Arab J Sci Eng (2014) 39:1775–1784 DOI 10.1007/s13369-013-0811-y

RESEARCH ARTICLE - COMPUTER ENGINEERING AND COMPUTER SCIENCE

Sink Mobility Model for Wireless Sensor Networks Anas Abu Taleb · Tareq A. Alhmiedat · Reem Abu Taleb · Osama Al-Haj Hassan

Received: 14 June 2012 / Accepted: 14 July 2013 / Published online: 7 September 2013 © King Fahd University of Petroleum and Minerals 2013

Abstract Using mobile sinks to collect data in wireless sensor networks and investigating the effect of mobility models on the network performance has been an interesting area of research. In this paper, a De Bruijn graph-based network topology is adopted. Subsequently, we propose a new sink mobility model that can be obtained or calculated based on the properties of De Bruijn graph. Moreover, De Bruijn graph routing algorithm has been modified in this paper to take the existence of a mobile sink into consideration. As a result, the proposed model and routing algorithm combine the use of single hop and multi hop communication to collect data from static sensor nodes. Finally, the performance of the proposed mobility model and routing algorithm has been studied, in terms of end-to-end delay and data success rate, through simulation with different speeds of the mobile sink and different network sizes. Keywords Wireless sensor network · De Bruijn graph · Mobile sink

A. A. Taleb (B) · O. A.-H. Hassan Department of Computer Science, Isra University, P. O. Box 22, 33, Amman 11622, Jordan e-mail: [email protected] O. A.-H. Hassan e-mail: [email protected] T. A. Alhmiedat Department of Computer Science, Zarqa University, P.O. Box 132222, Amman 13132, Jordan e-mail: [email protected] R. A. Taleb Department of Management Information Systems, Al Balqa’a Applied University, Al Salt 19117, Jordan e-mail: [email protected]

1 Introduction The advances in wireless communication and electronics made it possible to develop low-cost sensor nodes, which can be deployed easily in specific areas to accomplish a specific mission by forming a wireless sensor network (WSN). As a result, WSN has become a vital research area due to their wide ranging applications including civilian, industrial, agricultural, and military applications. For some applications such as military and industrial, sensor networks are expected to operate in inhospitable environment. Therefore, sensor nodes are expected to operate for periods ranging from days to years without any human intervention [1–6]. Because sensor nodes are battery powered, limited battery power and lifetime are main challenge for these nodes. As a result, reducing the energy consumption of sensor nodes has been the subject of many research studies to prolong the life time of sensor networks [7–11]. Moreover, sensor nodes consist of three subsystems, namely computing subsystem, sensing subsystem, and communication subsystem. According to Patel et al. [12] the energy consumed by the communication subsystem is several magnitudes higher than that

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consumed by the computation subsystem and is dependent on the transmission distance and the attenuation exponent. Therefore, to reduce the transmission distance, multi-hop routing was introduced to deliver the sensed data to the base station, because the transmission distance for each node is smaller than that needed in single-hop. On the other hand, higher delay is introduced by multi-hop routing when compared with single-hop. Hence the success rate of the network will be affected. As a result, in this paper we introduce the use of a mobile sink on a De Bruijn graph-based sensor network. In other words, sensor nodes are deployed to form De Bruijn graphbased topology. After that, the mobile sink will move along specific paths that can be derived from De Bruijn graph, to collect the sensed data from the sensor nodes. Thus, static sensor nodes that fall on the movement path of the mobile sink will use single-hop routing to communicate with the mobile sink. On the other hand, sensor nodes that do not fall on the movement path of the mobile sink will use multi-hop routing to communicate with the mobile sink. Consequently, the sensor nodes in the network are divided into two groups; the first group will communicate with the mobile sink using single-hop, while multi-hop routing will be used by the second group. The rest of this paper is organized as follows: in Sect. 2 the related work is discusses. Furthermore, the basic definitions and notations are presented in Sect. 3. In Sect. 4 the mobility model and the routing algorithm are discussed. Furthermore, simulation environment along with the simulation scenarios and results are presented in Sect. 5. Finally, the paper is concluded in Sect. 6.

