Wireless Sensor Networks (WSNs) have many potential applications, which include environmental monitoring, tracking, healthcare, surveillance, smart homes and so forth [1–4]. Since sensors are battery powered, prolonging the network lifetime of WSNs is crucial for the usage of sensors in this wide range of applications. Communication is one of the major sources of energy consumption. With limited transmission range, sensors typically deliver their readings to the sink in a multi-hop manner. This behavior will raise the problem of unbalanced energy since the sensors closer to the sink have heavier data-relaying workloads and thus exhaust their energies much faster than the more distant sensors [5–7]. As a result, the network will be partitioned and hence the sink can become unreachable by other sensors.

Instead of constructing a data collection tree from a fixed sink to all sensors, a number of studies [8–11] have employed a mobile data collector (or mobile sink) moving along some predefined trajectory to migrate the data-relaying workload from one sensor to another. In [8] and [9] a trajectory which enables the mobile sink to directly communicate with sensors was constructed. However, the length of trajectory increases with the size of the monitoring region. This is because the constructed trajectory has to pass through the transmission range of each sensor. As a result, sensors have to wait for a long time to be visited by mobile sink again, leading to a long visit latency.

Zhao et al. [10] selected some sensors as the tree roots and then constructed a tree from all the other sensors to each root. By visiting the selected roots in turn, a mobile sink can collect the readings generated by all sensors based on the constructed tree in a multi-hop manner. Compared to studies [8] and [9], the scheme proposed in [10] significantly reduces the trajectory length of the mobile sink. Nevertheless, the data-relaying workloads of roots are higher than those of the other sensors, resulting in an energy-unbalanced problem.

Alsalih et al. [11] considered a circular monitoring region. All sensors are assumed to be uniformly deployed over the monitoring region. As shown in Figure 1, the mobile sink whose transmission range is r moves along the boundary of the monitoring region to collect readings. The sensors located at the boundary, called boundary sensors, can be visited by mobile sink while the remaining sensors have to deliver their readings to the mobile sink in a multi-hop manner due to the limited transmission range.

To forward the collected readings to the sink, the boundary sensors will receive and store the readings and then wait for mobile sink to pass through their transmission ranges. However, sensors closer to the center of the monitoring region would have much fewer data-relaying workloads than the boundary sensors. For example, as shown in Figure 1, each of red nodes only needs to deliver their own readings to their neighbors without any data-relaying workloads. Consequently, the boundary sensors and the red nodes have different energy consumptions, leading to an energy-unbalance problem. This paper proposes an Energy-Balanced Data Collection mechanism, called EBDC, which determines a trajectory such that the data-relaying workloads of all sensors can be totally balanced. Similar to the network environment of study [11], this paper considers a circular monitoring region which has been geographically partitioned into a number of circular tracks. To balance the data-relaying workloads, the mobile sink moves along different tracks with predefined sweep repetitions. At any given time, each sensor is able to derive the track where the mobile sink is visiting currently. Therefore, each sensor can send its reading to the appropriate neighbor such that the reading can reach the mobile sink in a multi-hop manner.

Furthermore, the proposed EBDC mechanism can be applied to a wide range of applications. For example, in an environmental monitoring application, a large number of sensors can be randomly deployed over a monitoring region to monitor temperature, humidity or air quality. Instead of reporting data frequently, sensors in such application only need to report their readings to the sink periodically. Hence, this scenario motivates us to use a mobile sink to collect data.

The remaining part of this paper is organized as follows: Section 2 presents the network environment and problem formulations of our approach, while Section 3 presents the details of the proposed EBDC mechanism. Sections 4 and 5 investigate the theoretical analysis and the performance of the EBDC mechanism, respectively. Finally, the conclusions of this paper are given in Section 6.

This section initially introduces the network environment and the assumptions of the given WSN. Then, the notations used in this section and the problem formulations of our approach are proposed.

