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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper considers the problem of designing power efficient routing with guaranteed delivery for sensor networks with unknown geographic locations. We propose HECTOR, a hybrid energy efficient tree-based optimized routing protocol, based on two sets of virtual coordinates. One set is based on rooted tree coordinates, and the other is based on hop distances toward several landmarks. In HECTOR, the node currently holding the packet forwards it to its neighbor that optimizes ratio of power cost over distance progress with landmark coordinates, among nodes that reduce landmark coordinates and do not increase distance in tree coordinates. If such a node does not exist, then forwarding is made to the neighbor that reduces tree-based distance only and optimizes power cost over tree distance progress ratio. We theoretically prove the packet delivery and propose an extension based on the use of multiple trees. Our simulations show the superiority of our algorithm over existing alternatives while guaranteeing delivery, and only up to 30% additional power compared to centralized shortest weighted path algorithm.

Wireless

Position awareness in sensor networks improves the efficiency of route discovery and broadcasting algorithms. The fundamental idea behind position awareness (referred also as ^{2}) messages for route discovery and require

Nevertheless, position information provided by devices is not always a feasible solution for sensor networks since GPS do not work in every environment. GPS are bulky, energy-costly and expensive. Without such positioning devices, the option is to assign nodes ’virtual’ geographical coordinates with an

The authors of [

In this paper, we focus on designing an energy-aware and scalable routing protocol that guarantees delivery for sensor networks where nodes are not aware of any positioning information. We introduce HECTOR, a Hybrid Energy-effiCient Tree-based Optimized Routing protocol. HECTOR builds two sets of virtual coordinates:

HECTOR has the following properties:

We then propose an extension of HECTOR based on multiple trees and theoretically prove the packet delivery. Simulations show that HECTOR provides fair performances regarding the energy efficiency and the path length. In addition, as far as we know, it is the first algorithm to propose a geographic routing protocol where nodes are not aware of their positions, which is both energy-efficient and guaranteed-delivery. Moreover, HECTOR does not rely on specific assumptions (e.g., Unit Disk Graph) or any radio propagation model. It may be applied in any general topology. For all these reasons, to our knowledge, HECTOR has no competing solutions. Indeed, classical routing protocols such as AODV [

The global analysis of HECTOR is performed by assuming that the network topology remains stable for at least the time needed to route a packet from its source to its final destination.

This paper is organized as follows. We briefly cover related work in Section 2. In Section 3, we present the way of assigning the two sets of coordinates and introduce our model and assumptions. We describe HECTOR in Section 4. The HECTOR extension to multiple trees is motivated in Section 5. Then, we compare HECTOR’s performances to existing methods in Section 6 by simulations and conclude in Section 7.

Routing in wireless sensor networks is a challenging task. Many different approaches have been proposed in the literature. We can identify three main classes of routing protocols:

Each of two families of georouting protocols (with exact and virtual coordinates) can be divided based on its properties with respect to the metric used (hop count or power), and whether or not it guarantees delivery. Therefore there are four classes of algorithms:

There are two well-known algorithms for the case where nodes are aware of their exact geographical coordinates available from GPS [

Greedy georouting has then been enhanced in two directions, toward changing hop count to another metric, and toward providing guaranteed delivery. Power aware greedy routing algorithms were first studied in [

In [

We now describe approaches that rely exclusively on virtual coordinates, derived from either relative distances or hop counting to a set of landmark nodes in the network, without the intervention of external location services. The general idea is to define a virtual coordinate system and use it to induce a routing protocol based on the virtual coordinates. We survey some of them below (Jumps [

In VCap and JUMPS [

Liu and Abu-Ghazaleh [

In LTP [

In this paper, we propose a routing protocol that combines early results from the literature in order to provide a protocol routing that at the same time

Our routing process uses two sets of coordinates (_{V}_{T}

These coordinates are similar to the ones in VCap [_{1}, . . . , _{k}_{1}, . . . , _{k}_{i}_{i}_{V}_{V}_{V}_{V}

Obviously, using only these coordinates does not guarantee delivery since the node coordinates are not unique (

We build ^{th}_{T}_{T}

As described in [

Let _{V}_{V}_{V}_{V}_{T}_{T}_{T}_{T}

Although HECTOR is cost model-independent, for the sake of proof of concept, we use the most common energy model [^{α}

The optimal transmission radius,

Let us introduce the functions _{T}_{V}_{T}_{V}

Run at each node

1: | |

2: | exit {/*Routing has succeeded*/} |

3: | |

4: | _{T}_{T}_{T}_{V} |

5: | |

6: | {/*No node is closer to |

7: | _{T}_{w∈NT} (_{T} |

8: | |

9: | _{V}_{w}_{∈}_{H}_{V} |

10: | |

11: | |

12: | |

13: | |

14: | |

15: | |

16: |

In this paper, we assume every node is able to control its transmitting power (and thus its range) and to estimate the Euclidean distance between itself and every of its neighbor, based on the received signal strength (RSSI).

