate the shortest path between the source and destination.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig11_HTML.gif
Fig. 11

The Euclidean dilation for the two position-based routing protocols

This would mean that the 3-DRSS protocol reduces the energy consumption of a network via controlling the nodes’ transmission power [27]. This is reflected in Fig. 12. In this Figure, the 3-D GEDIR outperforms the 3-DRSS in terms of power dilation when w is set to 2. However, as the value of w increases, the 3-DRSS consumes much less power compared to the 3-D GEDIR, which makes the 3-DRSS to be considered as a power-aware routing protocol. These observations are due to the same reasons mentioned when measuring the Euclidean dilation for both protocols.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig12_HTML.gif
Fig. 12

The power dilation for the two position-based routing protocols

From Fig. 13, the 3-DGEDIR protocol outperforms the 3-DRSS, since it has simpler forwarding criteria. However, as the ratio Rc/Rs increases, the routing protocols spend much more time in their forwarding decisions since the number of neighbors increases for each node. As the ratio continues to increase, the delay starts to become much less. This is due to the fact that the destination starts to become closer than before. In the next Subsection, we evaluate our novel dynamic position-based protocol when encountering partially covered networks.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig13_HTML.gif
Fig. 13

The delay for the two position-based routing protocols

5.2 Partially covered networks

In this Section, we experiment our novel 3-D Randomized Sensing Sphere version 1 (3-DRSSv1) routing protocol based on partially covered networks. We, first, present the simulation model used, performance metrics, and the simulation results for our new protocol compared to the existing 3-D Geographic Distance (3-D GEDIR) routing protocol.

5.2.1 Simulation model and performance metrics

For our simulation, we use the Chipset Coverage Model, but instead of having fully covered networks, we want to have partial covered networks. This is obtained by extracting some sensor nodes from our fully covered networks obtained from the previous experiment. This is analogous to the case when sensor nodes turn off due to their insufficient battery power. Also we set the sensing range (Rs) = 7.5 m to reduce the level of coverage in a region. All these modifications makes the underlying network to become disconnected.

Sending and receiving packets would depend on the 3-DRSSv1 and the 3-D GEDIR routing protocols. we evaluate them in term of delivery rate, where this rate refers to the percentage of delivered packets between all pair of nodes. We experiment the 3-DRSSv1 and the 3-D GEDIR routing protocols based on 100 nodes, the first 100 nodes are extracted from each of the ten experimental networks obtained from the fully covered experiment, where we vary the term w (2, 2.13, 2.27, 2.4, 2.53, 2.66, 2.8), Rc = w * Rs, to obtain the following Rc values: 15 m, 16 m, 17 m, 18 m, 19 m, 20 m, 21 m. In another experiment, we set the term w = 2, and we vary the number of sensors from 100 nodes to 500 nodes. The first 100 nodes are extracted from each of the ten experimental networks obtained from the fully covered experiment, and the same applies to the 200, 300, 400, and 500 nodes. The delivery rate when it is as a function of the transmission range or as a function of density is averaged over ten experimental networks.

5.2.2 Simulation results

As can be seen from Fig. 14, the 3-DRSSv1 achieves much better delivery rate than the 3-D GEDIR even though the transmission range increases. This strictly means that the 3-D GEDIR fails to deal with node failure, by dropping too many packets. In Fig. 15, the 3-DRSSv1 achieves much better delivery rate than the 3-D GEDIR even though the network density increases. Hence, adding more nodes to the network does not make any difference, and even though the delivery rate of the 3-D GEDIR improves, the 3-DRSSv1 is still considered much better and almost achieves 100% delivery rate.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig14_HTML.gif
Fig. 14

The delivery rate for the two position-based routing protocols as a function of the transmission range

https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig15_HTML.gif
Fig. 15

The delivery rate for the two position-based routing protocols as a function of density

These observations are due to the following reason. The 3-DRSSv1 has a dynamic routing behavior when forwarding the packets towards the destinations. Specially, if a local minima occurs, the 3-DRSSv1, with a displaced value (α) of 0.25, enables the current node holding the packet to move in the direction of the intended destination. This increases the chances to find new neighbours that either satisfy the routing protocol’s main criteria, or are neighbours of the destination. Therefore, our new 3-DRSSv1 is a more realistic protocol than the 3-D GEDIR when dealing with partially covered networks. In the next Section, we discuss the major findings obtained from our experiments along with their importance. In addition, we illustrate the limitation of the Chipset Coverage Model and Algorithm, and propose a possible solution that can still obtain fully covered networks.

