Mobile Sink (MS) based routing strategies have been widely investigated to prolong the lifetime of Wireless Sensor Networks (WSNs). In this paper, we propose two schemes for data gathering in WSNs: (i) MS moves on random paths in the network (RMS) and (ii) the trajectory of MS is defined (DMS). In both the schemes, the network field is logically divided into small squares. The center point of each partitioned area is the sojourn location of the MS. We present three linear programming based models: (i) to maximize network lifetime, (ii) to minimize path loss, and (iii) to minimize end to end delay. Moreover, a geometric model is proposed to avoid redundancy while collecting information from the network nodes. Simulation results show that our proposed schemes perform better than the selected existing schemes in terms of the selected performance metrics.

1. Introduction

WSNs consist of wireless sensors/nodes, which are equipped with a processor, a radio transceiver, a GPS, memory, and a battery [1]. These nodes are widely used in habitat and ecosystem, seismic, groundwater contamination, rapid emergency response monitoring and perimeter security surveillance, and so forth. WSNs must be energy efficient, robust, self-configurable, scalable, and secure. In considered WSNs, nodes are randomly deployed in the field for sensing physical attributes. After gathering data these nodes are supposed to transmit it for further processing. Nodes consume energy during sensing and transmission of data. They have limited energy resources (batteries attached to them). If the distance between the nodes and sink is greater, more energy will be consumed during transmission. Moreover, energy consumption of nodes is inversely proportional to the network lifetime.

There are two communication modes used in WSNs: direct and multihop [2]. In direct communication mode, the distant nodes consume more energy than nodes near the sink and die soon. These dead nodes create coverage hole leading to information loss. In multihop transmission, nodes send data to sink through intermediate nodes and maintains a routing table from source to destination. Intermediate nodes receive data of faraway nodes and relay it to the sink. This process minimizes the energy consumption of distant nodes. However, if the network is dense, nodes near the sink drain out quickly because of relaying faraway nodes’ data. Furthermore, clustering schemes are introduced to save nodes energy. Whole network is divided into subnetworks (clusters). In [3], authors propose a static clustering scheme in which the entire network is logically divided into circular ring shaped clusters. Each cluster has its own Cluster Head (CH) with associated member nodes. CHs consume more energy than member nodes as, along with their own sensed data, they also aggregate and forward the data of other nodes to sink. Energy is also consumed in cluster formation and in the selection of CHs. However, in comparison with direct and multihop transmission schemes, the clustering schemes perform better [4].

In clustering and multihop schemes, nodes close to the sink die quickly due to forwarding data of distant nodes. In this scenario, link between sink and nodes is disconnected and sink is not able to receive data from the faraway nodes. To balance the load on intermediate nodes, neighbors of sink should be changed periodically. In this way maximum nodes get chance to get closer to sink and relay data of distant nodes.

In this regard, an approach towards balanced system is the use of Mobile Sink (MS) which moves inside the network area for data gathering. MS has no energy constraints, although nodes have limited energy. Sink mobility in the network minimizes energy consumption among the neighboring nodes. It also minimizes energy consumption in unnecessary processes [5], like cluster formation and CHs selection. MS is considered as a small vehicle which moves in the field and collects data from nodes, either directly or via multihop. In this way, the communication distance is minimized that leads towards minimized energy consumption and maximized throughput [6].

In our proposed models, we exploit MS on random trajectory (RMS) and on defined path (DMS) by considering network as a geometric model. Reason for selecting random path is the presence of obstacles between MS and nodes. MS sets priorities for dense areas and moves towards dense areas first to collect data and then collect data from sparse areas; such kind of motion is termed as density aware random mobility. In the other scheme DMS, trajectory of MS is defined that visits the stop in defined order and collects data from the nodes. Different techniques in [5, 7, 8] addressed various problem with MS in terms of delay tolerance, network lifetime, and throughput. Change in trajectories of MS plays an important role on network lifetime, stability, and throughput. We also proposed a mathematical model to support our schemes: RMS and DMS.

The rest of the paper is organized as follows. Section 2 describes the related work. Section 3 discusses the motivation for the proposed schemes. Section 4 contains the network model. In Section 5 proposed methods of MS trajectories are explained. Simulation results are presented in Section 6. Section 7 concludes the paper and presents future directions.