This section presents the details of the proposed EBDC mechanism which is executed by the mobile sink for constructing the trajectory J min E B − T. At a conceptual level, the EBDC mechanism is composed of three major phases: Initialization Phase, Energy Estimation Phase, and Trajectory Construction Phase. In the Initialization Phase, the number of sensors |S_i| in each track k_i will be evaluated while the Energy Estimation Phase mainly measures the energy consumption of each sensor when the mobile sink traverses any track for one sweep repetition. In the Trajectory Construction Phase, the trajectory J min E B − T can be planned by the information obtained in the previous two phases. These three phases are executed by the mobile sink. After determining the trajectory J min E B − T, the mobile sink will flood its movement plan, including the movement velocity in each track, the number of sweep repetitions in each track, the starting location and the starting time, to all sensors in the monitoring region. Each sensor can therefore derive the track k_collect the mobile sink is currently visiting. The following presents the details of the three phases.

Section 3 shows the details of the proposed EBDC mechanism. By applying EBDC mechanism, the data-relaying workloads of all sensors can be totally balanced in an efficient way. In addition to the degree of energy balancing, another crucial factor considered in WSNs is the network lifetime. Herein, the network lifetime is measured by the time interval starting from the time that sensors have been deployed to the time that a coverage hole appears. To verify the performance of the network lifetime, this section further compares the proposed EBDC mechanism against the RMDC scheme proposed in [11]. The RMDC scheme is considered as approach to compare because RMDC outperforms related schemes [5–10]. In general, the related data collection schemes can be mainly classfied into fixed sink schemes [5–7] and mobile sink schemes [8–11]. Unlike the fixed sink schemes [5–7] which are based on a fixed sink, RMDC employed a mobile sink to collect data. Hence, the RMDC has a better performance than the existing fixed sink schemes [5–7] in terms of network lifetime. Recall that the mobile sink applying the efforts described in [8,9] has to pass through the transmission range of each sensor, thereby leading to a long data collection latency of each sensor. On the contrary, the mobile sink which applies the RMDC scheme does not need to pass through the transmission range of each sensor. Therefore, the waiting time for each sensor sending its readings to the mobile sink can be reduced significantly. Furthermore, by applying the RMDC scheme, the number of sensors which can directly communicate with the mobile sink is more than that by applying the approach presented in [10]. That is to say, by applying the RMDC scheme, the data-relaying workloads can be reduced, prolonging the network lifetime. As a result, the RMDC scheme also outperforms the existing mobile sink schemes [8–11].

The considered network environment is a circular monitoring region M which has been geographically partitioned into n circular tracks. In the proposed EBDC mechanism, the trajectory J min E B − T = ( x n min , x n − 1 min , … , x 1 min ) is scheduled by the proposed three-phase execution. Let t round EBDC denote the time duration of each round. For simplicity and without loss of generality, assume that the time duration for mobile sink traversing each track for one sweep repetition is set to t. The value of t round EBDC can be evaluated by Equation (27): (27) t round EBDC = x 1 min t + x 2 min t + … + x n − 1 min t + x n min t = t × ∑ i = 1 n x i min

Since the data-relaying workloads of all sensors can be balanced in each round, to simplify the analysis, the following discusses the energy consumption of the sensor, s_i ∈ S_n where S_n denotes the set of sensors located in the outmost (boundary) track k_n. Let e n total denote the total energy consumption required for any sensor belonging to set S_n in each round. According to Equation (24), the value of e n total can be calculated by the Equation (28): (28) e n total = e 1 < n x 1 min + e 2 < n x 2 min + … + e ( n − 1 ) < n x n − 1 min + e n = n x n min

Let e l . unit EBDC denote the energy consumption required for sensor s_l in each time unit. The e l . unit EBDC can be formulated by Equation (29): (29) e l . unit EBDC = e n total t round EBDC = e 1 < n x 1 min + e 2 < n x 2 min + … + e ( n − 1 ) < n x n − 1 min + e n = n x n min t × ∑ i = 1 n x i min