2 Related Work Several researches have approached the problem of deploying mobile nodes or sinks in WSNs. As a result, several mobility models or patterns have been proposed. According to Vasanthi et al. [13], mobility models can be divided into two groups, namely dependent (group) and independent (individual) models. As the name implies, in dependent mobility models, nodes move in a group fashion. In other words, every mobile node moves based on the movement or the position of other mobile nodes, while in the independent mobility models every mobile node moves without out taking the mobility or position of other mobile nodes into consideration. Since we propose the use of a single mobile node, we will review and focus on independent mobility models because this category is closely related to the work proposed in this paper. The Random Way Point model, which is a very simple mobility model, has been presented in [14]. This mobility model is based on dividing the motion of the mobile node

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into pause periods and motion period. In the pause period, the mobile node will stay in its current position for a specific period of time. However, in the motion period, the mobile node will choose a random direction and will start moving to the new direction with a random speed. After arriving at the new position, the mobile node enters the pause period and stays in that position for the same period of time used in the previous position. Although this model is simple, it suffers from poor choice of velocity distribution and uniform distribution [15]. The research proposed in [16] introduced the concept of data mules that use Random Mobility modes. According to Shah et al. [16], the sensor network is traversed randomly by the data mules. When a data mule enters the communication range of a sensor node, it collects data from that node. On the other hand, the research proposed in [17] introduced a Predictable Mobility model where sensor nodes know the path that will be used by the mobile sink. As a result, to save energy, a sensor node enters sleep mode until the predicted time for data transfer. After that, the sensor node goes to alive mode and starts sending its data to the mobile sink. Instead of moving mobile nodes randomly, the Controlled Mobility Model was proposed in [18] where the mobile node visits sensor nodes based on a predefined schedule that is built based on the sampling rate of sensors and event occurrence rate. Additionally, when building such schedule, the time between two consecutive visits for the same sensor node must be taken into account. In other words, the time between two consecutive visits must not be too long so that sensor nodes will not suffer from buffer overflow. A decentralized mobility model for data collection was proposed in [19]. The purpose of the research proposed in [19] was to collect data from sensor nodes through coordination of decentralized mobile nodes. Therefore, two mobility models were proposed to manage the movement of mobile nodes. In addition, bidding strategies were used to schedule data collection requests and to determine the winner. Moreover, the research proposed in [20] introduced an algorithm to calculate mobility patterns for mobile nodes using cluster formation and artificial potential functions. In order to calculate the mobility models, the artificial potential function uses two schemes, namely potential field and particle based. A sensor network with mobile agents (SENMA) architecture was proposed in [21] where the use of stationary sensor nodes is combined with the use of mobile and more resource rich nodes. The main idea of the proposed architecture is to shift the computation burden from the stationary sensor nodes to the mobile nodes because the mobile nodes have more processing power than the stationary sensor nodes. Furthermore, it is assumed that the mobile nodes might be manned or unmanned vehicles that might collect data by moving on the ground or aerially. Moreover, these mobile agents are not present all the time in the network; in other words, they

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will be operational when there is a need to collect data from stationary sensor nodes. In [22] a random direction mobility model is proposed were a mobile node keeps moving in one direction until it reaches the boundaries of the area covered by the sensor network. Upon reaching the boundary, the node may stop for a period of time; after that, a new direction is chosen according to specified parameters. Additionally, the period of time according to which the mobile node will travel in the chosen direction is specified. Additionally, a coverageoriented mobility model where mobile nodes move towards the area with the lowest coverage within each mobile node neighborhood was proposed in [23]. In contrast with the [21], the research in [23] assumes that all nodes in the network are mobile. Thus the mobility of all nodes in the network might result in having areas of low or even no coverage of sensor nodes in the deployment area. In this section, we have reviewed the mobility models proposed in the area of sensor networks. It can be observed that the reviewed models can be divided into two groups: random mobility models [14,15,21,22] and predicted or calculated mobility models [17–20,23]. Random mobility models have the advantage of easily selecting the next position of the mobile sink. However, they suffer from unfairness in the frequency according to which sensor nodes are visited. In other words, some nodes might get visited frequently by the mobile node while others might not be visited at all. On the other hand, predicted or calculated mobility models can guarantee a certain level of fairness in visiting static sensor nodes. Additionally, since static sensor nodes can predict when they will be visited by the mobile sink, they can go to sleep or power saving mode to conserve their energy. Nevertheless, static sensor nodes might suffer from long delays or wait time until they get visited by the mobile sink. Figure 1 shows a classification of mobility models according to the above discussion.

The mobility model proposed in this paper can be classified under predicted or calculated mobile models category. The research proposed in this paper differs from those discussed above in several aspects. First, based on our work in [24], we assume that the stationary sensor nodes communicate with each other to form a De Bruijn graph based topology. Second, after studying the performance of a De Bruijn base sensor network consisting of stationary nodes only, we propose to use mobile sink that moves according a mobility model that is derived from the properties of De Bruijn graph. Finally, the performance of networks with different sizes is studied when using a single mobile node moving with different speeds according to the derived mobility model.