HECTOR uses RSSI rather than the angle of arrivals or triangulation that require additional communication overhead. In addition, even if some obstacles or external environment impact could mislead the computing of the distance based on RSSI, this computed distance reflects the state of the link. If a short link is seen as long by the node because of low RSSI, the link will be less likely to be used, which is a positive point. Virtual distances are not suitable in the cost calculation since they do not reflect the real cost of the transmission.

Each node

The routing algorithm combines advantages of both kinds of coordinates :

The basic idea is the following. A source node _{T}_{T}_{T}_{T}_{V}_{T}_{T}

If _{V}_{w∈NV} (_{V}

Otherwise (that is, if _{T}_{w∈NT} (_{T}

_{V}_{V}_{T}_{T}

Proof Let us assume that node _{V}_{V}_{V}_{T}_{i∈NT} (_{T}

Proof We introduce an order among all nodes with respect to combined distance to destination _{T}_{V}_{T}_{T}_{V}_{V}_{0} is the source of a packet, _{1} the next hop chosen by node _{0}. If _{T}_{1}, _{T}_{0}, _{V}_{1}, _{V}_{0}, _{1} < _{0} in our order. Let _{T}_{1}, _{T}_{0}, _{1} < _{0}. Our routing process therefore strictly reduces distances to destination regarding

Proof Let us consider a source _{V}_{T}_{T}

It is worth noting that the progress made on

Proof Each node has a unique label due to the labeling process described in Section 3. This ensures that the destination of a packet is unique and that at each step of the routing protocol, a next hop closer to the destination can be found. Based on Lemmas 1, 2 and 3, if a path exists (if the network is connected), the routing protocol will find it in a greedy way.

As we could see, in Hector, the packet delivery is guaranteed because of the use of a tree. Nevertheless, following that tree may lead to important stretch factors in the routing path. One way to bypass this drawback is to use multiple trees. All trees are built independently as explained in Section 3.2. Each node has one label per tree. The _{i}_{i=0,..,t−1} where _{i}

A 2-tree example is displayed by

Hence, the use of several trees allows the use of more routes, which provides a better load balancing and shorter paths. In our example, node 0 will follow Tree

The use of several trees may even allow even shorter paths since the choice of the tree is performed independently at each routing step. If we look back at our example, node 0 computes the distance between each neighbor of its and the destination on every tree. It finds out that it has to send the message through Tree

This is the motivation of multiple-tree HECTOR.

Note that building several trees bring obviously better performances but also presents a higher costs linked to the construction and maintenance of several trees. The evaluation performed in Section 6.4 shows the trade-off to adopt between cost and performance.

For using multiple trees, some additional notations are introduced.

Let Ω be the set of trees. We note _{mT}_{Ti}_{T}_{mT}_{mT}_{mT}_{mT}

Based on this, we can now define the _{mT}

By replacing 1-tree notations by these new notation, the same algorithm as _{mT}_{mT}_{mT}_{V}

Run at each node

1: | |

2: | exit {/*Routing has succeeded*/} |

3: | |

4: | _{mT}_{mT}_{mT}_{V} |

5: | |

6: | {/*No node is closer to |

7: | _{mT}_{w∈NmT (u)} _{mT} |

8: | |

9: | _{V}_{w}_{∈}_{H}_{V} |

10: | |

11: | _{t}_{′∈Ω,}_{w}_{∈}_{H}_{′} |_{t}_{′} ( |

12: | |

13: | |

14: | |

15: |

Indeed, some cases may appear in which, from the local point of view of the current node, every tree provides the same progress to the destination. For instance, let us consider node 13 on

Nevertheless, these two rules do not prevent from having nodes choosing at random, as it is the case if node 0 handles a packet for node 6. It has the choice between Tree

We now prove that

Proof Let us assume 3 nodes with labels

Lemma 5 can easily be extended to

We now give two definitions for a subtree. Definitions 3 and 4 are equivalent.

Proof This is true based on Lemma 5, because there is no possible

This theorem means that, if a path from a node to another node in the same subtree exists, this path (by using this tree) is the shortest path. The two previous theorems mean that the

This section presents the simulation results of our algorithm. We compare our solution to the geographical algorithms of the literature that assume no position information: VCost [_{T}_{V}

As we focus our performance evaluation study on network layer mechanisms, for our performance results to be independent of the lower layers, we chose to use our home-made simulator that assumes ideal MAC (no packet collision, no delay) and Physical layers (no interference, BER = 0, isotropic radiation pattern). The network can be described as follows. Nodes are deployed in a 1,000 × 1,000 square following a two dimensional Poisson Point Process with different intensities

We compare HECTOR, LTP [

All results are the average of statistics retrieved from more than 100 simulation runs and meet a 98% interval. Note that the bootstrap cost induced by the coordinates setting is not integrated in these results. We keep for future work the evaluation of this cost and the maintenance of the virtual coordinates.