6 Discussion

The Chipset Coverage Model has proven to be a robust technique for achieving coverage in 3-D environments. While this model uses a small number of sensor nodes, it generates highly connected graphs. Moreover using fewer sensor nodes, which require battery power, this technique consumes less energy. In addition, this model improves routing protocols, making packet delivery much more reliable and finding shorter paths to the intended destination. We, therefore, summarize our findings as mentioned in Section 5.1.3 as follows. We showed that the protocols based on this model, the new 3-D Randomized Sensing Spheres protocol (3-DRSS), and the 3-D Geographic Distance (3-D GEDIR) protocol always guarantee packet delivery. Our simulation also showed that the 3-DRSS protocol has similar performance to existing position-based protocol in terms of network dilation and routing delay, where the delay is considered one of the Quality of Service (QoS) metrics. In addition, our findings show that the 3-DRSS protocol outperforms the existing 3-D position-based routing protocol in terms of Euclidean dilation and power dilation.

We found in one experiment, where we tested the 3-DRSS protocol, and the 3-D GEDIR protocols in terms of Euclidean dilation, that our protocol reaches the destination nodes via shorter routing paths than the GEDIR protocol. This refers to the fact that the new protocol also consumed less energy [27], which is reflected by the power dilation factor. Therefore, the new protocol prolongs the life of the network.

We found in another experiments, where we tested the new and existing protocols in terms of network dilation and routing delay, that both the 3-D GEDIR and the 3-DRSS protocols use similar number of intermediate nodes to reach the destinations. This implies that the speed of the 3-DRSS is as fast as the speed of the 3-D GEDIR. In addition, the 3-DRSS has a very low routing delay, which makes the new protocol efficient, especially in high critical missions (e.g. salvational missions). This significant fact along with the fact that the 3-DRSS reduces energy consumption, would make the 3-D GEDIR routing protocol to be completely replaced by the new 3-DRSS routing protocol.

From both experiments that measure the network and Euclidean dilations, we can see that although the 3-DRSS generally outperforms the 3-D GEDIR in terms of the Euclidean dilation for most of the Rc/Rs’s values, the 3-DRSS’s network dilation is close to that for the 3-D GEDIR. As can be seen from Fig. 10, and Fig. 11, when the ratio Rc/Rs = 2, the 3-DRSS has higher network and Euclidean dilations to these for the 3-D GEDIR. This is due to the execution of the recovery modes used by the 3-DRSS.

However, as the ratio increases, Heuristic a dominates the procedure of 3-DRSS. As a consequence, this protocol outperforms the 3-D GEDIR in terms of the Euclidean dilation and has a close network dilation to that for the 3-D GEDIR. This is illustrated in Fig. 16. In this figure,4 the dashed circles refer to the communication circles, small circles refer to the sensing circles, and the dotted line is the source-destination line. Also the dashed arrow refers to the 3-DRSS’s forwarding direction, while the other arrow refers to the 3-D GEDIR’s forwarding direction. As can be seen from this figure, although the ratio Rc/Rs = 3, the 3-DRSS still chooses the next hop such that its sensing sphere intersects the source-destination line and has a positive progress towards the destination, whereas the 3-D GEDIR still chooses the next hop that has only the best positive progress, might have equal or slightly higher progress to the next hop chosen by the 3-DRSS, towards the destination. And since the region is fully covered, we can see that both protocols somehow have almost same number of hops towards the destination. However, both of these protocols do not have similar Euclidean dilations. This applies to the ratio Rc/Rs > 3. In contrast to fully covered regions, partially covered networks were also used by turning off some of the deployed sensor nodes, i.e their batteries’ energies are burned out. Dealing with these partially covered networks, we demonstrated that the 3-D Randomized Sensing Spheres version 1 (3-DRSSv1) protocol outperforms the 3-D Geographic Distance (3-D GEDIR) protocol in terms of the delivery rate. Furthermore, if the 3-D GEDIR is enabled in such a way that makes it goes backward to previous intermediate nodes in order to find some other routing paths from these nodes to the intended destinations, then a significant delay may occur. Therefore, the 3-DRSSv1 is much more reliable than the 3-D GEDIR. However, this makes the 3-D GEDIR routing protocol to be completely replaced by the new 3-DRSSv1 routing protocol when dealing with partially covered networks.
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig16_HTML.gif
Fig. 16