3 Preliminaries The network topology has a great impact on the network performance. There are well-defined relationships between the topology, the packet delay, and the routing algorithm. For instance, the packet delay is directly proportional to the distance between the source and destination nodes, i.e., it depends on the number of hops required for the packet to reach its destination. The motivation behind this work is to investigate a new mobility model which could reduce the end-to-end delay and increase the success rate. Additionally, we propose a modification to the routing algorithm presented in [25]. Finally, we study the effect of the mobility model and the routing algorithm on the network performance [25]. The work proposed in this paper is based on De Bruijn graph [26]. This graph has interesting properties that make it important to investigate its use in WSNs. The degree of this graph is bounded, which means the degree of the network remains fixed even when the network size increases. In

Fig. 1 Mobility models classification Mobility Models

Group Mobility

Individual Mobility

Calculated/

Random Mobility

Predicted Mobility

Ref [17]

Ref [18]

Ref [19]

Ref [20]

Ref [23]

Ref [14]

Ref [15]

Ref [21]

Ref [22]

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addition, this graph has interesting properties such as small diameter, high connectivity, and easy routing. Furthermore, De Bruijn graph contains some important networks such as ring. Regarding fault tolerance and extensibility, these graphs maintain a good level of fault tolerance and selfdiagnosability. For instance, in the presence of a single fault in the network, it takes four additional hops to detour around the faulty node and the control information needed to do so can be integrated locally between the faulty node’s neighbors. Also, De Bruijn graph is extensible in two methods that are described in [26]. The De Bruijn graph denoted as DB(r, k) has N = r k nodes with diameter k and degree 2r . This corresponds to the state graph of a shift register of length k using r -ary digits. A shift register changes a state by shifting in a digit in the state number in one side and then shifting out one digit from the other side. If we represent a node by I = (i k−1 i k−2 , . . . , i 1 i 0 ),

(1)

where i, j ∈ 0, 1, . . . , (r − 1), 0 ≤ j ≤ (k − 1); then the node’s neighbors are represented by i k−2 i k−3 , . . . i 0 p and pi k−1 i k−2 , . . . , i 1 , where p = 0, 1, . . . , (r − 1).

(2)

The DB(2, k), which is called binary De Bruijn graph, can be obtained as follows: if we represent a node I by a k-bit binary number, say, I = Ik−1 Ik−2 , . . . , I1 I0 , then its neighbors can be presented as Ik−2 , . . . , I1 I0 0, Ik−2 , . . . , I1 I0 1, 0Ik−1 Ik−2 , . . . , I1 , and 1Ik−1 Ik−2 , . . . , I0 . Figure 2 shows the DB(2, 3) binary De Bruijn graph. Based on the properties of De Bruijn graph, two paths can be obtained to send or route a message from source to destination. For example, let the source address be x = xk−1 xk−2 , . . . , x1 x0 and the destination address be d = dk−1 dk−2 , . . . , d1 d0 . There are two paths between the source 001

000

011

010

100

101

111

110

Fig. 2 DB(2, 3) binary De Bruijn graph Fig. 3 Path 1 and path 2 calculation

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and the destination. The first path, path 1, is obtained by shifting the source address to the left and then appending the destination address bits to it. The second path, path 2, is generated by shifting the source address to the right and appending the destination address bits to it, see Fig. 3. The work presented in this paper is motivated by the properties of De Bruijn graph and the way according to which the two paths are obtained. However, instead of routing messages according to these paths, we make use of them to move the mobile sink through the network to collect data from stationary sensor nodes. Since the network topology is based on De Bruijn graph, the proposed work in this paper is suitable for indoor applications and areas where human intervention is possible. Hence, sensor nodes can be distributed in the area of interest according to the required topology.