Clustering scheme was first introduced to maximize throughput and network lifetime of WSN [4]. It forms clusters in the network field to minimize communication distance between nodes. After the formation of clusters, CH is selected by member nodes. CHs receive data from the member nodes, aggregate it, and then transmit it to the sink. Network lifetime is prolonged by increasing the data forwarding burden on certain nodes. A model is proposed that utilized clustering mechanism by changing the selection criteria of CH and gave better performance [2]. Routing scheme, based on clustering mechanism, RE-LEACH [9], works on the same principle as LEACH; however, it considers node’s residual energy during CH selection. Another scheme, DREEM-ME, a static clustering based routing protocol, minimizes the distance between nodes and CHs that ultimately saves transmission energy. However, energy is still consumed in periodic selection of CH. DYN-NbC [10] uses both clustering and MS. In this protocol, sink moves to the highest node density region, whereas, in the other regions of the network field, clusters are formed and the CH selection is based on LEACH criteria. Sink mobility along with clustering balances energy consumption to some extent; however, clustering itself is an energy consuming process. A MS based uneven clustering algorithm (UC-MS) is proposed in [11]. In this scheme, CH receives data from member nodes and waits for MS to stay at closer sojourn location for data transmission. Here, energy consumption of CH is minimized as it sends data at minimum distance; however, energy is still consumed in cluster formation and in the selection of CH.

Routing schemes are used to expedite communication between sink and nodes. In [6], authors proposed an energy efficient use of multiple MSs which results in longer network lifetime. They used Mixed Integer Linear Programming (MILP) to determine the locations of sink. They concluded that use of rigorous approach to optimize energy utilization leads to significant increase in network lifetime. Authors used this approach for dense field.

Amjad et al. [3] proposed a routing protocol DREEM-ME, in which square area is divided into concentric circles and each ring is further subdivided into four regions, whereas central circle remains the same. Eight outer regions are considered as clusters (four clusters are present in each central and outer circle). Each cluster selects CH on the basis of residual energy to gather data from member nodes. CHs in the outermost ring forward their data through relay from central ring’s CHs, on the basis of minimum distance. Authors in [8] consider the problem of speed and planning path of data mule (i.e., MS) in WSN. They consider different situations where this problem is encountered, like modeling the motion of a data-collecting Unmanned Aerial Vehicle (UAV) for structural health monitoring through nodes. They used MS to avoid multihop forwarding. These MSs can save energy of node and latency increases. In this paper, authors schedule MS framework to minimize data delivery latency. They formulated the problem and proposed an algorithm to minimize the trade-off between energy consumption and data latency.

In some networks, received data is sent to the sink in timely pattern. These networks are designed in such a way that nodes buffer data for some interval. Without being overflow, data is sent to the sink through multihop forwarding or direct transmission depending upon the distance between the node and sink. These are termed as delay tolerant networks.

In [12], the authors consider the clustering technique and data is gathered through CHs from member nodes. MS moves on a defined trajectory and collects data from the CHs. In this way energy consumption is minimized and as a result this scheme has increased throughput. However, CH nodes consume more energy during data forwarding and is depleted soon.

MMSR is proposed in [13], where there are three MSs deployed in the network and they gather data from different parts of the network. MSs move on different trajectories and gather data from the nodes. Nodes send sensed data direct to MS at minimum distance. In this way the energy consumption of nodes is minimized. In [14], authors proposed a novel joint optimization framework to study the trade-offs between delay tolerant and network lifetime in an MS aided WSN. They also devised a heuristic to find a hop-constrained trajectory for the MS. They also proposed an energy efficient routing protocol, where MS for the purpose of data gathering traverses along the fixed trajectory. The experimental results show that the proposed algorithm performs better in terms of network lifetime maximization. In [15], the authors explore the problem regarding MS in event-driven applications. There are applications of WSNs, where MS moves with limited velocity to harvest the sensed data from group of sensors. The data is collected in defined time slots. The authors used convex optimization model to support vector regression technique.

Also, in [16], two different models are proposed for lifetime maximization: delay tolerance and queue-based tolerance. Authors also proposed a column generation algorithm for data transmission from nodes to MS.

Basagni et al. in [5] defined a model, in which sink moves on predefined path. They exploit MS movement close to different nodes to minimize the energy consumption of the nodes. As a consequence, network lifetime increases. Authors proposed three schemes that represent different solutions for sink mobility. One of the schemes computes optimal sink routes and calculates sojourn times through proposed MILP formulation. Also, they considered realistic parameters of WSN and sink mobility. This scheme prolongs the network lifetime by considering MS movements depending upon node’s transmission costs in a centralized way. In [17], authors proposed mobility pattern of a MS that takes a discrete form where MS stop time is greater than movement time between two sojourn locations. This approach is investigated for balanced traffic load with MS and it results in improved network lifetime. They also studied the benefits of using MS versus a static sink. Authors simulated both grid network and a special in-building network with nodes forming a ring.