The behaviour of the two protocols

While the Chipset Coverage Algorithm efficiently effects the new protocols, some limitations in this algorithm should be pointed out. The coverage algorithm obtains fully covered regions when the sensor nodes are stationary. However, if the nodes are mobile or their batteries are dead, then the existing algorithm needs to be improved to deal with these challenges (see Fig. 17).5
https://static-content.springer.com/image/art%3A10.1007%2Fs11036-009-0183-4/MediaObjects/11036_2009_183_Fig17_HTML.gif
Fig. 17

Recovery Chipset Coverage Algorithm

A possible solution for this problem is to modify the proposed coverage algorithm as follows. If there is a sensor node that moves unintentionally to another region (this is caused by some factors, e.g.: ocean wave or animal movement), then the sensor node sends a message, containing its old location, to the sensor controller (Base station). In addition, the forced node keeps a copy of the pin which was intersected with the forced node, and once the node stops moving, the coverage algorithm checks if the new placed pin is covered by some other sensor nodes. If the new pin has not yet been covered, then the sensor controller places new sensor node(s) that fully covers the new pin. However, for the location where the node was residing, the sensor controller waits for a pre-defined threshold, if there are no forced nodes from some other locations to this uncovered location, then immediately the sensor controller dispatches a sensor node that covers the uncovered location. As can be seen from Fig. 17, the forced node keeps a copy of the original pin (with dashed pattern), after a pre-defined threshold, the sensor controller places a node on the original location of the forced node, and the same applies for the dashed pin. In the next Section, we conclude our work, and present some of the future work.

7 Conclusion

In this paper, we propose a new approach for covering a 3-D region which we call the Chipset Coverage Model and Algorithm. This algorithm makes sure that every single point in a region is fully covered by at least one sensing sphere. Moreover, this algorithm performs in O(l). Upon having full coverage, we construct new position-based routing protocol, which is referred to as the 3-D Sensing Spheres close to the Line (3-DSSL) routing protocol. This protocol showed to have a behaviour close to the behaviour of the 3-D Geographic Distance (3-D GEDIR) protocol in terms of network dilation and routing delay. Moreover, the 3-DRSS protocol outperforms the 3-D GEDIR in terms of Euclidean and power dilation. Thus, the new protocol reduces the energy consumption of the nodes and, therefore, prolongs the lifetime of the network. In contrast to routing in fully covered networks, we proposed a new 3-D dynamic position-based protocol that runs on partially covered networks. This protocol is referred to as the 3-D Sensing Spheres close to the Line (3-DRSSv1). This protocol showed to have a remarkable delivery rate compared to the delivery rate of the GEDIR. Therefore, the 3-DRSSv1 increases the level of salvational missions, and thus, protecting more lives. For future work, we will evaluate the 3-DRSSv1 in terms of power dilation. We will also improve the topological graph used (Unit Disk Graph) in order to improve the performance of the proposed routing protocols.

Footnotes
1

The projection is perpendicularly onto the straight line joining the current node and the destination node.

 
2

For this figure as well as for the next figures, we remove some of the sensor nodes for illustration purposes, and we assume that Rc = w*Rs, where w > 2.

 
3

Assume the nodes have movement capability when it is needed, such as the AUVs used in water environments and others.

 
4

For simplicity, the figure is shown in 2-D.

 
5

We remove many sensor nodes from the figure for illustration purposes.

 

Copyright information

© Springer Science+Business Media, LLC 2009