Forwarding via checkpoints: Geographic routing on always-on sensors

J. Parallel Distrib. Comput. 70 (2010) 719–731

Contents lists available at ScienceDirect

J. Parallel Distrib. Comput. journal homepage: www.elsevier.com/locate/jpdc

Forwarding via checkpoints: Geographic routing on always-on sensors Habib M. Ammari a,∗ , Sajal K. Das b a

Wireless Sensor and Mobile Ad-hoc Networks (WiSeMAN) Research Laboratory, Department of Computer Science, Hofstra University, Hempstead, NY 11549, USA

b

Center for Research in Wireless Mobility and Networking (CReWMaN), Department of Computer Science and Engineering, The University of Texas at Arlington, Arlington, TX, 76019, USA

article

info

Article history: Received 16 November 2008 Received in revised form 11 October 2009 Accepted 7 November 2009 Available online 21 December 2009 Keywords: Wireless sensor networks Geographic forwarding Delaunay triangulation Energy efficiency

abstract Data forwarding is an essential function in wireless sensor networks (WSNs). It is well-known that geographic forwarding is an efficient scheme for WSNs as it requires maintaining only local topology information to forward data to a central gathering point, called the sink (or base station), for further analysis and processing. In this paper, we propose an energy-efficient data forwarding protocol for WSNs, called Weighted Localized Delaunay Triangulation-based data forwarding (WLDT), with a goal to extending the network lifetime. Specifically, WLDT selects as forwarders the sensors with high remaining energy and whose locations lie nearer the shortest path between source sensors and a single sink, thus helping the sensors minimize their average energy consumption. More precisely, WLDT defines checkpoints to build energy-efficient data forwarding paths and uses a 1-lookahead scheme to guarantee data delivery to the sink. We show that WLDT, which favors data forwarding through short Delaunay edges, achieves an energy gain percentage in the order of 55% for the free space model and close to 100% for the multipath model compared to BVGF and GPSR, which forward data through long distances and which we have slightly updated to account for energy in the selection of next forwarders. We prove that these checkpoints yield an energy gain percentage in the order of 30% in comparison with a similar protocol, called WLDTw/c (or WLDT without checkpoints), which forwards data via short distances but does not use checkpoints. Published by Elsevier Inc.

1. Introduction Wireless sensor networks (WSNs) have emerged as an attractive technology for their wide range of applications in civil and military areas. In contrast to traditional wireless networks, energy efficiency is a critical determinant to extend the lifetime of WSNs [1]. A WSN consists of a large number of tiny sensor nodes1 that collect data through monitoring a field of interest and forward them to a central processing node, known as the sink (or base station), for further analysis and processing. Sensors communicate with each other via wireless, multi-hop links and have limited battery power (or energy), computation, sensing, communication, and storage capabilities, with energy being the most crucial resource. With these challenges in mind, the primary constraint that should be met in the implementation of WSNs is to design efficient and optimized protocols that can be used by the sensors in their sensing, communication, and processing tasks. Because energy is the most crucial resource for the sensors to perform efficiently and correctly,

∗

Corresponding author. E-mail addresses: [email protected] (H.M. Ammari), [email protected] (S.K. Das). 1 Throughout this paper, we use the terms sensor and sensor node interchangeably. 0743-7315/$ – see front matter. Published by Elsevier Inc. doi:10.1016/j.jpdc.2009.11.002

the design of energy-efficient data forwarding protocols for WSNs has been receiving much attention in order to extend the network lifetime. Geographic forwarding is an energy-efficient and practical scheme for WSNs in that the sensors are not required to maintain global and detailed information on the topology of the entire network. The sensors need only maintain local knowledge on their one-hop communication neighbors with respect to their geographic location information in order to progress data toward their final destinations. Our protocol is designed to efficiently use the limited energy of the sensors by minimizing their average energy consumption in forwarding data originated from source sensors (or simply sources) to a single sink with a goal to prolonging the operational network lifetime. 1.1. Contributions There is an ongoing debate on short-range versus long-range data forwarding in multi-hop wireless networks [12]. This paper supports the short-range data forwarding strategy for WSNs, where energy should be given the highest priority. Our key contributions can be summarized as follows: 1. We propose an energy-efficient data forwarding protocol for WSNs so they remain operational as long as possible. Our

720

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

protocol, Weighted Localized Delaunay Triangulation-based data forwarding (WLDT), uses the 1-lookahead scheme to guarantee data delivery to the sink. WLDT aims to minimize the average energy consumption of the sensors during data forwarding towards the sink. It exploits the geometric properties of the Delaunay triangulation [3] to build an energy-efficient path between the source and the sink as a sequence of sub-paths whose endpoints are called checkpoints. These checkpoints are selected based on their location in the field and their remaining energy. A sub-path between a pair of checkpoints consists of a series of forwarders, which are the endpoints of short Delaunay edges and are selected based on their location and remaining energy to forward the data between their checkpoints. 2. We compute a lower bound on the energy consumption in short-range data forwarding and the corresponding optimum number of forwarders between a source and the sink. This bound helps extend the battery lifetime of the sensors, thus prolonging the operational network lifetime. 3. We compute the energy gain percentage in data forwarding from a source to the sink. More precisely, we show that WLDT achieves an energy gain percentage in the order of 55% for the free-space model whose path-loss exponent α = 2, and close to 100% for the multi-path model, where α > 2, in comparison with the BVGF [30] and GPSR [15] protocols, which we have slightly updated so they account for energy in the selection of a next forwarder. Note that the BVGF and GPSR protocols forward data via long range. 4. We prove that the presence of checkpoints in WLDT introduces an energy gain percentage in the order of 30% in comparison with a similar protocol, called WLDT w/c (or WLDT without checkpoints), which forwards sensed data via short range but does not use checkpoints. The remainder of this paper is organized as follows. Section 2 reviews related work. Section 3 introduces the network and energy models. Sections 4 and 5 discuss WLDT. Section 6 addresses a few reliability issues of WLDT while Section 7 presents simulations results. Section 8 concludes the paper. 2. Related work In this section, we discuss a sample of energy-aware data forwarding protocols for WSNs. Boukerche et al. [7] proposed a protocol, called Variable Transmission Range Protocol, which solves the energy sink-hole problem by varying the transmission range of sensors in order to bypass sensors lying close to the sink and avoid their overuse. Boukerche et al. [8] proposed power-efficient data dissemination protocols that combine sleep/awake and probabilistic forwarding techniques. Boukerche et al. [9] also proposed a novel protocol, called energy-aware data-centric, which constructs a broadcast tree rooted at the sink. Our protocol, however, assumes that all sensors are always-on. Our future work will address duty-cycling. Xing, et al. [30] proposed a greedy geographic routing protocol, called Bounded Voronoi Greedy Forwarding (BVGF). The nodes eligible to act as the next hops are the ones whose Voronoi regions are traversed by the segment line joining the source and the destination. The BVGF protocol chooses as the next hop the neighbor that has the shortest Euclidean distance to the destination among all eligible neighbors. This protocol does not help the sensors deplete their battery power uniformly. Each sensor has, indeed, only one next hop to forward its data to the sink. Thus, any data forwarding path between a source sensor and the sink will always have the same chain of next hops, thus suffering from battery power depletion. Bose and Morin [5] proposed a Voronoi routing for Delaunay triangulations that moves data along the nodes whose Voronoi regions intersect the straight line between the sender and