By using QVF algorithm for target tracking, authors in [18] consider the problem of secure clustering in WSNs. They use Bayesian methods for joint selection of the optimal sensor and detection of malicious node to avoid attacks. Also, they consider the trade-off between quality of sensed data, transmit power, and initial energy of nodes. For detecting malicious nodes, they used the Kullback-Leibler Distance (KLD) between the current target position distribution and the forecasted sensor observation.

In [19], Shi et al. proposed Data Driven Routing Protocol (DDRP) to exploit the broadcast feature of wireless transmission. Control overhead is reduced because it requires no extra control messages for route learning. Overhearing of such data packet provides the route information to the MS and nodes.

MS, in the field, helps in reducing energy utilization of nodes by using direct transmission, whereas MS needs time scheduling to reduce data losses. Authors in [20] presented a model in which two MSs in a square network are present with different defined trajectories. By introducing two sinks, load is balanced and MSs expedite data gathering process and as a result network lifetime is prolonged. Related work is summarized in Table 1.

3. Problem Statement

In the literature, many MS based routing schemes have been proposed in WSNs: (i) sink mobility based schemes, (ii) clustering based schemes, and (iii) sink mobility along with clustering based schemes. In Section 2, we have already discussed some of the latest and relevant schemes subject to the three categories like [6, 8, 11]. Moreover, the drawbacks of all the discussed schemes are also highlighted in Section 2. From Section 2, we identify that the existing schemes use MS for data gathering. However, the MS based schemes do not consider node density as a priority which leads to inefficient data gathering resulting in less network throughput. Similarly, the clustering schemes consume high energy during formation of clusters and CH selection resulting in shortened network lifetime. Therefore, we aim to present an MS based routing strategy for (i) network lifetime maximization, (ii) path loss minimization, and (iii) end to end delay minimization. Moreover, we aim at a geometric model to avoid redundancy while collecting information from the network nodes.

4. Counter Part Schemes

We compared our proposed schemes with existing schemes and all the schemes use direct as well as multihop communication techniques depending upon the distance from the sink. The four schemes, that is, DREEM-ME, DYN-NbC, FTIEE [21], and UC-MS, were used for comparison with our proposed schemes. A brief overview of each of the four schemes is given below.


The designed WSN is two-dimensional with 100 m × 100 m. Network field is divided into three concentric circles of 20 m, 35 m, and 50 m radii, respectively. Inner circle is taken as it is and is considered as a single cluster. Each of the outer two circles is further divided into four sectors, which result in eight clusters. Now network has total nine static clusters. Deployment of nodes in the network is uniform random. Each cluster has nodes. The network has nodes and nine clusters. Each cluster selects its CH on the basis of residual energy. Sink is static and placed at center. To minimize the energy consumption, it is not mandatory for any node to send its data to its respective CH. Nodes of outermost clusters calculate their distance from adjacent cluster’s CH and send data to the least distant CH. So in this way, CHs of outermost regions send their data to sink through multihoping. The inner circle (central) CHs are responsible for transmission of data of outer circle. This scheme balances the energy consumption by implementing static clustering and node selection of closer CH for data sending with optimal CH selection by nodes.

4.2. DYN-NbC

This scheme has two features: need based clustering and dynamic sink mobility. This hybrid technique exploits the advantages of both features. Nodes are randomly deployed in the area of 100 m × 100 m field which is further divided into four quadrants named as , and . For simplicity each quadrant is further divided into four regions. Node density is calculated in each of the regions. Data is collected on priority basis from the region of high node density and is achieved by dynamic movement of MS to that region. The maximum number of nodes sends their data to MS by direct communication and thus minimizes the energy consumption of the network. Nodes, which are deployed far from the MS, have to wait for their turn. To avoid this delay clustering is done in the network. Clusters formed by the criteria defined by LEACH. In this scheme, clustering is done whenever there is a need; therefore, it is defined by the name “need based clustering.” CHs gather data from the member nodes and periodically send it to MS which is currently residing in the region of high density and collecting data from nodes there (direct communication). By taking the benefits of both communication schemes, DYN-NbC achieves longer network lifetime with greater throughput.