4 Mobility Model and Routing Algorithm 4.1 Mobility Model As mentioned in Sect. 3, two paths can be obtained to route packets from source to destination. However, instead of routing packets using these paths, we make use of these paths to move the mobile sink. As a result, the mobile sink will move between the static sensor nodes based on these paths to collect data. Before explaining the mobility model proposed in this paper, it is essential to note that the static sensor nodes in the network are numbered from 0 to n − 1. For example, if we have 8-node De Bruijn-based sensor network, the sensor nodes are numbered from 0 to 7. In order to make use of the paths (path 1 and path 2), the mobile sink will start at node 0 and is required to move to node n−1 based on one of the existing paths. According to the path in use, i.e. path 1 or path 2, the mobile sink periodically calculates its next hop or position that it needs to move to, based on the operations illustrated in Fig. 3. In other words, the movement of the mobile sink is divided into rounds based on the path in use. In the first round the mobile sink moves from node 0 to node n − 1 based on path 1. After reaching node n − 1, the mobile sink moves from node n − 1 to node 0 based on path 1 too. After reaching node 0 again, the first round is over. Consequently, the mobile sink starts moving

Path 1:

Path 2:

x = x k −1 x k − 2 , ..., x1 x0 ( source )

x = xk −1 xk − 2 , ..., x1 x0 ( source)

x k − 2 x k − 3 , ..., x1 x 0 d k −1

d 0 xk −1 xk − 2 , ..., x1

xk −3 xk −4 , ..., x1 x0 d k −1d k −2

d1d 0 xk −1 xk − 2 , ..., x2

Arab J Sci Eng (2014) 39:1775–1784 Fig. 4 a First half of round 1, b second half of round 1

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a

b

1 0

Fig. 5 a First half of round 2, b second half of round 2

0

3 7

a

7 4

6

1

3

b

0

7 4

from node 0 to node n − 1 using path 2. After reaching node n − 1, the mobile sink starts going back to node 0 based on path 2. As a result, the movement of the mobile nodes is divided into rounds where in each round, a different path is used by the mobile sink. To elaborate, consider the following example. Suppose we have 8-node De Bruijn-based sensor network, shown in Fig. 2, where stationary nodes are numbered from 0 to 7. The mobile sink is at node 0 and needs to move to node 7 (node n − 1). As a result, based on path 1 the mobile sink calculates its next hop or position which is equal to node 1. Next, the mobile sink moves near to node 1 and stays there for a period of time. Then, the next hop or position is calculated based on path 1 too and the mobile sink discovers that it needs to move to node 3. After visiting node 3, the next hop or position is calculated according to path 1. Consequently, the mobile sink starts moving to node 7 which represents node n − 1. When the mobile sink reaches node 7 the first half of round 1 is finished, see Fig. 4a. Later the mobile sink will try to move from node 7 to node 0 based on path 1. In other words, being at node 7, the mobile sink calculates the next hop which is node 6 based on path 1. After visiting node 6, the new position is calculated which is node 4. Subsequent to visiting node 4 the next position is calculated based on path 1. Hence the next node to be visited is node 0. After reaching node 0, which was the starting node of the first half of round 1, the second half of round 1 is over, see Fig. 4b, and the mobile sink assumes that round 1 has finished. It is worth mentioning that after calculating the next hop or position, the mobile sink moves to the new position and stays at it for a period of time. Then, the mobile sink calculates its new position. Note that the first round consists of Fig. 4a, b.

6

0

7

After finishing the first round (round 1), the mobile sink starts round 2. In other words, the mobile sink starts moving from node 0 to node 7 based on path 2. As a result, based on path 2 the mobile sink calculates its next hop or position which is equal to node 4. After visiting node 4, the next hop or position is calculated by the mobile sink based on path 1 too and the mobile sink discovers that it needs to move to node 6. Subsequent to visiting node 3, the next hop or position is calculated according to path 2. As a result, the mobile sink starts moving to node 7 which represents node n − 1. When the mobile sink reaches node 7, the first half of round 2 is over, see Fig. 5a. After that, the mobile sink will try to move from node 7 to node 0 based on path 2. In other words, being at node 7, the mobile sink calculates the next hop which is node 3 based on path 2. Next, the new position is calculated which is node 1. Subsequent to visiting node 1 the next position is calculated based on path 2. Hence the next node to be visited is node 0. After reaching node 0, which was the starting node of the first half of round 2, the second half of round 2 is finished, see Fig. 5b, and the mobile sink assumes that round 2 has finished. It is worth mentioning that after calculating the next hop or position the mobile sink moves to the new position and stays there for a specific period of time. Then, the mobile sink calculates its new position. Note that the second round consists of Fig. 5a, b. After finishing the second round (round 2), the mobile sink will start moving based on path 1. In other words, after finishing round 2 the mobile sink starts round 1 and when round 1 is over round 2 is started. As a result, it can be observed that the movement of the mobile sink is divided into rounds and the mobile sink keeps switching between the rounds described above.