the receiver. The major problem of this algorithm is that it requires the construction of the Voronoi diagram and the Delaunay triangulation of all the wireless nodes. This strategy is very expensive in distributed environments, such as sensor networks. Also, this protocol considers the same path between the source and destination, and hence would deplete the battery power of the sensors quickly. Karp and Kung [15] proposed a Greedy Perimeter Stateless Routing (GPSR) protocol for mobile wireless ad hoc networks. GPSR forwards data packets through long distances and hence consumes much energy. Our protocol, however, forwards sensed data through short Delaunay edges and hence achieves significant energy savings. Li, et al. [19] studied compass routing [17], random compass routing [17], greedy routing [6], and most forwarding routing [26] on different graphs. Wang, et al. [27] proposed a proxy-based sensor deployment protocol for mobile wireless sensor networks. A proxy sensor is a static sensor that is closest to the logical position of its delegated mobile sensor. As can be seen, checkpoints in our protocol differ from proxy sensors in Wang, et al.’s protocol [27]. However, both of them are used for energy efficiency purposes. Proxy sensors are introduced to help mobile sensors move only when needed so that they save their energy, while our checkpoints are introduced to shorten data forwarding paths between source sensors and the sink, and hence minimize the total energy consumption. Choi and Das [11] proposed an applicative indirect routing (AIR) protocol for ad hoc wireless networks using proxy candidates, which are defined as the neighbors that are shared by the sender and the receiver. Zhang, et al. [33] proposed a dynamic proxy tree-based data dissemination framework for mobile WSNs. Mobile sources and mobile sinks are associated with stationary source proxies and sink proxies, respectively, and proxies related to the same source form a proxy tree. The latter is used to multicast data from the source proxy to the sink proxies. When the distance between sources or sinks and their proxies do not change beyond the threshold distance, the sources and sinks will keep the same proxies. This situation could lead to a battery power depletion of the associated proxies. In our protocol, checkpoints dynamically change based on both their closeness to the shortest path between the senders and receivers and their remaining energy. The protocol of Zhang, et al. [33] introduces an overhead in reconfiguring the proxy tree due to source and sink mobility. The overhead introduced by our protocol is due to the construction of localized Delaunay triangulation which occurs only once as the WSN is static, thus yielding little overhead. Lindsey, et al. [21] presented a scheme, called PEGASIS (Power-Efficient Gathering in Sensor Information Systems), where each node can receive from and send to close neighbors. Zorzi and Rao [36] proposed a geographic random forwarding (GeRaF) technique for WSNs, where relay nodes are decided only after the transmission has started. Biswas and Morris [4] proposed an integrated and MAC protocol for multi-hop wireless networks, where a source sends a batch of packets destined to the same destination. Ye, et al. [32] proposed a scalable and efficient data delivery to multiple mobile sinks using two-tier data dissemination (TTDD) model. Intanagonwiwat, et al. [14] proposed a scheme, called directed diffusion, which provides robust multi-path delivery. Ammari and Das [2] proposed an information theory-based approach for data dissemination in WSNs with a mobile sink. Luo and Hubaux [22] proposed an energy efficient routing protocol for WSNs which exploits base station mobility and multi-hop routing. Kim, et al. [16] proposed a Scalable Energy-efficient Asynchronous Dissemination (SEAD) protocol for WSNs based on dissemination trees to disseminate data to mobile sinks. 3. Preliminaries In this section, we introduce basic concepts and present the necessary network and energy models.

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

721

3.1. Terminology Definition 1 (Voronoi Diagram). The Voronoi diagram [3] of a set of n sites in the plane S = {s0 , . . . , sn−1 }, denoted by VD(S ), is a subdivision of the plane containing S into n cells VC (si ), 1 ≤ i ≤ n, such that each cell VC (si ) includes only one site si with the property that any point p located in VC (si ) is closer to si than any other site in S (Fig. 1). The cell VC (si ) corresponding to site si is called the Voronoi cell of si , which is a (possibly unbounded) open convex polygonal region. The edges of a Voronoi cell are called Voronoi edges and its endpoints are called Voronoi vertices. The Voronoi diagram of S is the union of the Voronoi cells of all sites in S . •

Fig. 1. The Delaunay triangulation (bold lines) on top of the Voronoi diagram (dotted lines) of a sensor network.

Definition 2 (Delaunay Triangulation). The Delaunay triangulation, denoted by DT (S ), is the dual of the Voronoi diagram [3] (Fig. 1). The DT (S ) graph has an edge between two sites if and only if their Voronoi cells share a common edge. Moreover, the DT (S ) graph is a planar graph whose edges are orthogonal to their corresponding Voronoi edges. •

one-hop neighbors. A sensor can piggyback its location (only once at the start of the sensing task) and remaining energy on data packets being forwarded to the sink. According to [13], the energy spent in transmitting one message of size κ bits from sensor si to sensor sj is given by

Definition 3 (Transmission Range, Neighbor Set, and Transmission Graph). The transmission range of the sensor si is defined as a disk of radius r including its boundary, which contains a set of the sensors that si can communicate with in one hop. The set of onehop neighbors of si including si , is called neighbor set of si and denoted by NS (si ). A WSN is represented by its transmission graph G = (S , T ), where each sensor corresponds to a vertex in S and edge (si , sj ) ∈ T if and only if δ(si , sj ) ≤ r . •

and the energy spent in message reception is given by

Definition 4 (Data Forwarding Path). A data forwarding path is a path traversed by a data packet originated from a source sensor (or simply source) and destined to the sink. It includes all the sensors (including the source) that forwarded the data packet to the sink on behalf of the source. • Definition 5 (Long-range and Short-range Forwarding Schemes). A forwarding scheme is said to be long-range if each sensor in a data forwarding path can use at most one of its one-hop neighbors to forward a data packet toward its ultimate destination. A forwarding scheme is said to be short-range if the same data is forwarded through multiple neighbors of each sensor until the data reaches its destination. • According to the short-range forwarding scheme, a sensor always attempts to forward data to the closest node to it. Therefore, the transmission of a message may involve several forwarders within the communication range of the source sensor (i.e., the one that originated the message) or a current forwarder. The motivation behind this decision is to minimize the energy consumption given that it depends on the transmission distance between a sender and a receiver. However, using a long-range forwarding scheme, a sensor always attempts to forward data to the farthest node from it. Thus, the transmission of a message may involve at most one forwarder within the communication range of the source sensor or a current forwarder. The motivation behind this decision is to minimize the delay incurred in data forwarding to the sink given that it depends on the number of forwarders between a sender and a receiver.

Etr (si , sj ) = κ(Eelec + εδ α (si , sj )) Erec = κ Eelec

(2)

where Eelec represents the electronics energy, ε ∈ {εfs , εmp } is the transmitter amplifier in the free-space (εfs ) or the multi-path (εmp ) model, 2 ≤ α ≤ 4 is the path-loss exponent, and δ(si , sj ) is the Euclidean distance between si to sj . Thus, the total energy consumption for si when it receives a message and forwards it to sj is given by Etot (si , sj ) = 2κ Eelec + κεδ α (si , sj ).

Our protocol assumes that the sensors are static and homogeneous in terms of energy, sensing, and communication capabilities. In addition, the sensors and sink are aware of their location using a localization technique [10]. Also, the sensors are aware of the location of the sink and the location and energy information of their

(3)

It is worth mentioning that we implicitly assume that there will be a single (successful) message transmission for each hop along the path. 4. The WLDT protocol In this section, we describe WLDT in details. We also present several theoretical results supported by extensive numerical results showing the energy savings of WLDT. 4.1. Long-range versus short-range forwarding Let S = {s0 , . . . , sn−1 } be a set of n sensor nodes and sm the single sink connected by wireless links over a WSN. Lemma 1 states that, under some specific condition, data forwarding through a short-range forwarding scheme is more energy efficient than that using a long-range forwarding scheme. We assume that the sensors si and sj are one-hop neighbors of each other. Note that the ‘‘one-hop neighbor’’ relationship is symmetric. In other words, we assume that all the sensors are homogeneous, i.e., have the same physical capabilities and, in particular, their transmission range. Lemma 1 (Conditional Energy Savings). The total energy consumption for forwarding one data packet from the sensor si to the sensor sj along a short-range path is smaller than the energy spent along a long-range path between them if there is a sensor sk ∈ NS (si ) such that

s 3.2. Network and energy models

(1)

δ(sk , sk,p ) <



d2 2

−

Eelec

ε

2/α −

d2 4

(COND)

where δ(si , sj ) = d and sk,p is the orthogonal projection of sk on the segment si sj . Proof. Let us compute the critical distance d0 between sk and sk,p for which long-range and short-range data forwarding consume

722

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

path between the source s0 and the sink sm . Moreover, we assume that all the forwarders are located at the perimeter of the transmission ranges (within distance r from each other). The average energy consumption of the sensors participating in longrange data forwarding is given by Eashv g (si ) = 2κ Eelec + κε r α . We assume that we deal with two-hop data forwarding, where half of the sensors lie on the shortest path [s0 , sm ] and the other half lie above it as shown in Fig. 2, where δ(si , si+1 ) =



r2 2

−

Eelec

1/α

ε

(see

Lemma 1). Hence, the average energy consumption of the sensors in two-hop data forwarding is Eathv g (si ) = 2κ Eelec + κεδ α (si , si+1 ). Thus, Eathv g (si ) = 2κ Eelec + κε Fig. 2. Single-hop vs. two-hop data forwarding.

Note that

E1-hop (si , sj ) = 2κ Eelec + κεδ α (si , sj ) E2-hop (si , sj ) = 4κ Eelec + κε(δ α (si , sk ) + δ α (sk , sj ))

Eelec

ε

be the energy consumption required to forward the data from si to sj through 1-hop and 2-hop paths, respectively. It is easy to check that E2-hop (si , sj ) reaches its minimum when δ(si , sk ) = δ(sk , sj ). Thus, E1-hop (si , sj ) = E2−hop (si , sj ) implies

δ(si , sk ) =

2

−

Eelec

1/α

ε

d0 =

d2 2

−

Eelec

ε

Eelec

2/α −

d2 4



ε

Eelec

ε



.