Since the energy consumption of sensor s_l can be derived by the total energy consumption in track k_n divided by the total number of sensors in track k_n, Equation (30) can be obtained by substituting Equations (20) and (23) into Equation (29): (30) e l . unit EBDC = ( E 1 < n x 1 min + E 2 < n x 2 min + … + E ( n − 1 ) < n x n − 1 min + E n = n x n min t × ∑ i = 1 n x i min ) ( 1 | S n | )

Furthermore, the total energy consumption in track k_n can be evaluated by the multiplication of the total number of packets and the energy consumption required for transmitting a packet, Equation (31) can be obtained by substituting Equations (19) and (22) into Equation (30): (31) e l . unit EBDC = ( P n 1 < n x 1 min + P n 2 < n x 2 min + … + P n ( n − 1 ) < n x n − 1 min + P n n = n x n min t × ∑ i = 1 n x i min ) ( e unit | S n | )

Since each sensor generates p packets in each time period t, based on the Equations (18) and (21), the e l . unit EBDC can be further derived by Equation (32): (32) e l . unit EBDC = ( x 1 min ∑ i = n n | S i | + x 2 min ∑ i = n n | S i | + … + x n − 1 min ∑ i = n n | S i | + x n min ∑ i = 1 n | S i | t × ∑ i = 1 n x i min ) ( p × e unit | S n | ) = ( | S n | x 1 min + | S n | x 2 min + … + | S n | x n − 1 min + x n min ∑ i = 1 n | S i | t × ∑ i = 1 n x i min ) ( p × e unit | S n | ) = ( ∑ j = 1 n − 1 x j min + x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min ) ( p × e unit t )

Equation (32) indicates that the energy consumption of sensor s_l∈S_n is highly impacted by the parameters, including the number of sweep repetitions performed by the mobile sink and the total number of sensors in each track.

On the other hand, the energy consumption of RMDC scheme is analyzed below. Recall that the key idea of RMDC scheme is that mobile sink moves along the boundary track of M for collecting data generated by all sensors in M. For simplicity, we discuss the energy consumption of sensor s_l that is located in the boundary track k_n. To facilitate the analysis, herein, the round of data collection in RMDC scheme is initially introduced. As shown in Figure 1, when a mobile sink completes the movement of boundary track k_n one sweep repetition in the clockwise direction, the mobile sink is said to move along the boundary of M in one round.

Let S denote the set of all sensors in M. Let S_n denote the set of boundary sensors, each of which can communicate with mobile sink when the sink passes through its transmission range. Since the mobile sink always moves along the boundary track k_n, only sensors belonging to set S_n are able to play the relay roles to deliver the data generated by the sensors belonging to sets S − S_n to mobile sink. Let P round RMDC denote the workloads of sensors belonging to set S_n by applying RMDC scheme. The value of P round RMDC can be evaluated by Equation (33): (33) P round RMDC = p × ∑ i = 1 n | S i |

Let E round RMDC denote the total energy consumption required for all sensors belonging to set S_n in each round. The value of E round RMDC can be calculated by Equation (34): (34) E round RMDC = P round RMDC × e unit

Let e l round denote the energy consumption of sensor s_l in each round. The value of e l round can be derived by Equation (35): (35) e l round = E round RMDC / | S n |

Assume that the time duration for mobile sink traversing track k_n for one sweep repetition is also set to t. The energy consumption e l . unit RMDC required for sensor s_l in each time unit can be estimated by Equation (36): (36) e l . unit RMDC = e l round t = E round RMDC | S n | × t = P round RMDC × e unit | S n | × t = p × ∑ i = 1 n | S i | × e unit | S n | × t = ( ∑ i = 1 n − 1 | S i | ) ( p × e unit t )

To compare the proposed EBDC mechanism with the existing RMDC scheme in terms of network lifetime, Equations (32) and (36) are further observed. It is obvious that the relations: (37) ∑ i = 1 n − 1 | S i | = ∑ i = 1 n − 1 | S i | × ∑ j = 1 n x j min ∑ j = 1 n x j min > x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j minand: (38) ∑ j = 1 n − 1 x j min + x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min > x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j minhold. For the ease of presentation, let: a = ∑ i = 1 n − 1 | S i | , b = ( ∑ j = 1 n − 1 x j min + x n min ∑ i = 1 n − 1 | S i | ) / ∑ j = 1 n x j min , and c = ( x n min ∑ i = 1 n − 1 | S i | ) / ∑ j = 1 n x j min .