4.3. FTIEE

This scheme proposes an efficient protocol that reduces CH selection overhead in the network. By using machine learning technique any node of the cluster can be a CH. This process minimizes the energy consumption during the repeated elections of CH. FTIEE is the hierarchical-based protocol. In this scheme unlike other clustering techniques, cluster shape is square and remains fixed. However, the size of clusters may vary and follows a certain rule. Clusters located close to sink are smaller than the clusters that are located far from the sink. Basically, the size of the clusters increases with increase in distance between sink and node. In this scheme, once in the whole network lifetime clusters are formed and afterwards CHs are selected for them. This scheme is distributed and finds optimal CH node by learning system. CHs are selected by using the algorithm and nodes are not involved in CH selection. Therefore, energy consumption and network overhead are reduced. CH selection criteria include its current state, neighbors, and residual energy and are called -learning which uses two -values: residual energy of the node and distance between a node and the sink. This scheme also improves packet delivery ratio and packet delay along with network lifetime.

4.4. UC-MS

This scheme combines the UC algorithm with MS and proposed a MS based uneven clustering algorithm. This algorithm is distributed clustering algorithm and is similar to that of LEACH. CH role is rotated among the nodes periodically, whereas selection of CH is mainly based on the competitive range and the residual energy of the nodes. Initially, the protocol implemented the UC algorithm by placing sink at the center of a network. After performing simulations and studying the behavior for energy consumption and network lifetime, MS is introduced instead of fixed sink. MS collects fused data under similar environment. All nodes participate in the competition of CH selection. It is CH’s responsibility to aggregate the data received from member nodes and forward the aggregated data to the MS. CHs get aware of MS’s location when they receive broadcast message from MS. Upon receiving broadcast message from MS trajectory and the sojourn locations are set in advance. When a CH finds the closest sojourn position of the MS, it then sends the gathered information when MS arrives. Nodes, present within the cluster, use multihop as well as direct communication with CH depending upon the distance between them. CHs are selected on the basis of residual energy. UC-MS enhances network lifetime along minimizing energy consumption.

5. Network Model

In our proposed schemes, RMS and DMS, nodes are homogeneous in terms of initially assigned energy, that is, . We consider energy consumption only during the transmission of sensed data. A square network area is considered that is further logically divided into sixteen small squares. Nodes are randomly deployed in the network field. The center of each small square is a sojourn location of MS, from where it directly receives data from the nodes that come in its sensing range. Sensing range of MS is a circle (i.e., ) which is shown in Figure 1 with dotted lines. Pause signs are labeled with and and represents two sojourn locations from the whole network field (there are total sojourn locations). For simplicity and solving the equations for geometry they are also labeled as and . The intersection area between two circles is shown shaded in this figure. The radius of circular sensing range is (=) and is the distance between two intersecting points and . MS moves to the next sojourn location and portion of previously sensed region also comes in next circular area as shown in Figure 1. To cope with this problem, nodes that have previously sent their data do not participate in current transmission. To understand the geometry of transmission ranges (shown in Figure 1) consider the following discussion.

When MS stops at a sojourn location, it receives data from the nodes of connected subregions that come in its sensing range. On its forward movement to the next location, the MS sensing range overlaps with the previously visited region which may have few common nodes. The overlapped sensing range is shown in Figure 2 to provide more clarity. In order to avoid surplus data reception from nodes that have previously sent their data, a mathematical model is formulated. Both sensing ranges have same radii ; however, to make calculation simple, we label them as and . Our goal is to calculate the shaded overlapped region between two sensing ranges. For this purpose, we first calculated cord length with the help of end points and , shown in Figure 3, that is, and , where . Cord end points are located at the intersection points of circles as shown in Figure 3. Equation of first sensing range with radius is a circle equation given below:Equation for second sensing range with radius isfrom (1) and (2)Putting value from (3) in (1)In the considered case radii of both circles are the same; that is, . Substituting this value in (4), we get the value of .Area of lens shaped overlapping region iswhere “” is a distance as shown in Figure 2. Also, we have considered as for our proposed schemes RMS and DMS. Eventually, when MS moves onward, already sensed areas are excluded from next location’s sensing range given by (6). Each node delivers data to MS once during an epoch. Epoch is defined as the time duration in which all the nodes send their data to MS once. To elaborate the proposed schemes, network is modeled as directed graph , where are vertices and are edges. In our case we take nodes as vertices and edges are links between nodes and MS. We define set of sojourn locations as . For all and , , iff and are within a square transmission range .

MS covers the entire area and directly receives data from each node in epoch, . At each sojourn location MS collects data from nodes in its sensing range and then moves on. Traveling time between two sojourn locations is negligible. Link between a node and MS is represented as . Also, if sink sojourn location is , then ; otherwise , . We maximize network lifetime by using MS on different trajectories.