< r α , for all α ≥ 2. Thus,

, Then

E1-hop (si , sk ) + E1-hop (sk , sj ) < E1-hop (si , sj ). • Corollary 1 recommends two-hop data forwarding between any pair of sensors si to sj only if they are separated by a distance δ(si , sj ) such that

δ(si , sk )δ(sk , sj ) >

where δ(si , sj ) = d. By Pythagorean Theorem, δ 2 (si , sk ) δ 2 (si , sk,p ) + d20 , where d0 = δ(sk , sk,p ), i.e.,

s 

−

2

−

Corollary 1 (Energy Savings in the Free Space Model). Assume α = 2 (free space model) and sk ∈ NS (si ) lies on si sj . If δ(si , sk )δ(sk , sj ) >

and

d2

r2 2

r2

Eathv g (si ) < Eashv g (si ). •

the same energy. Let







=

Eelec

ε

where sk is a forwarder that lies on the line segment [si , sj ]. 4.2. A two-step data forwarding protocol

.

Thus, a short-range path between the sensors si and sj contains at least one forwarder between them if δ(sk , sk,p ) < d0 . • The condition given in Lemma 1 helps a sensor si decide on whether to send/forward data directly to the ultimate destination sj or through an intermediate sensor (i.e., relay sensor) sk . If the energy consumption associated with the path (si , sk , sj ) is less than that associated with the path (si , sj ), the use of a relay sensor sk is more energy efficient. Otherwise, direct transmission without any further forwarding is the best choice. The WLDT protocol is based on Lemma 1 and the result in [2] which states that the total energy consumption for forwarding one data packet from the source s0 to the sink sm reaches its minimum value only when all forwarders between s0 and sm lie on the line segment [s0 , sm ] between s0 and sm . Lemma 2 compares the average energy consumption of the sensors in short-range and long-range data forwarding schemes. Lemma 2 (Average Energy Consumption). Long-range data forwarding leads to higher average energy consumption of the sensors than short-range data forwarding even when the total energy consumption in both schemes is the same. Proof. According to Lemma 1, it is clear that when δ(sk , sk,p ) = d0 , the total energy consumption required for long-range and shortrange data forwarding is the same. Without loss of generality, let us assume that long-range data forwarding uses the shortest

We propose a data forwarding protocol (Fig. 3), which benefits from the energy gain introduced by short-range data forwarding as stated in Lemmas 1 and 2 and Corollary 1, and uses the geometric properties of the Delaunay triangulation (DT). Since we are interested in the area between the sending and the receiving sensors, the neighbor set NS (si ) of the sensor si will contain only the sensors located between si and the sink sm . Let us first define the notions of localized Delaunay triangulation and candidate checkpoints. Definition 6 (Localized Delaunay Triangulation). A localized Delaunay triangulation of the sensor si , denoted by LDT (si ), is the Delaunay triangulation computed by si with respect to NS (si ) and sm . • Definition 7 (Candidate Checkpoints). The candidate checkpoints of the sensor si , denoted by CCP (si , sm ), are the sensors that are adjacent to the sink sm in the LDT (si ). • The WLDT protocol is composed of two steps: checkpoint selection and checkpoint-based short-range data forwarding. 4.2.1. Checkpoint selection We consider a scenario where the source s0 wishes to forward its sensed data to the sink sm . The goal of this step is to identify a subset of candidate checkpoints, CCP (s0 , sm ), of NS (s0 ) that are closest to the sink sm . First, the source s0 constructs its localized Delaunay triangulation, LDT (s0 ). Intuitively, only the sensors in CCP (s0 , sm ) will be able to get the sensed data out of the

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

723

Fig. 4. Localized DT and candidate checkpoints.

maximum (ci = 1) when si lies on [s0 , sm ]. Intuitively, the source s0 and the sink sm are the first and last checkpoints, respectively. The intuition behind the concept of checkpoints is to make the data forwarding path not to deviate much from the shortest path between the current sender (i.e., the source of the message or any current forwarder) and the sink. In other words, checkpoints allow data to be forwarded on a path that is as close as possible to the segment line connecting the source to the sink. 4.2.2. Checkpoint-based short-range forwarding The objective is to forward the sensed data to the checkpoint sp that was selected in the previous step. First, the source s0 assigns weights to each of the Delaunay edges adjacent to it as follows: if sj is an adjacent node to s0 in the LDT (s0 ), then the weight placed on the edge (s0 , sj ) is CEDj (s0 ) = cj ej dj , where

δ(s0 , sp ) δ(s0 , sj ) + δ(sj , sp ) Erem (sj ) P ej = Erem (sk ) cj =

sk ∈Adj(s0 )

and dj =

1/δ(s0 , sj )

P sk ∈Adj(s0 )

Fig. 3. The WLDT protocol.

transmission range of s0 . Fig. 4 shows the LDT (s0 ) and the subset CCP (s0 , sm ) that includes sp1 , sp2 , sp3 , sp4 , and sp5 , which are adjacent to the sink sm in the LDT (s0 ). From the subset of candidate checkpoints, CCP (s0 , sm ), the source s0 selects the checkpoint sensor sp such that CEp = max{CEi = ci ei : si ∈ CCP (s0 , sm )} where ci =

δ(s0 , sm ) δ(s0 , si ) + δ(si , sm )

and ei =

Erem (si )

P sj ∈CCP (s0 ,sm )

Erem (sj )

.

As can be seen, the weight ci measures the degree of closeness of si to the shortest path [s0 , sm ], while the term ei is the percentage of the remaining energy of the sensor si with respect to the total remaining of the subset of sensors CCP (s0 , sm ). Note that ci attains its

1/δ(s0 , sk )

where Adj(s0 ) denotes the subset of sensors adjacent to s0 in the LDT (s0 ). As can be observed, the term dj measures the degree of closeness of the sensor sj to the source s0 . This means that s0 favors closer sensors so it transmits its sensed data over short distances and hence saves its energy. Then, the source s0 selects its next forwarder using 1-lookahead scheme described as follows: 1. The source s0 sorts the list of Delaunay edges adjacent to it, sorted-list, based on their weights in decreasing order. 2. The source s0 considers the node, sh , with the highest weight and examines its adjacent neighbors in the LDT (s0 ). If sh has at least one path that originates from one of its adjacent sensors and leads to the checkpoint sp using only positive progress (condition COND, given in Lemma 1), the node sh is selected as the next forwarder. Otherwise, the source s0 repeatedly picks the next node in sorted-list and checks if it satisfies COND. The WLDT protocol is said to be 1-lookahead because any forwarding sensor uses the information about the adjacent of its adjacent sensors so that it can make appropriate forwarding decision. At the end of this phase, the source sensor identifies its appropriate forwarder and forwards the sensed data to it. By Lemma 1, the source s0 prefers to forward its data to its corresponding checkpoint (located at the perimeter of its transmission

724

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

Fig. 5. Data forwarding path between s0 and sp2 .

range) through a series of forwarders, hence favoring short-range over long-range data forwarding. This will enable all the sensors deplete their energy slowly, thus extending the network lifetime. From the function CEDj , it is clear that when the sensor s0 selects a forwarder sk , it takes into consideration three metrics: remaining energy of the sensor sk , position of the sensor sk with respect to the shortest path [s0 , sp ], and the Euclidean distance, δ(s0 , sk ), between the sensors sk and sj ; recall that Etr (s0 , sk ) ∝ δ(s0 , sk ). This means that WLDT attempts to build energy-efficient sub-paths between the source and its checkpoint or between any pair of consecutive checkpoints, which include a series of forwarders linked by short Delaunay edges. Then, the source s0 fills in two fields in the data packet, namely Checkpoint, which contains the checkpoint sp , and Forwarder, which contains the forwarder sh , and forwards the data to sh . When a node sk receives the sensed data, it will examine both fields to check whether it is a checkpoint or a forwarder. If sk is a checkpoint, it will act like the source s0 by running steps 1 and 2. Otherwise, it will run only step 2. The pseudo-code of WLDT is given in Fig. 3. 4.3. Illustrative example Fig. 5 shows a path marked by arrows between the source s0 and its checkpoint sp2 . Data is forwarded by s1 , s2 , s3 , and s4 along the corresponding Delaunay edges before it reaches sp2 . In order to identify its checkpoint, s0 constructs LDT (s0 ). Then, it computes its forwarder s1 , sets up fields Checkpoint = sp2 and For w arder = s1 , and forwards its data to s1 , which in turn forwards it to s2 . The same forwarding process repeats until sp2 receives the data. When sp2 gets the data, it will act as s0 in order to forward the data to its next checkpoint. The entire process of determining checkpoints and series of forwarders between any pair of consecutive checkpoints repeats until the sink sm receives the data. At each forwarding step, the fields Checkpoint and Forwarder are updated accordingly. 5. Analysis of WLDT In this section, we prove that any checkpoint on the data forwarding path between the source s0 and the sink sm is reachable (Lemma 3), and hence the sink itself (Corollary 2). Next, we approximate the length of any edge in the transmission graph G = (S , T ) (Lemma 4) and deduce the length of any Delaunay edge in LDT (si ) (Lemma 5). Then, we analyze the energy consumption in short-range data forwarding (Theorems 1 and 2) and compare WLDT with BVGF and GPSR, which implement a long-range data forwarding scheme (Theorems 3 and 4). Finally, we show that checkpoints have a positive impact on data forwarding in terms of energy savings (Theorem 5). Lemma 3 (Checkpoint Reachability). Any checkpoint between the source s0 and the sink sm is reachable. Proof. Let us prove that the checkpoint of the source s0 , say sp , is reachable. Assume that the current forwarder (the sensor that