Equation (39) can be obtained according to Equations (37) and (38) (39) a − c = ∑ i = 1 n − 1 | S i | − x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min = ∑ i = 1 n − 1 | S i | × ∑ j = 1 n x j min ∑ j = 1 n x j min − x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min = ∑ i = 1 n − 1 | S i | × ∑ j = 1 n − 1 x j min ∑ j = 1 n x j min > ∑ j = 1 n − 1 x j min ∑ j = 1 n x j min = ∑ j = 1 n − 1 x j min + x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min − x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min = b − c

As a result, we have a − c > b − c. That is to say, we have: (40) a > b ⇒ ∑ i = 1 n − 1 | S i | > ∑ j = 1 n − 1 x j min + x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min

Equation (40) indicates that the relation holds: e l . unit RMDC = ( ∑ i = 1 n − 1 | S i | ) ( p × e unit t ) = a ( p × e unit t ) > b ( p × e unit t ) = ( ∑ j = 1 n − 1 x j min + x n min ∑ i = 1 n − 1 | S i | ∑ j = 1 n x j min ) ( p × e unit t ) = e l . unit EBDC

This implies that the proposed EBDC mechanism outperforms the existing RMDC scheme in terms of network lifetime.

This section examines the performance improvement of the proposed EBDC mechanism compared with the Angle-based approach. Furthermore, the proposed EBDC mechanism is also compared with the existing approaches proposed by studies [6] and [11] which are referred to as Fixed and RMDC, respectively.

The Angle-based approach is a heuristic-based algorithm which initially partitions the circular monitoring region M into f = 360/g fans based on the angle g. These fans can be sequentially numbered from 1 to f in the clockwise direction. In general, the fans will be classified into two sets: odd and even sets. The odd set consists of fans numbered with odd numbers while the even set comprises the remaining fans numbered with even numbers. As shown in Figure 5(a,b), in the odd (even) round, the mobile sink traverses the edges of each fan belonging to the odd (even) set one by one in an increasing order of fan number.

The odd and even rounds will be applied by the mobile sink in turn until the energy of the mobile sink is exhausted. Herein, we assume that all sensors know the traverse rules as mentioned above and are able to estimate the current location of the mobile sink at any given time. The Fixed approach employs a fixed sink located at the central point of M to collect data while the RMDC approach uses a mobile sink moving along the boundary track of M to collect the readings as shown in Figure 1.

Table 3 gives the parameters used in our simulation. Each simulation result is obtained from the average of 100 independent runs and the 95% confidence interval is always smaller than 5% of the reported values. The following depicts the results of our performance evaluations.

Figure 6(a,b) compare the proposed EBDC mechanism with the Fixed, Angle-based, and RMDC approaches in terms of network lifetime. Herein, the network lifetime is measured by the time interval starting from the time that sensors have been deployed to the time that a coverage hole appears. The four mechanisms are compared by varying the number of sensors and data report time t in Figure 6(a,b), respectively.

As shown in Figure 6(a), since there is no sleep-wake scheduling mechanism applied to the WSN, all sensors should keep working on sensing and communication. Thus, the time that the first coverage hole appears does not change a lot in the four approaches compared. As a result, the network lifetimes of Fixed, Angle-based, RMDC, and the proposed EBDC approaches maintain constant curves. On the contrary, as shown in Figure 6(b), the network lifetimes of Fixed, Angle-based, RMDC, and the proposed EBDC approaches increase with the data report time t. This is because the lower value of data report time means that all sensors will report their readings more frequently, resulting in poor performances in terms of network lifetime.