Equation (7) defines the objective function of maximizing network lifetime. is total network lifetime and is the time during one epoch. Therefore, sum of is the total network lifetime. Equation shows that during one epoch sink is located at one stop for the collection of data from nodes that are present in its sensing range. Equation describes incoming and outgoing flow constraints shown in Figure 4. Function is the amount of data sent over an edge between the node and MS during epoch and is the hello packet sent by MS during stay on specific sojourn location. In , denotes the collected data during the network lifetime. Equation is the energy conservation constraint. is the energy used by the nodes during the transmission of the data towards sink, whereas is the initial energy of nodes. Equation is the rate constraint. Total information sent over the link should not exceed the link capacity, ; it is the upper bound of the transmission rate. Finally, shows that starting and ending locations of MS are the same.

6. Proposed Schemes: RMS and DMS

The objective of our proposed schemes, RMS and DMS, is to analyze the performance of MS on different trajectories in the field. RMS trajectory follows node density based random path (i.e., density aware motion of MS) whereas DMS trajectory has a predefined path. Often WSNs are used to detect foreign chemical agents in the air and the water; DMS scheme can be implemented for such scenarios, whereas RMS scheme can be used in natural disasters like flood, where the MS can be any drowned helicopter or boat. When there is an urgent need, MS visits that place first.

Another important parameter is sojourn period of MS. Sojourn period is the time duration for which the MS stays at a sojourn location and collects data from the neighboring nodes. In our schemes, sojourn period is adaptively calculated. MS moves to the next location when all nodes of the specific subregion completely transmit data. We calculate the sojourn period at one sojourn location as , where is single sojourn time, is total time of a round, and is total number of sojourn locations in the field. If we calculate sojourn time of a complete trip of MS, it shows that time consumed in gathering data during one round isTherefore, is the total lifetime of the network.

For RMS, MS has global knowledge of all stops on the basis of node density. DMS trajectories are initially defined and MS follows the fixed path.

6.1. RMS Trajectories

RMS trajectory is random because MS collects data on the basis of node density as it moves from dense to sparse region(s). This movement is also very useful as in some cases it is difficult to follow the defined path due to obstacles or hills.

Network field is 100 m × 100 m which is logically divided into equal subregions and the central point of each subregion is the stop for MS. Sojourn stops are equal to the number of partitions of field which are in proposed schemes. MS randomly collects data from the nodes, by giving priority to highest node density region. This is due to the fact that the chances of overflow or loss of sensed data increase with an increase in the node density. Also, MS directly collects data from nodes, so energy used in data transmission is minimized. The complete functionality of RMS is shown in (Figure 5).

The working scheme of RMS is shown in Figure 6. Logically, MS starts its traveling from dense to sparse subregion in the network field. We also assume that traveling time is negligible as compared to sojourn time ().

6.2. DMS Trajectories

We assume here a square field in which nodes are randomly deployed. Network field is logically divided into small subregions. Network field dimensions are 100 m × 100 m. It consists of sixteen small squares each of area 25 m × 25 m as shown in Figure 7.

Central point of each subregion is the sojourn location of MS, moving pattern of which is predefined, and it is like a square spiral inside a square field. This trajectory covers the complete area of network. MS stops on a first sojourn location and broadcasts advertisement message to all nodes in its sensing range.

Nodes then establish a link and start data transmission. Once data transmission is completed, MS moves to the next location and the same procedure repeats. Working scheme of DMS is pictorially shown in Figure 8.

All nodes send the sensed data to MS once in a round. MS is aware of its sojourn locations and also has the knowledge of network boundaries. Path of MS is designed in such a way that every node is able to deliver data at a minimum distance.

Moreover, the network is working in a sleep awake manner. Nodes get awake and transmit their data to MS, whenever they receive a beacon message from MS. Otherwise, nodes go to sleep mode to save their energy. As the area of subregion is small, minimum energy is used in data transmission.

6.3. Analytical Analysis

We proposed two schemes RMS and DMS, which collect data on priority and periodic bases, respectively. Nodes are randomly deployed in the network. In RMS, MS first collects data from those regions which are denser, whereas, in DMS, trajectories for MS are predefined and fixed. The path in DMS is predefined; however, the nodes are randomly deployed. Therefore, we aim to optimize three network performance metrics: (i) maximize network throughput, (ii) minimize end to end delay, and (iii) minimize path loss.