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Therefore, it can be noted that the movement of the mobile sink is divided into rounds based on the path used. It is worth mentioning that every round starts at node 0 and finishes at the same node. After reaching the node at which the round has started, a new round is initiated based on the path that has not been used in the previous round. The use of the above-mentioned two rounds is proposed to take fault tolerance into account. In other words, suppose the mobile sink is at the beginning of the first half of the first round and node 1 has consumed its battery energy and failed. As a result the mobile sink will not be able to finish the first half of the round. However, the mobile sink can switch to path 2. As a result, all static sensor nodes that fall on the movement path of the mobile sink can be visited. 4.2 Routing Algorithm From the example mentioned in Sect. 4.1, it can be observed that for small size De Bruijn-based networks the mobile sink will visit most of the static sensor nodes in the network. However, when the network grows in size, the mobile sink will not be able to visit all static sensor nodes. In other words, the mobile sink will visit the static sensor nodes that are part of path 1 and path 2. As a result, the routing algorithm has to be modified so that static sensor nodes that are not visited by the mobile sink can route their messages or the information they have to a node that participates in one of the paths traversed by the mobile sink. Therefore, when a static sensor node wants to send information to the mobile sink it will check whether the mobile sink is a neighbor to it. After that, if it is a neighbor of the mobile sink, the message or information will be sent directly to the mobile sink in a single hop. On the other hand, if the static sensor node is not a neighbor of the mobile sink, the message or the information it has will be routed based on De Bruijn routing. That is, it will follow the same process followed by the mobile sink to determine the next position, mentioned in Sect. 3, to calculate the next hop for the message using path 1 or path 2. However, the static sensor node will use the information gained from the calculation to route the message instead of deciding its new position. As a result, the message will be routed from one static sensor node to another until it reached a static sensor node that falls on the movement path of the mobile sink i.e. a neighbor of the mobile sink. After that, the message will be forwarded to the mobile sink. A flowchart of the routing algorithm can be found in Fig. 6.

5 Simulation The mobility model and the routing algorithm presented in the paper were implemented in C++. After that, the perfor-

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mance of the proposed mobility model and routing algorithm was studied and analyzed by simulating them using a C++ based simulator which is called SENSE [27]. In the simulation we used MAC IEEE 802.11 DCF as the MAC layer protocol because it is already implemented in SENSE. Furthermore, the use of IEEE 802.11 with Distributed Coordination Function (DCF) is suitable for sensor networks because it helps sensor nodes to operate in a distributed manner rather than a centralized [28]. Thus, the performance of the network is improved. Furthermore, IEEE 802.11 DCF works in two different modes, namely infrastructure mode and ad hoc mode. In the infrastructure mode a central node is used when nodes need to communicate with each other. On the other hand, nodes can communicate with each other without a need for a central node in the ad hoc mode [29]. As a result, it can be concluded that the ad hoc mode is suitable for the operation of sensor networks because it helps sensor nodes to operate in a distributed manner. Table 1 shows the parameters that were used in the simulation. 5.1 Simulation Results In this section, we present the results obtained from simulating the proposed mobility model and routing algorithm under different network sizes (8, 16, 32, 64, 128, 256, and 512 nodes) and under different speeds of the mobile sink, namely 0, 5, 10, 15, and 20 m/s. First, we fix the network size at eight nodes and study the performance according to the speeds mentioned earlier in this section. After that, the network size is increased and fixed at 16 nodes to study the performance under the speeds mentioned before. This process continues until the performance of all the network sizes mentioned earlier is studied. Furthermore, the performance of a network with a mobile sink was compared to a fully static network of the same size. For example, after studying the performance of 8-node De Bruijn-based network with a mobile sink, the performance of the network is compared with that of a fully static De Druijnbased network of the same size. Since our mobility model uses the two paths that can be obtained from De Bruijn graph, see Sect. 3 for information on how the two paths are obtained. The performance of the network that uses a mobile sink is compared with the performance of a fully static network that uses path 1 to route messages. After that, the performance of the network that uses a mobile sink is compared with the performance of a fully static network that uses path 2 to route messages. Note that the topology in each network is based on De Bruijn graph and the result obtained for each case is the average of running the simulation ten times. Also for each run there are ten random sources. Figure 7 shows the performance, in terms of the end-toend delay, of the proposed mobility model and routing algo-

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Fig. 6 Routing algorithm Start

Yes

Addr(curr) == Addr(dest) No

Accept packet Yes

Addr(dest) == Addr(neigh)