Moreover, as shown in Figure 6(a,b), in the Fixed approach, the sink is fixed and thus the data-relaying workloads totally concentrate on a small number of sensors, leading to a poor network lifetime. As a result, the network lifetime of Fixed approach is much shorter than those of the Angle-based, RMDC, and EBDC approaches. In the RMDC approach, since the mobile sink always moves along the outmost (boundary) track, the number of sensors which can be visited by the mobile sink is smaller than those of Angle-based and EBDC approaches. Hence, the network lifetime of the RMDC approach is shorter than those of Angle-based and EBDC approaches. By applying the Angle-based approach, the mobile sink traverses the edges of each fan belonging to odd or even sets one by one, as shown in Figure 5(a,b), respectively. Therefore, the number of sensors which can be visited by the mobile sink is obviously larger than that of RMDC approach. Applying the proposed EBDC approach, the mobile sink moves with a well established schedule and hence the data-relaying workloads are shared by all sensors. Consequently, the performance of Angle-based is worse than EBDC. In general, as shown in Figure 6(a), the average network lifetime of the proposed EBDC mechanism is approximately five times longer than that of the Fixed approach, 1.6 times longer than that of the RMDC scheme, and 1.2 times longer than that of the Angle-based approach. On the other hand, as shown in Figure 6(b), the average network lifetime of the proposed EBDC mechanism is approximately three times longer than that of the Fixed approach, 2.2 times longer than that of the RMDC scheme, and 1.2 times longer than that of the Angle-based approach.

Figure 7 further measures the monitoring quality when the coverage hole appears. It compares the proposed EBDC, Angle-based, Fixed, and RMDC approaches in terms of the coverage ratio σ. Let A_cover denote the area size which is covered by sensors in the monitoring region. Let A_M denote the area size of the monitoring region. The coverage ratio σ can be formulated by the Expression (41): (41) σ = A cover / A M

The four approaches have 100% coverage ratio for 20 days starting from the day that the four approaches are applied. Since the data-relaying workload of the Fixed approach is totally shared by a small number of sensors, the curve of the Fixed approach drops earlier than the curves of the other compared schemes. The coverage ratio of RMDC approach is decreased with the elapsed days. In particular, it is interesting that the RMDC curve has a stair shape. This is because the mobile sink always moves along the boundary track (track k_n) of the monitoring region. Hence, the sensors located in the boundary track simultaneously exhaust their energies. As a result, the RMDC curve drops significantly. After that, the mobile sink will treat track k_n−1 as the new boundary track. The coverage ratio of the Angle-based approach is also decreased with the elapsed days. However, in the Angle-based approach, since the number of sensors which share the data-relaying workloads is larger than that of RMDC, the Angle-based curve drops slower than RMDC curve. In the proposed EBDC mechanism, the mobile sink moves along trajectory J min E B − T to collect data. As a result, the energy consumptions of all sensors can be balanced and thus the EBDC curve keeps a constant shape. In general, the proposed EBDC mechanism has either 0% or 100% coverage ratios.

Figure 8 compares the proposed EBDC, Angle-based, Fixed, and RMDC approaches in terms of the data report ratio ξ. Let p_success denote the number of packets which are successfully forwarded to the sink. Let P_total denote the total number of packets which are generated by all sensors. The data report ratio ξ can be formulated by the Expression (42): (3) ξ = p success / P total

In the Fixed approach, the neighboring sensors of the fixed sink will exhaust their energies prior to other sensors. Once these sensors fail, no sensor can directly communicate with the fixed sink, resulting in network partition. As a result, as shown in Figure 8, the Fixed curve sharply drops when the neighboring sensors of the fixed sink fail. The Angle-based, RMDC, and EBDC approaches employ mobile sink to collect data. By applying these three approaches, the readings generated by sensors can always be forwarded to mobile sink since these three schemes maintain the network connectivity using mobile sink. Consequently, the data report ratios of Angle-based, RMDC, and EBDC keep constant values. However, the proposed EBDC mechanism guarantees no coverage holes appeared in the monitoring region while the Angle-based and RMDC approaches result in coverage holes, as shown in Figure 7.