The graphical analyses are carried out subject to (i) throughput maximization, (ii) delay minimization, and (iii) path loss minimization. For these three objectives, the bounds are found through Monte Carlo simulations. Figures 911 show the respective feasible regions (where all feasible solutions lie) for the objective functions while respecting their bounds. In RMS, regions with high node density send more packets as compared to DMS. Objective function is defining the combined throughput of both schemes in 21 × 103 sec (time in which MS completes one trip). Combined throughput of RMS and DMS isObjective function is

According to the bounds provided in (10b), (10c), and (10d), Figure 9 shows the bounded region formed by intersecting lines , and . Combined throughput of both schemes is lying within the boundaries of illustrated region. This bounded region shows the feasible solution. Values on each vertex are obtained asat ,at ,at ,at .

Consider path loss (PL) for one round trip of MS in both schemes: RMS and DMS. PL in RMS is greater than DMS because it receives data from high node density region. As a consequence, diffraction and reflection are greater in this scheme. Feasible region for combined PL is shown in Figure 10 in 21 × 103 sec. This represents the range of maximum value of PL in any round of MS (in which it gathers data from the nodes in the network). Objective function iswhere

Bounded region is formed by the intersection of , and lines, which shows feasible region of PL in Figure 10. These bounds are shown in (10b), (10c), and (10d) that forms the feasible region. Values on each vertex are obtained asat ,at ,at ,at .

Combined PL of both schemes is lying within the boundaries of illustrated region.

Another performance parameter is end to end delay of RMS (D-RMS) and DMS (D-DMS) during single trip in which MS gathers data from the field. That is represented asObjective function and constraints are given as

Feasible region is shown in Figure 11 that is formed by the intersection of , and lines. The values for these bounds are given in (13b), (13c), and (13d). Values on each vertex are obtained asat ,at ,at ,at . falls within the boundaries of illustrated region. The bounded region shows the maximum value of the delay when all the nodes are alive in the network. As the network evolves the nodes in the network consume energy that depends upon the distance between nodes and MS. With the passage of time when nodes start depleting their energies delay decreases. The feasible region represents the minimum and maximum range of the delay.

7. Simulation Results

Following performance parameters are considered to evaluate the simulation results.

7.1. Performance Parameters: Definitions

For evaluating performance of RMS and DMS, the following metrics are used:(1)Network lifetime: total time duration (sec) of network operation from start till the death of last node.(2)Stability period: time duration (sec) from start of the network till the death of first node.(3)Unstability period: it is the time duration (sec) from the death of first node till the death of last node during network operation.(4)Throughput: number of successfully received packets by the MS per unit time (packet/sec).(5)Packets dropped: number of packets dropped due to bad link quality. We considered random uniformed model [22] for packet dropped calculation, in which the probability of packet drop is set to .(6)End to end delay: Time, a packet takes, to travel from source node to sink (sec).(7)PL: PL includes all the propagation losses due to attenuation of electromagnetic waves, refraction, diffraction, and reflection, between source and sink. It is calculated in dB.

Note. From the literature review in Section 2, the network lifetime has been defined in many ways like total time duration from the establishment of network till the death of first node, the total time duration from the establishment of the network till the death of 10% nodes, and the total time duration from the establishment of the network till the death of last node. In this research work, we have analyzed the first node death time and the last node death time. The first node death time is also called stability period of the network. Thus, we have chosen the last node death time as the network lifetime.

We use first-order radio model for energy consumption [4] and distance is taken between source node and MS. Depending upon the distance, free space ( power loss) and multipath ( power loss) channels are used. Equations for energy consumption of -bit packet over a distance are given as

In Figure 12, the radio model shows that the energy consumption is directly proportional to the distance between sender and receiver nodes. To minimize this distance, MS plays a key role. It receives data from the nodes at minimum distance and thus MS minimizes nodes’ energy consumption.

Radio model parameters that we used for simulations are shown in Table 2. nodes are randomly deployed in a network. Network field is logically divided into small squares of equal area, that is, 25 m × 25 m. Due to random deployment of the nodes, density of nodes varies in the subregions, where it is high; there are chances of information loss due to data overflow. Our proposed RMS scheme addresses this problem; that is, MS visits dense region first, whereas DMS considers predefined paths. In both cases, sojourn locations are defined.