We evaluate the energy consumption overhead (ECO) of each algorithm based on the energy model described in Section 3. As in [^{7} and ^{*} = 100 [_{i}^{*} be the energy consumed using any described protocol and the centralized SP protocol, respectively. We define the energy overhead as the ratio

We also evaluate the mean path length and mean hop length obtained for each protocol and give visual results of routing process.

As expected, for each case, HECTOR provides a greater overhead than VCost. This is due to the routing process in HECTOR that tries to provide a progress in the tree at any step. Therefore, the tree root position is important for minimizing the energy consumption for a given source and destination, but it is not possible to have an optimal tree root position for all possible source-destination pairs.

Nevertheless, as

Note that an exception occurs for low densities of HECTOR with 3 landmarks. This is due to, by construction and because of the low densities, the path followed by VCost can be far from the label root, which forces HECTOR not to follow the VCost coordinates but the LTP labels. This is less the case in topologies with holes because VCost coordinates also bypass the hole, which make the path followed by VCost closer to the root. This explains this phenomenon. We integrated this explanation in the revised version.

In

When VCost fails, HECTOR and HECTOR’ make decision based on

Another interesting feature to point out is that globally, HECTOR provides longer paths than HECTOR’ and VCost while it spends less energy. This also shows that HECTOR distributes the energy spending over the nodes on the paths.

We can see in

In

It is worth noting that the landmarks and the tree root positions have a great impact on the routing process. In VCost, landmarks position may affect the success rate. In LTP, the tree root position may increase the path length, and in HECTOR, the path may be different depending on these positions.

Till now, we have evaluated HECTOR by comparing it to other existing algorithms by running them in a restricted area and by making the node density grow. In this section, we fix the node density to _{max}

Indeed, in such a scenario, the energy consumption will necessary grow since nodes may be further one from the others and more hops are needed to connect them than in previous scenarios. This section allows us to check the scalability of HECTOR (in terms of growing area rather than increasing node density) in very large networks by being sure that we still ensure a low ECO.

One can notice that for homogeneous networks, even if the network grows as well as the route length, the energy overhead compared with the optimal shortest path consumed by HECTOR grows slowly with the network size. This is because HECTOR can follow

We now measure the benefit of using multiple trees for HECTOR as described in Section 5. Indeed, paths is tress should be shortened but in return, this means that there are several trees to maintain and there is a cost. To do so, we compare the energy consumption of paths found by HECTOR with different numbers of trees, both when VCost succeeds and when it fails. Tree roots are spread randomly in the network. Results are displayed in

We can notice that globally, the energy consumption is lower when VCost succeeds. This is still because HECTOR is more likely to follow the VCost coordinates. What is interesting to notice is that in both cases, using two trees instead of one allows the great enhancement of the energy consumption while using more than two trees does not bring a lot, since energy consumed by HECTOR is globally the same whatever the number of trees. When the network is sparse, it can be worth using a third tree but this is only for some low density scenarios.

This means that two trees are enough to find appropriate paths by switching from one tree to another one. This is confirmed by results shown in

In this paper, we introduce HECTOR, a Hybrid Energy-effiCient Tree-based Optimized Routing protocol. HECTOR is a geometric routing protocol designed for wireless sensor networks. Unlike the approaches proposed in the literature, HECTOR is

The next step of this work is to provide a more reliable way to build the tree coordinates in HECTOR. Indeed, a weakness of HECTOR is due to the underlying tree(s) used for one set of coordinates. Building a tree with energy-aware properties would make HECTOR even more efficient. At last, other aspects to analyze are the study of HECTOR towards node mobility, asymmetric links and extension to heterogeneous networks [

On

Illustration of the use of multiple trees.

Network topologies.

ECO when VCost succeeds for 3 and 5 landmarks for a homogeneous topology.

ECO when VCost succeeds for 3 and 5 landmarks for a topology with a hole.

Success rate of VCost routing algorithm (

ECO when VCost fails for a homogeneous topology.

ECO when VCost fails for a topology with a hole.

Mean hop length.

Path length in number of hops when VCost succeeds (3 landmarks).

Path length in number of hops when VCost does not succeed. For VCost: number of hops before failing (3 landmarks).

Illustration of the paths followed by each algorithm with the use of 5 landmarks. Source is in the right side. VCost and HECTOR follow the same path while LTP and HECTOR’ passes through the tree root.

Illustration of the paths followed by each algorithm with the use of 5 landmarks. VCost fails after the second hop, LTP passes through the tree root and HECTOR combines both

ECO when the network grows.

Energy consumption overhead.

Path length.

Classification of Georouting Protocols.

Exact Position | Virtual Position | |
---|---|---|

hop count (HC) | MFR [ |
VCap |

Energy-efficient (EE) | COP [ |
VCost [ |

HC+Guaranteed-delivery (GD) | GFG [ |
LTP [ |

EE+GD | EtE [ |
HECTOR |