currently holds the sensed data) is si . If the sensor si has a Delaunay edge (si , sp ) in LDT (s0 ), then si could either directly forward the data to sp (long-range) or forward the data to sp through a series of forwarders (short-range) depending on the length of the Delaunay edge (si , sp ) compared to the length of other Delaunay edges adjacent to si . The WLDT protocol uses a 1-lookahead scheme, which helps the sensors choose appropriate forwarders. Therefore, si selects its forwarder sj only if there is at least one path from sj to sp along the Delaunay edges, where the x-coordinate of any forwarder along this path is less than the x-coordinate of sp . This means that the checkpoint sp will be reached using only positive progress from any forwarder between the source s0 and the sink sm . Using the same argument as above, we can prove that every checkpoint between s0 and sm is reachable. • The sink sm is also a checkpoint, and hence should be reachable. Corollary 2 below follows directly from Lemma 3. Corollary 2 (Guaranteed Sensed Data Delivery). Any sensed data originated from the source s0 is guaranteed to reach the sink sm , assuming no packet loss. • The total energy consumption in data forwarding depends on the distance between the sending and receiving nodes. Lemma 4 approximates the minimum length of any edge between any pair of sensors in the transmission graph G = (S , T ). Lemma 4 (Minimum Edge Length). The minimum edge length in the transmission graph G = (S , T ) can be approximated by

 dmin =

Eelec

ε

1/α

.

(4)

Proof. According to [13], Etr (si , sj ) = κ Eelec + κεδ α (si , sj ) and Erec (si ) = κ Eelec . Thus, there must exist a minimum transmission distance between any pair of sensors that leads to minimum transmission energy. Since the minimum energy consumption is due to the reception energy, it is reasonable to assume that the second part in the transmission energy Etr (si , sj ) is equal to the reception energy Erec (si ) for some distance between the sensors si and sj . In other words, κεδ α (si , sj ) = Erec (si ). Thus, κεδ α (si , sj ) = κ Eelec . Thus, the minimum transmission distance between si and sj is given by

δmin (si , sj ) = dmin =



Eelec

ε

1/α

.

In other words, there is a minimum transmission distance dmin such that Etr (si , sj ) = 2Erec (si ). • Lemma 5 computes the length of any Delaunay edge in a localized DT, LDT (si ), based on the result of Lemma 4. Lemma 5 (Delaunay Edge Length). The length of any Delaunay edge between two sensors sj and sk , denoted by (sj , sk ), in a localized DT, LDT (si ), satisfies dmin ≤ (sj , sk ) ≤ r . Proof. Let G(si ) be the sub-graph of the transmission graph G = (S , T ) induced by NS (si ) ∪ {sm }, and LDT (si ) the localized DT of si . First, both G(si ) and LDT (si ) have the same vertex set NS (si ) ∪ {sm }. By definition of G(si ), an edge tj,k = (sj , sk ) if and only if δ(sj , sk ) ≤ r. On the one hand, if δ(sj , sk ) = dmin , then the corresponding Voronoi diagram should have two Voronoi cells VC (sj ) and VC (sk ) with a common Voronoi edge. By definition of the DT, there must be a Delaunay edge connecting sj and sk whose length is (sj , sk ) = δ(sj , sk ). Thus, (sj , sk ) = dmin . It is worth noting that dmin is the minimum transmission distance that leads to the least energy consumption. However, the distance between

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

any two neighbors could be less than dmin , equal to dmin , or larger than dmin . It all depends on the sensor spatial density. A sensor always attempts to select a sensor that is located at a distance at least equal to dmin . In this paper, we assume that the sensors are uniformly and densely deployed. Thus, when a sensor builds its localized Delaunay triangulation, it will exclude those neighbors which are located at a distance that is less than dmin in order to make sure that its data would be transmitted through a distance that is at least equal to dmin . On the other hand, no edge between two sensors exists unless they are within the transmission range of each other. That is, by definition of the notion of neighbors, that the distance between any two neighbors cannot exceed the radius of their communication range, r. Therefore, the maximum length of any Delaunay edge cannot exceed r. Hence, (sj , sk ) ≤ r. Both results yield

α=2

0.06 0.05

E(m)

0.04 0.03 0.02 0.01

dmin ≤ (sj , sk ) ≤ r . •

0

0

50

α−1

Emin (s0 , sm ) = 2

κ

δ(s0 , sm ) dmin

× [(α − 1)Eelec + 21/α (α − 1)1/α−1 ε dαmin ]

(5)



α−1

1/α

δ(s0 , sm )

2

dmin

of forwarders and checkpoints is given by mopt (s0 , sm ) = m = ∗

(6)

Proof. Assume that there are m forwarders including s0 (s0 , s1 , . . . , sm−1 ) between the source s0 and the sink sm . The total energy Etot (s0 , sm ) spent in forwarding one sensed data packet from the source s0 to the sink sm is computed as

X i=1...m−1

2κ Eelec + κεδ α (si , si+1 ).

i=0...m−1

In general, the distances between all pairs of consecutive forwarders are not equal. Indeed, Etot (s0 , sm ) reaches its minimum when all distances δ(si , si+1 ) are the same. In other words, δ(si , si+1 ) = δ(s0m,sm ) . Thus, Etot (s0 , sm ) ≥ E (m), where E (m) =

X

2κ Eelec + κε



δ(s0 , sm ) m

i=0...m−1

α

.

Thus, E (m) = 2mκ Eelec + κε

δ α (s0 , sm ) mα−1

.

The function E (m) reaches its minimum when easy to check that

∂ 2 E (m∗ ) ∂ 2 m∗

1/α

2

δ(s0 , sm ) dmin

δ(s0 , sm ) Emin (s0 , sm ) = 2α−1 κ dmin

Theorem 1 shows that we made a good approximation of the transmission distance dmin between any pair of sensors in the transmission graph G = (S , T ). Given that 2 ≤ α ≤ 4, we have 0.707 ≤



α−1

1/α

2

≤ 1.107.

Thus, using the above result and Eq. (6), we obtain

δ(s0 , sm ) dmin

.

Thus, we get

where Etot (s0 , s1 ) = κ Eelec + κεδ (s0 , s1 ) (see Eq. (2)), Etot (sm ) = κ Eelec (see Eq. (1)), and Etot (si , si+1 ) = 2κ Eelec + κεδ α (si , si+1 ) (see Eq. (3)). Thus,

X

α−1

and hence the minimum energy consumption required in data forwarding between the source s0 and the sink sm is

mopt (s0 , sm ) ≈

Etot (si )

α

Etot (s0 , sm ) =



× [(α − 1)Eelec + 21/α (α − 1)1/α−1 ε dαmin ]. •

.

Etot (s0 , sm ) = Etot (s0 , s1 ) + Etot (sm ) +

150

Fig. 6. Energy function E (m) for α = 2.

and the corresponding optimum number of forwarders is mopt (s0 , sm ) =

100 m

Theorem 1 computes the minimum energy consumption and the corresponding optimum number of forwarders required for forwarding one data packet from the source s0 to the sink sm . Theorem 1 (Minimum Energy Consumption and Optimum Number of Forwarders). The lower bound on the energy consumption required to forward one sensed data packet from the source s0 to the sink sm along [s0 , sm ] is given by

725

(7) ∂ E (m∗ ) ∂ m∗

= 0. It is

> 0, for all α ≥ 2. That is, E (m) is ∂ E (m∗ )

strictly convex as shown in Figs. 6 and 7. Hence, m∗ in ∂ m∗ = 0 corresponds to the minimum of E (m). Thus, the optimum number

δ(s0 , sm )

(2Eelec + ε dαmin ). dmin This means that the energy consumption reaches its minimum when the distance between any pair of consecutive forwarders is dmin . The numerical values of all the constants are as follows: κ = 216, Eelec = 50 nJ/bit, εfs = 10 pJ/bit/m2 , and εmp = 0.0013 pJ/bit/m2 . Figs. 6 and 7 show the plot of E (m) (see Eq. (7)), where dmin = 70.71 m for α = 2 and dmin = 156.68 m for α = 3 (see Eq. (4)). According to Theorem 1, the optimum number of forwarders (see Eq. (6)) is mopt (s0 , sm ) ≈ 50 for α = 2 and mopt (s0 , sm ) ≈ 23 for α = 3 given that δ(s0 , sm ) = 3500 m. It is easy to check that 50 × 70.71 m ≈ 3500 m and 23 × 156.68 m ≈ 3500 m. Theorem 2 computes the minimum and maximum energy required by the WLDT protocol in data forwarding from the source s0 to the sink sm . Emin (s0 , sm ) ≈ κ

Theorem 2 (Energy Consumption). The minimum and maximum energy spent in forwarding one data packet from the source s0 to the sink sm are respectively given by min min Eexp (s0 , sm ) = (2κ Eelec + κε dαmin ) × (Nexp (s0 , sm ) + 1) max Eexp

α

(s0 , sm ) = (2κ Eelec + κε dmin ) × (

max Nexp

(s0 , sm ) + 1)

(8) (9)

726

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

α=3

0.035 0.03

E(m)

0.025 0.02 0.015 0.01 0.005 0

Fig. 8. Progress made towards sp and sm .