7.2. Performance Parameters: Discussions
7.2.1. Network Stability

Figure 13 shows the comparison of network lifetime of proposed and compared schemes. Each node is equipped with same initial energy 0.5 J. DMS shows improved and extended stability period in comparison to the other schemes. MS broadcasts a beacon, when it stops at a particular location. Nodes which come in the transmission range of MS receive the beacon and transmit their sensed data. As a consequence nodes minimize their energy consumption with the help of direct communication with sink. This results in longer stability period as well as network lifetime. Sink mobility in proposed scheme reduces energy consumption to existing schemes. Moreover, the CHs bear the burden of their respective member nodes in terms of data forwarding and aggregation. Thus, the CHs consume energy at faster rate as compared to normal nodes. In DMS and RMS, we compared the mobility patterns, predefined trajectory of MS and random trajectory from dense region to sparse regions of the network, respectively. In RMS, nodes from sparse regions transmit data towards the sink at larger distance, therefore, consuming more energy. As a result, RMS showing shorter stability period; however, network lifetime is similar to DMS. DREEM-ME has also longer stability period due to uniform random distribution of the nodes and minimum transmission distance. After  sec the nodes in the outer most and central region drain energies and the nodes present in the inner most region only send data towards the sink. UC-MS has longer network lifetime than LEACH due to the presence of MS.

7.2.2. Throughput

Throughput of proposed and compared schemes is shown in Figure 14. The schemes with MS have higher throughput because of direct communication between nodes and MS and low PL. DREEM-ME and FTIEE are clustering routing protocols; their throughput is less as compared to the other four MS schemes. RMS has greater throughput because MS gives priority to dense regions for data gathering; that is, more number of nodes send data packet directly, thereby increasing throughput. In UC-MS, CHs collect data from member nodes and wait for the control message from MS (when it arrives on nearby stop). MS visits on predetermined stops and directly receives data from the CHs at a minimum distance. This reduces the energy consumption of CHs. DYN-NbC and UC-MS are clustering schemes with sink mobility and are more efficient in comparison with DREEM-ME and FTIEE. However, we further minimize energy consumption by excluding clustering mechanism in RMS and DMS. DYN-NbC contains clustering as well as MS. So its throughput lies in between the throughput of clustering schemes (FTIEE, DREEM-ME) and schemes with MS (DMS, RMS). From the start of the network operation, throughput of each scheme linearly increases, whereas after the end of stability period throughput decreases. Reason for low throughput is decreased number of alive nodes in the network. That shows maximum possible output during one complete trip of MS when it receives data from all nodes.

7.2.3. End to End Delay

End to end delay varies in all schemes. In Figure 15, DREEM-ME has the least packet delay because it is clustering scheme; number of hops for data transmission decreases and load is well balanced among the CHs and the member nodes. Also, it has uniform random distribution of nodes. DREEM-ME has static clusters and they stay the same till the end of network. Its clusters are design in such a way that nodes interact with CHs which further transmit data to sink at a minimum distance. Delay of DMS is the least among the compared schemes that have MS. In this case, MS has defined trajectory and data is received in less time because of assumption that sink’s traveling time is negligible between two adjacent sojourn locations. No priority is given to any node in receiving data from nodes when MS is present at any sojourn location. End to end delay of RMS is greater than that of DMS because MS randomly moves in the field to collect data. The analytical analysis of delay of both schemes during a single trip of MS in the network field is shown in Figure 11. There, bounded region shows the maximum and minimum values of delay. FTIEE is a clustering scheme and it has greater end to end delay as compared to the proposed schemes. This is because nodes first send data to the CH and then CH forwards the aggregated data to the sink and takes extra time (i.e., longer delay). It also possesses dynamic clustering which rotates clusters after certain time, and again CH selection and association phase occurs. That results in delay. DYN-NbC has higher delay because it utilizes clustering as well as MS, where clustering uses multihop communication that results in longer delay. First the denser region on the basis of number of nodes is selected; then remaining regions form clusters; and CHs are selected; also, nodes association phase takes place. In UC-MS clustering is done first; then association of nodes occurs. The difference is CH waits for MS for data forwarding. From the start of the network till the death of first node, end to end delay linearly increases and afterwards remains constant.

7.2.4. Number of Packets Dropped

Figure 16 shows that those schemes which have high throughput also have high packet drop probability. This model assumes that greater packets sending rate results in greater number of packets drop. DREEM-ME and FTIEE are clustering schemes, where nodes sense the data and periodically transmit it to CH. CH after receiving data from the member nodes aggregates it and sends it to the sink. UC-MS has both clustering and MS. First nodes send data to CH; then after receiving data from member nodes CH waits for MS. Chances of packet drop increase in this way. DYN-NbC has need based clustering; however, MS is covering directly. In of the network field there is clustering and CHs receive data from member nodes and transmit it to MS. Its packet drop is less than UC-MS in comparison. It is obvious from our proposed schemes that RMS has less packet drop because it receives data from the nodes of maximum dense region on the priority basis. DMS is visiting each region on predefined trajectories and there are chances that in some regions nodes are waiting for so long for MS’s arrival and ultimately drop the packet.