No

End Next = Addr(neigh) Flag == 1 Yes

No

Next = path 1 x k − 2 x k −3 , ..., x1 x 0 d k −1

Next = path 2 d 0 x k −1 x k − 2 , ..., x1

hop = hop + 1

Table 1 Simulation parameters Parameter name

Parameter value

Packet size

127 bytes

Simulation time

500 s

Radio model

Two ray ground

Antenna type

Omni antenna

Grid size

100 × 100

MAC protocol

802.11 DCF

RXThresh

3.652e−10

CSThresh

1.559e−11

rithm for different network sizes under different speeds of the mobile sink. From Fig. 7 it can be observed that the proposed mobility model and routing algorithm obtained low end-to-end delay, less than or equal 0.02 s, for all network sizes. This can be regarded to the use of the mobile sink. In other words, using a mobile sink would reduce the number of hops needed by a message to reach its destination which is in this case the mobile sink. On the other hand, when the speed of the mobile sink was increased the end-to-end delay would increase because the mobile sink did not stay within the range of nearby static sensor nodes for enough time to be able to collect incoming messages. As a result, messages have to go

through more hops to reach the destination. Note that the variation in the readings of some network sizes can be regarded to the random selection of data sources because ten random data sources are selected for each case of the simulation. Figure 8 shows the data success rate under different network size and different speeds for the mobile sink. From Fig. 8 it can be observed that all networks managed to obtain relatively high data success rate, around 90 %, when the mobile sink speed was less than or equal 10 m/s. In addition, Fig. 8 shows that when the network size increases, the success rate decreases. This can be regarded to the sink mobility model. As mentioned before, the mobile sink moves according to paths that are calculated based on De Bruijn graph. Thus, the percentage of nodes visited by the mobile sink is lower when increasing the network size. To elaborate, the static sensor nodes can be divided into two groups: in the first group, sensor nodes use single-hop to communicate with the mobile sink because these sensor nodes are part of the movement path of the mobile sink. However, sensor nodes in the second group use multi-hop to communicate with the mobile sink since they are not part of the movement path of the mobile sink. As a result, when increasing the network size, the proportion of static sensor nodes that use single-hop to communicate with the mobile sink gets lower when compared with the total number of nodes in the network.

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Fig. 7 End-to-end delay

Fig. 8 Success rate

Figure 9 shows a comparison of the performance in terms of end-to-end delay between fully static sensor networks and sensor networks with mobile sink under different network sizes and with a fixed speed of 10 m/s for the mobile sink. Note that the speed of 10 m/s was chosen because all networks have obtained relatively high performance under this speed. Figure 9 presents the end-to-end delay for sensor networks that use a mobile sink much less than that of fully static sensor networks, because the use of the mobile sink reduces the number of hops for messages. As a result, the end-to-end delay is decreased. Figure 10 shows a comparison of the performance in terms of data success rate between fully static sensor networks and sensor networks with a mobile sink under different networks sizes and with a speed of 10 m/s for the mobile sink.

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From Fig. 10 it can be observed that fully static networks obtained higher success rate than that of sensor networks with a mobile sink because the mobile sink will be moving according to the paths of De Bruijn graph described before. As a result the static sensor nodes that are on the mobility path of the mobile sink will receive most of the messages destined to the mobile sink. Hence, the number of messages passing through those nodes is high which increases the drop rate or the number of packets that get dropped by the nodes that fall on the mobility path of the mobile sink which results in lower success rate than that of fully static sensor networks.

6 Conclusion and Future Work In this paper, a new sink mobility model derived from De Bruijn graph properties was presented. Furthermore, a rout-

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Fig. 9 End-to-end delay comparison

Fig. 10 Success rate comparison

ing algorithm that provides static sensor nodes with the ability to communicate with the mobile sink was developed and presented. The performance, in terms of end-to-end delay and data success rate, of the presented mobility model and routing algorithm was studied by simulating the network with different sizes and by using different speeds for the mobile sink. Hence, our results show that for low speeds of the mobile sink we can get high data success rate 90 % and above and low end-to-end delay which is equal to 0.02 s in the worst case.

For future work, we aim to study the performance of the mobility model and the routing algorithm in terms of energy consumption. Furthermore, fault tolerance is an important issue to be considered when studying sensor networks. Hence, we plan to extend the work presented in this paper to take fault tolerance into consideration. Also, we aim to study the performance and the behavior of our work in the presence of faults in the network. Additionally, we plan to extend the work presented in this paper to use other paths to increase the number of nodes visited be the mobile sink.

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