0

50

Now, we consider data forwarding paths that do not coincide with the shortest path [s0 , sm ]. Let P (r , θ ) be the progress made towards the sink at each forwarding action, where θ = 6 sp , s0 , sm is the maximum angle between segments [sp , s0 ] and [sp , sm ] (Fig. 8). By definition, P (r , θ ) = δ(s0 , sm ) − δ(sp , sm ),

150

100 m

Fig. 7. Energy function E (m) for α = 3.

– dmin : the minimum length of a Delaunay edge. – r: the distance between any pair of consecutive checkpoints (r is the transmission range l of themsensors). min – Nexp (s0 , sm )

δ(s0 ,sm )

− 1: the minimum number of dmin forwarders and checkpoints that l m liel on [s0 , msm ]. sm ) r max – Nexp (s0 , sm ) = × δ(Ps(0r,,θ) − 1: the maximum P (dmin ,θ0 ) =

number of forwarders and checkpoints that lie on the data forwarding path between p s0 and sm . – P (r , θ) = δ(s0 , sm ) − r 2 + δ 2 (s0 , sm ) − 2r δ(s0 , sm ) cos θ : the progress made towards q the sink sm . – P (dmin , θ0 ) = r −

d2min + r 2 − 2dmin r cos θ0 : the progress made

towards a checkpoint. – θ = 6 sp , s0 , sm stands for the maximum angle between segments [sp , s0 ] and [sp , sm ], where sp is a checkpoint of the source s0 (Fig. 8), and θ0 = 6 si , s0 , sp as shown in Fig. 8. Proof. The minimum energy consumption in data forwarding occurs when all forwarders and checkpoints between the source s0 and the sink sm lie on [s0 , sm ]. Because the checkpoints are located at the perimeter of the transmission range of the sensors, the distance between any pair of consecutive checkpoints is r. Thus, the minimum l number m of checkpoints between the source s0 δ(s0 ,sm )

and the sink sm is

− 1. Similarly, the minimum number

r

of between any pair of consecutive checkpoints is l forwarders m r dmin

where δ(sp , sm ) = r 2 + δ 2 (s0 , sm ) − 2r δ(s0 , sm ) cos θ and r is the distance between two consecutive checkpoints. Thus, the l m

p

where:

− 1, where the distance between any pair of consecutive

forwarders is dmin . Recall that our protocol prefers forwarding the sensed data via a series of forwarders linked by short Delaunay edges in LDT (si ). Thus, the minimum total number of forwarders and checkpoints is given by min Nexp (s0 , sm ) =



r dmin



 ×

δ(s0 , sm ) r



 −1=

δ(s0 , sm )



dmin

− 1.

Because Etot (s0 ) = κ Eelec + κε dαmin , Etot (sj ) = 2κ Eelec + κε dαmin (sj is a forwarder or a checkpoint) and Etot (sm ) = κ Eelec , the minimum energy consumption is min min Eexp (s0 , sm ) = [Etot (s0 ) + (2κ Eelec + κεdαmin )Nexp (s0 , sm )]

+ Etot (sm ). Thus, min min Eexp (s0 , sm ) = (2κ Eelec + κε dαmin ) × (Nexp (s0 , sm ) + 1).

maximum number of checkpoints is,

δ(s0 ,sm ) P(r ,θ )

− 1. Likewise, the

maximum number between any pair of consecutive l of forwarders m checkpoints is

r P (dmin ,θ0 )

− 1, where the distance between any

pair of consecutive forwarders is dmin . Therefore, the maximum number of forwarders and checkpoints between the source s0 and the sink sm is max Nexp

(s0 , sm ) =



 δ(s0 , sm ) × − 1. P (dmin , θ0 ) P (r , θ ) r





Thus, the maximum energy consumption for forwarding one sensed data packet from the source s0 to the sink sm is given by max max Eexp (s0 , sm ) = (2κ Eelec + κε dαmin ) × (Nexp (s0 , sm ) + 1).

•

min Fig. 9 shows the plot of the function Eexp (s0 , sm ) (see Eq. (8)) for different values of the distance, δ(s0 , sm ), between the source s0 and the sink sm . As can be seen, the minimum energy consumption grows proportionally to the distance separating the source and max the sink. Fig. 10 shows the plot of the function Eexp (s0 , sm ) (see Eq. (9)) for α = 2 and different values of r and θ while keeping δ(s0 , sm ) constant. We observe that when the angle θ increases, the length of the data forwarding path between the source and the sink increases. As a result, more energy consumption will be introduced. In other words, any deviation from the shortest path between the source and the sink will increase the number of forwarders and hence yields additional costs in terms of energy consumption. We also observe that small and large values of r yield more energy consumption. Because the distance between any pair of checkpoints is r, the number of checkpoints is determined by the value of r. Thus, there are an optimum number of checkpoints that need to be used to optimize the deviation from the shortest path max (s0 , sm ). According and hence leads to a minimum value of Eexp to Fig. 10, for θ = π /7, the optimum value or r is ropt = 400 m, implying that the optimum number of checkpoints is d3500/400e = 9.

6. Short-range versus long-range In this section, we compare the WLDT protocol with the BVGF [30] and GPSR [15] protocols. We show that WLDT outperforms BVGF and GPSR even when BVGF considers its optimal path in terms of network dilation or number of hops between the source s0 and the sink sm .

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

2.6

δ(s ,s )

0 m In fact, The BVGF protocol performs forwardings of the r data packet along [s0 , sm ], where two consecutive forwarders are separated by a distance equal to r. Likewise, the total energy consumption required by the WLDT protocol is

α=2

x 10-3

727

2.5 2.4

EWLDT (s0 , sm ) = (2κ Eelec + κε dαmin )

2.3

δ(s0 , sm ) dmin

.

δ(s ,s )

2.2

Indeed, the WLDT protocol requires d0 m forwardings of the min sensed data along [s0 , sm ]. The energy gain percentage of the WLDT protocol compared to the BVGF protocol is

2.1 2

EGP (s0 , sm ) = 1 −

1.9

1−1/α

EWLDT (s0 , sm )

3ε 1/α Eelec

=1−

EBVGF (s0 , sm )

2Eelec +

r

εr α

. •

1.8

Theorem 4 computes the energy gain percentage of WLDT compared to the GPSR using the non-direct data forwarding path between s0 and sm .

1.7 1.6 3500

4000

4500

5000

5500

Theorem 4 (Energy Gain Along Non-direct Path). The energy gain percentage of our protocol compared to the GPSR protocol along the non-shortest path between the source s0 and the sink sm is given by

δ(s0,sm) min Fig. 9. Eexp (s0 , sm ) for α = 2.

2.3

EGP (s0 , sm ) = 1 −

α=2

x 10-3

3Eelec 2Eelec + ε r α

where P (dmin , θ0 ) = r −

2.25

2.15 2.1

(11)

d2min + r 2 − 2dmin r cos θ0 is the progress

Proof. We assume that the distance between any pair of consecutive forwarders in GPSR and checkpoints in WLDT is equal to r. Thus, the total energy consumption of GPSR is given by

2.05 2

EGPSR (s0 , sm ) = (2κ Eelec + κε r α )

1.95

δ(s0 , sm ) P (r , θ ) δ(s ,s )

300

400

500 r

600

700

since the sensed data will be forwarded P (0r ,θm) times. On the other hand, the total energy consumption of WLDT is

800

EWLDT (s0 , sm ) = (2κ Eelec + κε dαmin )

max Fig. 10. Eexp (s0 , sm ) for α = 2.

r P (dmin , θ0 )

×

δ(s0 , sm ) P (r , θ )

where

6.1. Energy gain

P (r , θ ) = δ(s0 , sm ) −

The BVGF and GPSR protocols follow a greedy forwarding approach, where the data is forwarded to the sensor with the closest distance to the sink, thus enabling long-range data forwarding. The WLDT protocol, however, enables short-range transmission of the data between a source and its checkpoint or between any pair of consecutive checkpoints. Theorem 3 computes the energy gain percentage of our protocol compared to the BVGF protocol. Theorem 3 (Energy Gain Along Shortest Path). The energy gain percentage of our protocol compared to the BVGF protocol along the shortest path [s0 , sm ] between the source s0 and the sink sm is given by 1−1/α

EGP (s0 , sm ) = 1 −

r P (dmin , θ0 )

made towards the sink along any segment between any pair of consecutive forwarders (checkpoint), θ0 = 6 si+1 , si , sm is the angle between the segments [si , si+1 ] and [si , sm ], si and si+1 are two consecutive forwarders, and r is the radius of the transmission range of sensors.