7.2.5. PL

In RMS, as MS moves towards dense region, the number of packets sent by the nodes is greater. In Figure 17 PL is shown; it increases till the nodes in the network are sensing and transmitting the data. Throughput of RMS is greater; therefore, PL is also greater. In DMS, PL is relatively less than that of RMS. Combined PL of both schemes RMS and DMS is provided in Figure 10. That shows the maximum value of PL during one complete data collection round of MS (when it receives data from all alive nodes of the network). Stability period of DMS is greater than all compared schemes that is seconds. From Figure 17, PL for DMS increases linearly till and after that nodes start depleting their energies and PL curve also alters its behavior. UC-MS and DYN-NbC both have clustering mechanism and MS. However, in UC-MS there is higher PL as compared to DYN-NbC because it has uneven clustering and data transmission is only through CHs.

DREEM-ME and FTIEE both are clustering schemes; however, FTIEE has higher PL because of dynamic clustering; that is, shape and number of nodes associated with the CH are not fixed. Some CHs have large number of associated nodes and during data reception, propagation delay or attenuation may occur which results in maybe increased PL.

7.2.6. Residual Energy

In all the analyzed protocols, initial energy is the same, that is, 0.5 J. It is obvious from Figure 18 that due to noncontinuous transmissions in RMS and DMS energy consumption is linear. In DYN-NbC, energy is consumed during clustering and CH selection. UC-MS also consumes more energy in cluster formation, CH selection, and data aggregation.

7.3. Performance Parameters: Trade-Offs

We discuss the performance trade-offs of proposed and existing routing schemes. Also, we make the possible comparison of all schemes under consideration. Enhancement in a performance metric in each scheme is achieved by paying the cost in any other performance metric as shown in Table 3. DMS achieves higher stability period at the cost of throughput as compared to RMS. However, end to end delay of DMS is also less than RMS. End to end delay depends upon the number of packets received at sink. As in RMS a larger number of nodes (from dense region) directly transmit data to MS, congestion in network may occur and because of this end to end delay increases. RMS has higher throughput because it gathers data from dense regions on priority basis at the cost of stability period. E2ED of nodes in these schemes is less in comparison to the UC-MS, DREEM-ME, DYN-NbC, and FTIEE. In UC-MS nodes first send their sensed data to the CHs and CHs wait for MS to come at their closer stop. Once MS stops at nearer stop, CHs transmit their own data, as well as received data. Due to waiting for MS and multihop communication, UC-MS has higher E2ED. DYN-NbC is also clustering scheme with MS. Its working strategy is different from UC-MS. First the whole network is divided into small subregions like RMS and DMS. After that highly dense region where the number of nodes is maximum is identified. DYN-NbC’s E2ED is less than UC-MS, however, greater than DREEM-ME and FTIEE. For packet drop ratio we used random uniformed model. DMS has a higher packet drop ratio in comparison to other compared schemes because it visits all the regions in the network on its turn. Packet drop increases in some areas where nodes have to wait for MS for long time period. RMS receives data from nodes on priority; high node density regions send their sensed data earlier; as a result, it achieves higher throughput and less packet drop. In DMS consumption of energy is almost the same like RMS.

8. Conclusion and Future Work

In our proposed RMS and DMS schemes, the field is logically divided into small squares to find MS locations and also to calculate its maximum distance from the nodes. Doing this, we achieved enhanced throughput and prolonged network lifetime. We compared our proposed protocols with DREEM-ME in which the field is divided into concentric circles and depending upon the distance between node and sink, data is either directly transmitted or via the intermediate nodes. We also compared our proposed schemes with UC-MS and DYN-NbC; these possess clustering as well as MS. Results show that RMS performs better than DMS in terms of data collection from dense regions first and remaining afterwards, while in terms of stability, DMS trajectory shows better performance.

In future, our goals are to explore more trajectories and geometries of sink. We also want to introduce more than one sink to minimize the transmission cost and prolong the network lifetime. Also end to end QoS metric will be under consideration for gateway selection schemes.

Competing Interests

The authors declare that there is no conflict of interests.


This research project was supported by a grant from the “Research Center of the Female Scientific and Medical Colleges,” Deanship of Scientific Research, King Saud University.