2.2

1.9 200

q

×

3ε 1/α Eelec

r

(10)

2Eelec + ε r α

where r is the radius of the transmission range of the sensors. Proof. The total energy consumption required by BVGF [30] to forward a data packet from the source s0 to the sink sm is EBVGF (s0 , sm ) = (2κ Eelec + κε r α )

δ(s0 , sm ) r

.

p

r 2 + δ 2 (s0 , sm ) − 2r δ(s0 , sm ) cos θ

and P (dmin , θ0 ) = r −

q

d2min + r 2 − 2dmin r cos θ0 .

In fact, there are δ(s0 , sm )/P (r , θ ) checkpoints between s0 and sm and r /P (dmin , θ0 ) forwarders between any pair of consecutive checkpoints. Thus, EGP (s0 , sm ) = 1 −

= 1−

EWLDT (s0 , sm ) EGPSR (s0 , sm ) 3rEelec

(2Eelec + εr α )P (dmin , θ0 )

. •

Fig. 11 shows the impact of the radius of the transmission range of sensors, r, and the angle θ0 on EGP (s0 , sm ) (see Eq. (11)), assuming α = 2. We observe that the maximum energy gain percentage is obtained when every series of forwarders lie on the segment between their corresponding checkpoints, i.e., θ0 = 0. When θ0 = 0, the BVGF and GPSR protocols are similar in the sense that both of them forward the data to the closest sensors to the sink on the shortest path [s0 , sm ]. We find that the energy gain percentage of WLDT compared to BVGF and GPSR is about 55%. As θ0 increases,

728

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

α=2

0.6

forwarding one sensed data packet from the source s0 to the sink sm is given by

0.55

EGP (s0 , sm ) = 1 −

0.5

EGP(s0,sm)

0.45

(12)

where

0.4

P (dmin , φ) = δ(s0 , sm )

0.35

q − δ 2 (s0 , sm ) + d2min − 2dmin δ(s0 , sm ) cos(π /2 − φ)

0.3

P (r , φ) = δ(s0 , sm )

0.25

p − δ 2 (s0 , sm ) + r 2 − 2r δ(s0 , sm ) cos(π /2 − φ)

0.2

and φ is an infinitesimal angle in radian.

0.15 0.1 250

300

350 r

400

450

Fig. 11. Impact of r and θ0 on EGP (s0 , sm ).

Proof. In order to measure the energy gain introduced by checkpoints, let us consider a similar protocol to WLDT, which forwards the sensed data through short distances but does not use checkpoints. For the sake of clarity of the notation, let us call this protocol NoCP (No Checkpoint). The progress made towards the sink using the NoCP scheme is given by P (dmin , θ ) = δ(s0 , sm )

1

q − δ 2 (s0 , sm ) + d2min − 2dmin δ(s0 , sm ) cos θ

0.9 0.8

0.4

where θ = 6 si+1 , si , sm , si and si+1 are two consecutive forwarders, and dmin is the distance between any pair of consecutive forwarders. Therefore, the number of forwarders between the δ(s ,s ) source s0 and the sink sm is given by NF (NoCP ) = P (d 0 m,θ ) . Thus, the min total energy consumption required by the NoCP protocol for forwarding one sensed data packet from the source s0 to the sink sm is

0.3

ENoPF (s0 , sm ) = (2κ Eelec + κε dαmin ) × NF (NoCP ).

0.7 EGP(s0,sm)

rP (dmin , φ) dmin P (r , φ)

0.6 0.5

0.2 0.1 0 250

300

350 r

400

450

Fig. 12. Impact of α on EGP (s0 , sm ).

the length of the path between two consecutive checkpoints increases and hence more energy will be spent to forward the sensed data towards the next checkpoint. Notice that when r increases, GPSR would consume more energy as EGPSR (s0 , sm ) ∝ r, while WLDT transmits data over short Delaunay edges. Thus, EGP (s0 , sm ) increases with r as shown in Fig. 11. Thus, WLDT achieves significant energy savings for higher values of r compared to the GPSR protocol. Fig. 12 shows the impact of r and α on EGP (s0 , sm ), assuming θ0 = 0. As r and α increase, EGP (s0 , sm ) increases and tends towards 100% except for α = 3. When α = 3, the energy gain decreases for r ∈ [250 m, 350 m] until EGP (s0 , sm ) = 0 at r = 350 m and then increases. 6.2. Controlled short-range data forwarding As mentioned earlier, the presence of checkpoints helps build short data forwarding paths between the source s0 and the sink sm by reducing their deviation from the shortest path [s0 , sm ]. Theorem 5 states that the use of checkpoints yields short data forwarding paths and hence significant energy savings. Theorem 5 (Energy Gain Due to Checkpoints). The energy gain percentage of our protocol due to the presence of checkpoints in

On the other hand, our protocol requires the sensed data be forwarded through checkpoints. These checkpoints lie on or closely to the shortest path [s0 , sm ]. Thus, the progress made towards the sink using the WLDT protocol is given by P (r , φ) = δ(s0 , sm ) −

p

δ 2 (s0 , sm ) + r 2 − 2r δ(s0 , sm ) cos(φ)

where φ < θ and r is the distance between any pair of consecutive checkpoints. In order to compare the WLDT protocol to the NoCP protocol, the progress made towards any checkpoint is P (dmin , θ − φ). Thus, the total number of forwarders and checkpoints is N =

δ(s0 , sm ) r × . P (r , φ) P (dmin , θ − φ)

In fact, there are

δ(s0 ,sm ) P (r ,φ)

checkpoints between the source s0 and the

r

sink sm and P (d ,θ−φ) forwarders between any pair of consecutive min checkpoints. Therefore, the total energy consumption for forwarding one sensed data packet from the source s0 to the sink sm is given by EWLDT (s0 , sm ) = (2κ Eelec + κε dαmin ) × N . Thus, the energy gain percentage of WLDT compared to NoCP is given by EGP (s0 , sm ) = 1 −

= 1−

E (s0 , sm ) ENoCP (s0 , sm ) rP (dmin , θ ) P (r , φ)P (dmin , θ − φ)

. •

Fig. 13 shows the impact of r and δ(s0 , sm ) on EGP (s0 , sm ) (see Eq. (12)), where θ = π /3 and φ = π /7. We observe that the minimum energy gain percentage using checkpoints is about 28% for r = 250 m and 31% for r = 650 m. This result shows the

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

0.32

α=2

0.315

EGP(s0,sm)

0.31 0.305 0.3 0.295 0.29 0.285 0.28 250 300 350 400 450 500 550 600 650 r Fig. 13. Impact of r on EGP (s0 , sm ).

0.3047

α=2

0.3046

729

from which it has received the sensed data packet. In other words, as soon as the checkpoint sp forwards the sensed data towards the sink, it replies back with a message saying that the data has been successfully forwarded to its next forwarder. Therefore, when the forwarder sk does not hear from its checkpoint sp before a certain time-out, it will understand that sp went down. In this case, the forwarder sk will have to act like a checkpoint. Thus, the sensor sk will run phase 1 of the WLDT protocol to identify a new checkpoint and forward the sensed data to it through a series of forwarders. Case 2. A checkpoint goes down before having the sensed data forwarded to it: If a forwarder, say sk , learns that its checkpoint sp has disappeared, it will ignore it and find another checkpoint. Then, it forwards the sensed data towards this new checkpoint through a series of forwarders. 2. What if a forwarder fails? If a forwarder disappears before forwarding the sensed data to its next forwarder or checkpoint, the sensed data will be lost. To solve this problem, an acknowledgment with a timeout could be used to check whether a forwarder has successfully forwarded the sensed data towards the sink. Therefore, any forwarder has to send back an acknowledgment message to inform the previous forwarder (or checkpoint) that the sensed data packet has been sent out to the next forwarder. Otherwise, the previous forwarder will have to select another sensor as a forwarder so the sink can receive the sensed data.

EGP(s0,sm)

0.3046 0.3045 0.3045 0.3044 0.3044 0.3043 3500 4000 4500 5000 5500 6000 6500 7000 7500 δ(s0,sm) Fig. 14. Impact of δ(s0 , sm ) on EGP (s0 , sm ).

benefits of using checkpoints, which shorten the data forwarding paths between sources and the sink and hence yield significant energy savings. This will extend the network lifetime. Fig. 14 shows the impact of the distance between the sources and the sink on the energy gain percentage, which increases slowly with δ(s0 , sm ) and reaches about 30%. 7. Disscussion Scalability is another important issue. Our protocol works well with densely deployed sensor networks, so a short-range data forwarding scheme can be applied. By increasing the number of sensors, it would be always possible to forward data through short Delaunay edges. Therefore, dense networks are in favor of our WLDT protocol working strategy, and hence our protocol scales well with large-scale WSNs. In this section, we briefly discuss sensor reliability issues, which are left for future work. When the sensors fail, WLDT may also fail to forward the data to the sink. 1. What would WLDT do when the checkpoints fail? We need to consider the following two cases: Case 1. A checkpoint goes down before forwarding the sensed data to its next forwarder: Any checkpoint sp is required to send back an acknowledgment message to its previous forwarder sk

8. Conclusion 8.1. Summary In this paper, we have proposed a data forwarding protocol for WSNs, which helps sensors save their energy by forwarding the sensed data towards the sink over short distances. In addition, preference is always given to the sensors with high remaining energy and whose locations lie on or closely to the shortest path between the source and the sink. The objective of our protocol is to prolong the network lifetime by controlling sensed data transmission. Specifically, the proposed protocol builds a data forwarding path between the source and the sink as a sequence of sub-paths, each of which is composed of a series of forwarders between two endpoints, called checkpoints. These checkpoints are selected based on their remaining energy and closeness to the sink based on the geometric properties of Delaunay triangulation. The data should be forwarded to the sink through these checkpoints. To demonstrate the effectiveness of the WLDT protocol, we have presented theoretical results supported by extensive numerical results. We have computed the lower bound on the energy cost of forwarding one sensed data packet from a source to the sink as well as the corresponding optimum number of forwarders between them. We have proved that the proposed protocol yields significant energy savings. We have also compared WLDT with BVGF and GPSR, which enable data forwarding through long distances, and have found that WLDT achieves an energy gain percentage in the order of 55% for the free space model and close to 100% for the multi-path model. We have also proved that the checkpoints help shorten data forwarding paths between the sources and the sink. We have found that WLDT yields an energy gain percentage in the order of 28% for r = 250 m and 31% for r = 650 m. These significant energy savings will definitely increase the network lifetime. There is an ongoing debate on short-range versus long-range data forwarding in multi-hop wireless sensor networks. We believe that the primary concern of WSNs is energy saving to prolong the network lifetime. The WLDT protocol supports, indeed, the short-range strategy to achieve this goal.

730

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731

8.2. Future work While our main concern is to implement the WLDT protocol using a real sensor testbed, our future work focuses on extending the WLDT protocol to promote its use in real applications. We consider the following relaxations and extensions: 1. The communication model that we have used for WLDT assumes a unit disk model. However, it has been found that the communication range of radios is highly probabilistic and irregular [34,35]. We plan to relax WLDT by considering sensors with irregular transmission ranges. 2. The WLDT protocol is designed for homogeneous sensors, i.e., sensors with the same communication capability and initial battery power. It has been, however, proved that a sensor heterogeneity improves network reliability and extend its lifetime [28,31]. We intend to relax WLDT by considering heterogeneous sensors in terms of their initial levels of energy and transmission ranges. 3. Most of the existing geographic forwarding protocols assume that the radios of all sensors are always on during forwarding. In real-world scenarios, however, sensors switch between on and off states to save energy. Thus, it is important to duty-cycle sensors [23] so that they deplete their energy uniformly and slowly. Unfortunately, duty-cycling may create a problem when forwarding a message to the next hop while it is asleep. We plan to extend WLDT to handle highly dynamic networks that experience time-varying connectivity due to sensor duty-cycling. 4. In static WSNs, sensors located around the sink suffer from severe battery power depletion problems. Indeed, these sensors act as relays on behalf of the sensed data transmitted to the sink by all other sensors. As a consequence, such heavily loaded sensors deplete their battery power more quickly implying no data can reach the sink anymore, thus disconnecting the network. This problem is known as the energy sink-hole problem [20,18, 24,25,29]. We plan to extend WLDT to WSNs with a mobile sink. Indeed, sink mobility helps neighbors of the sink change over time, thus avoiding the energy sink-hole problem. 5. Finding an energy-efficient solution to the problem of reliability and fault tolerance of the sensors, and, in particular, the checkpoints.

Acknowledgments The authors gratefully acknowledge the insightful comments of the anonymous reviewers which helped improve the quality and presentation of the paper significantly. The work of H.M. Ammari is partially supported by the US National Science Foundation (NSF) grant 0917089 and a New Faculty Start-Up Research Grant from Hofstra College of Liberal Arts and Sciences Dean’s Office. The work of S.K. Das is partially supported by the AFOSR grant A9550-08-10260 and NSF grants IIS-0326505 and CNS-0721951. His work is also supported by (while serving at) the NSF. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. References [1] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, E. Cayirci, Wireless sensor networks: A survey, Computer Networks 38 (March) (2002) 393–422. [2] H.M. Ammari, S.K. Das, Data dissemination to mobile sinks in wireless sensor networks: An information theoretic approach, in: Proc. IEEE MASS, 2005.

[3] F. Aurenhammer, Voronoi diagrams — A survey of a fundamental data structure, ACM Computing Surveys 23 (3) (1991). [4] S. Biswas, R. Morris, ExOR: Opportunistic multi-hop routing for wireless networks, in: Proc. ACM SIGCOMM 2005 Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communication, 2005, pp. 133–143. [5] P. Bose, P. Morin, Online routing in triangulations, SIAM Journal on Computing 33 (4) (2004) 937–951. [6] P. Bose, P. Morin, I. Stojmenovic, J. Urrutia, Routing with guaranteed delivery in ad hoc wireless networks, ACM/Kluwer Wireless Networks 7 (6) (2001) 609–616. [7] A. Boukerche, I. Chatzigiannakis, S. Nikoletseas, A new energy efficient and fault-tolerant protocol for data propagation in smart dust networks using varying transmission range, Computer Communications 4 (29) (2006) 477–489. [8] A. Boukerche, I. Chatzigiannakis, S. Nikoletseas, Power-efficient data propagation protocols for wireless sensor networks, Simulation 81 (6) (2005) 399–411. [9] A. Boukerche, X. Cheng, J. Linus, Energy-aware data-centric routing in microsensor networks, in: Proc. ACM MSWiM, 2003, pp. 42–29. [10] N. Bulusu, J. Heidemann, D. Estrin, GPS-less low cost outdoor localization for very small devices, IEEE Personal Communications Magazine 7 (5) (2000) 28–34. [11] W. Choi, S. Das, Design and performance analysis of a proxy-based indirect routing scheme in ad hoc wireless networks, Mobile Networks and Applications 8 (5) (2003) 499–515. [12] M. Haenggi, D. Puccinielli, Routing in ad hoc networks: A case for long hops, IEEE Personal Communication Magazine 43 (10) (2005) 93–101. [13] W. Heinzelman, A. Chandrakasan, H. Balakrishnan, An application-specific protocol architecture for wireless microsensor networks, IEEE Transactions on Wireless Communications 1 (4) (2002) 660–670. [14] C. Intanagonwiwat, R. Govindan, D. Estrin, Directed diffusion: A scalable and robust communication paradigm for sensor networks, in: Proc. ACM/IEEE MobiCom, 2000, pp. 56–67. [15] B. Karp, H. Kung, GPSR: Greedy perimeter stateless routing for wireless networks, in: Proc. ACM/IEEE MobiCom, 2000, pp. 243–254. [16] H. Kim, T. Abdelzaher, W. Kwon, Minimum-energy asynchronous dissemination to mobile sinks in wireless sensor networks, in: Proc. ACM SenSys, 2003, pp. 193–204. [17] E. Kranakis, H. Singh, J. Urrutia, Compass Routing on Geometric Networks, in: Proc. Canadian Conference on Computational Geometry, CCCG, 1999, pp. 51–54. [18] J. Lian, K. Naik, G. Agnew, Data capacity improvement of wireless sensor networks using non-uniform sensor distribution, International Journal of Distributed Sensor Networks 2 (2) (2006) 121–145. [19] X.-Yang Li, G. Calinescu, P.-Jun Wan, Y. Wang, Localized Delaunay triangulation with application in ad hoc wireless networks, IEEE Transactions on Parallel and Distributed Systems 14 (10) (2003) 1035–1047. [20] J. Li, P. Mohapatra, An analytical model for the energy hole problem in manyto-one sensor networks, in: Proc. IEEE VTC, 2005, pp. 2721–2725. [21] S. Lindsey, C. Raghavendra, K. Sivalingam, Data gathering algorithms in sensor networks using energy metrics, IEEE Transactions on Parallel and Distributed Systems 13 (9) (2002) 924–935. [22] J. Luo, J.-P. Hubaux, Joint mobility and routing for lifetime elongation in wireless sensor networks, in: Proc. IEEE Infocom, 2005, pp. 1735–1746. [23] S. Nath, P.B. Gibbons, Communicating via fireflies: Geographic routing on dutycycled sensors, in: Proc. IPSN, 2007, pp. 440–449. [24] S. Olariu, I. Stojmenovic, Data centric protocols for wireless sensor networks, in: Handbook of Sensor Networks: Algorithms and Architectures, 2005, pp. 417–456. [25] S. Olariu, I. Stojmenovic, Design guidelines for maximizing lifetime and avoiding energy holes in sensor networks with. uniform distribution and uniform reporting, in: Proc. IEEE Infocom, 2006. [26] I. Stojmenovic, X. Lin, Loop-free hybrid single-path/flooding routing algorithms with guaranteed delivery for wireless networks, IEEE Transactions on Parallel and Distributed Systems 12 (10) (2001) 1023–1032. [27] G. Wang, G. Cao, T. La Porta, Proxy-based sensor deployment for mobile sensor networks, in: Proc. IEEE MASS, 2004, pp. 493–502. [28] W. Wang, V. Srinivasan, K.-C. Chua, Using mobile relays to prolong the lifetime of wireless sensor networks, in: Proc. ACM/IEEE MobiCom, 2005, pp. 270–283. [29] X. Wu, G. Chen, S.K. Das, On the energy hole problem of nonuniform node distribution in wireless sensor networks, in: Proc. IEEE MASS, 2006, pp. 180–187. [30] G. Xing, C. Lu, R. Pless, Q. Huang, On greedy geographic routing algorithms in sensing-covered networks, in: Proc. ACM MobiHoc, 2004, pp. 31–42. [31] M. Yarvis, N. Kushalnagar, H. Singh, A. Rangarajan, Y. Liu, S. Singh, Exploiting heterogeneity in sensor networks, in: Proc. IEEE Infocom, 2005, pp. 878–890. [32] F. Ye, H. Luo, J. Cheng, S. Lu, L. Zhang, A two-tier data dissemination model for large-scale wireless sensor networks, in: Proc. ACM/IEEE MobiCom, 2002, pp. 148–159. [33] W. Zhang, G. Cao, T. La Porta, Dynamic proxy tree-based data dissemination schemes for wireless sensor networks, in: Proc. IEEE MASS, 2004, pp. 21–30. [34] J. Zhao, R. Govindan, Understanding packet delivery performance in dense wireless sensor networks, in: Proc. ACM SenSys, 2003, pp. 1–13. [35] G. Zhou, T. He, S. Krishnamurthy, J. Stankovic, Impact of radio irregularity on wireless sensor networks, in: Proc. MobiSys, 2004, pp. 125–138. [36] M. Zorzi, R. Rao, Geographic Random Forwarding (GeRaF) for ad hoc and sensor networks: Multihop performance, IEEE Transactions on Mobile Computing 2 (4) (2003) 337–348.

H.M. Ammari, S.K. Das / J. Parallel Distrib. Comput. 70 (2010) 719–731 Habib M. Ammari is an Assistant Professor of Computer Science in the Department of Computer Science at Hofstra University and is the founding director of the Wireless Sensor and Mobile Ad-hoc Networks (WiSeMAN) Research Laboratory at Hofstra University. He received the Ph.D. degree in Computer Science and Engineering from The University of Texas at Arlington (UTA) in May 2008 and the M.S. degree in Computer Science from Southern Methodist University in December 2004. He also received the Doctorat de Specialite and the Diploma of Engineering degrees in Computer Science from the Faculty of Sciences of Tunis, Tunisia, in 1996 and 1992, respectively. He was on the faculty of the Superior School of Communications of Tunis (Sup’Com Tunis), Tunisia, from 1992 to 2005 (engineer of computer science, 1992–1993; lecturer of computer science, 1993–1997; assistant professor of computer science, 1997–2005; received tenure in 1999). His main research interests lie in the areas of wireless sensor and mobile ad hoc networking, and multihop mobile wireless Internet architectures and protocols. In particular, he is interested in coverage, connectivity, energy-efficient data routing and information dissemination, fault tolerance, and security in wireless sensor networks, and the interconnection between wireless sensor networks, mobile ad hoc networks, and the global IP Internet. He received the US National Science Foundation (NSF) Research Grant Award and the Faculty Research and Development Grant Award from Hofstra College of Liberal Arts and Sciences, both in 2009. He published his first book ‘‘Challenges and Opportunities of Connected kCovered Wireless Sensor Networks: From Sensor Deployment to Data Gathering’’ (Springer, 2009). He received the John Steven Schuchman Award for 2006–2007 Outstanding Research by a Ph.D. Student and the Nortel Outstanding CSE Doctoral Dissertation Award, both from UTA in 2008 and 2009, respectively. He was a recipient of the TPC Best Paper Award from EWSN’08 and the Best Contribution Paper Award from IEEE PerCom’08—Google Ph.D. forum. Also, he was an ACM Student Research Competition (ACM SRC) nominee at ACM MobiCom’05. He was selected for inclusion in the 2006 edition of Who’s Who in America and the 2008–2009 Honors Edition of Madison Who’s Who Among Executives and Professionals. He serves as an Associate Editor of the International Journal of Communication Systems and the International Journal of Network Protocols and Algorithms. He is on the Editorial board of the International Journal of Mobile Communications and the International Journal on Advances in Networks and Services. Also, he is on the Editorial Review Board of the International Journal of Distributed Systems and Technologies. He is the founder and co-editor of the Sciences Undegraduate and Graduate Research Experiences (Sciences U-AGREE) Journal, which is published at Hofstra University. He served as Program Co-Chair/Workshop Co-Chair of WiMAN’10, IWCMC’10, IQ2S’09, and WiMAN’09. He has served as a reviewer for several international journals, including IEEE Transactions on Mobile Computing, IEEE Transactions on Parallel and Distributed Systems, ACM Transactions on Sensor Networks, IEEE Transactions on Vehicular Technology, IEEE Transactions on Wireless Communications, Mobile and Network Applications, Wireless Networks, Ad Hoc Networks,

731

Computer Networks, Ad Hoc & Sensor Wireless Networks, International Journal of Sensor Networks, Information Processing Letters, Computer Communications, Journal of Parallel and Distributed Computing, Information Sciences, International Journal of Computer and Applications, and Data and Knowledge Engineering Journal, and as a Technical Program Committee member of numerous IEEE and ACM conferences and symposia, including IEEE Infocom, IEEE ICDCS, IEEE PerCom, SSS, IEEE MASS, IEEE MSN, IEEE LCN, and EWSN.

Sajal K. Das is a University Distinguished Scholar Professor of Computer Science and Engineering and the Founding Director of the Center for Research in Wireless Mobility and Networking (CReWMaN) at the University of Texas at Arlington (UTA). He is currently a Program Director at the US National Science Foundation (NSF) in the Division of Computer Networks and Systems. He is also an E.T.S. Walton Professor of Science Foundation of Ireland; a Visiting Professor at the Indian Institute of Technology (IIT) at Kanpur and IIT Guwahati; an Honorary Professor of Fudan University in Shanghai and International Advisory Professor of Beijing Jiaotong University, China; and a Visiting Scientist at the Institute of Infocomm Research (I2R), Singapore. His current research interests include wireless and sensor networks, mobile and pervasive computing, smart environments and smart heath care, pervasive security, resource and mobility management in wireless networks, mobile grid computing, biological networking, applied graph theory and game theory. He has published over 400 papers and over 35 invited book chapters in these areas. He holds five US patents in wireless networks and mobile Internet, and coauthored the books ‘‘Smart Environments: Technology, Protocols, and Applications’’ (Wiley, 2005) and ’’Mobile Agents in Distributed Computing and Networking (Wiley, 2009). Dr. Das is a recipient of the IEEE Computer Society Technical Achievement Award (2009), IEEE Engineer of the Year Award (2007), and several Best Paper Awards in various conferences such as EWSN’08, IEEE PerCom’06, and ACM MobiCom’99. At UTA, he is a recipient of the Lockheed Martin Teaching Excellence Award (2009), UTA Academy of Distinguished Scholars Award (2006), University Award for Distinguished Record of Research (2005), College of Engineering Research Excellence Award (2003), and Outstanding Faculty Research Award in Computer Science (2001 and 2003). He is frequently invited as a keynote speaker at international conferences and symposia. Dr. Das serves as the Founding Editor-in-Chief of Elsevier’s Pervasive and Mobile Computing (PMC) Journal, and also as an Associate Editor of IEEE Transactions on Mobile Computing, ACM/Springer Wireless Networks, IEEE Transactions on Parallel and Distributed Systems, and Journal of Peer-to-Peer Networking. He is the founder of IEEE WoWMoM symposium and co-founder of IEEE PerCom conference. He has served as General and Technical Program Chair as well as TPC member of numerous IEEE and ACM conferences. He is a senior member of the IEEE.