Figure 9(a,b) investigate the total energy consumptions required for sensors located in the boundary track (track k_n) and center track (track k₁), respectively. We randomly select a boundary sensor and a central sensor that are located in the boundary and center tracks, respectively, and then observe their energy consumptions.

The Fixed approach deploys a fixed sink located at the central point of the monitoring region. This implies that the selected boundary sensor only needs to deliver its reading to its neighbor without any packet forwarding workloads. Hence, as shown in Figure 9(a), the Fixed scheme has better performance than the other three compared approaches. However, as shown in Figure 9(b), the Fixed scheme has the worst performance since sensors closer to the fixed sink would have much higher data-relaying workloads. By applying the RMDC approach, the mobile sink always moves along the boundary track to collect data. Consequently, the boundary sensor has much higher data-relaying workloads while the central sensor only needs to deliver its reading without any packet forwarding workload. As a result, the RMDC has the best performance in Figure 9(b) and the worst performance in Figure 9(a). In the proposed EBDC and Angle-based approaches, both selected boundary and central sensors will be visited by mobile sink. Therefore, the performances of the proposed EBDC and Angle-based approaches in Figure 9(a,b) are between the Fixed and RMDC approaches. In particular, since the proposed EBDC mechanism takes into consideration the factor of energy balancing, the performance of EBDC is better than that of Angle-based scheme, as shown in Figure 9(a,b).

Figure 10 compares the proposed EBDC, Fixed, and RMDC approaches in terms of the degree of energy balancing. Without loss of generality, we investigate the average energy difference between the central and boundary sensors. The average energy differences of the Fixed and RMDC approaches are increased with the elapsed days. This is because the two sinks applying the Fixed and RMDC approaches execute the data collection task in the center and boundary tracks, respectively. The data-relaying workloads of Fixed and RMDC approaches are hence concentrated on the central and boundary sensors, respectively, leading to an energy-unbalance problem. In the proposed EBDC mechanism, the data-relaying workloads of all sensors can be totally balanced in each round. Therefore, as shown in Figure 10, the average energy difference of the proposed EBDC mechanism periodically drops to 0 Joule when the mobile sink completes the data collection task in each round. In general, the proposed EBDC mechanism outperforms the Fixed and RMDC schemes in terms of the degree of energy balancing in all cases.

Figure 11 further compares the proposed EBDC mechanism with the Angle-based approach in terms of the degree of energy balancing. The fan angle g of Angle-based approach is set to 10°, 30°, 60°, and 90°. Similar to Figure 10, we investigate the average energy difference between the randomly selected boundary and central sensors. In the Angle-based approach, the mobile sink traverses the edges of each fan starting form the center of the monitoring region. As shown in Figure 5(a,b), the central sensor will be visited when mobile sink completes the traverse of the edges of each fan. Therefore, as shown in Figure 11, the three Angle-based curves are increased with the elapsed days most of the time. In particular, the three curves drop only when the boundary sensor is visited by mobile sink. However, since the Angle-based approach does not consider the factor of energy balancing, the three Angle-based curves cannot drop to 0 Joule. On the contrary, the EBDC curve periodically drops to 0 Joule when mobile sink completes the data collection task in each round. In general, the proposed EBDC mechanism outperforms the Angle-based approach in terms of the degree of energy balancing in all cases.

This paper proposes an EBDC mechanism for mobile sinks to collect data generated by all sensors. Initially, the circular monitoring region is geographically partitioned into a number of circular tracks. Then, the mobile sink moves along the scheduled trajectory J min E B − T for data collection such that the energy consumptions of all sensors can totally be balanced. The proposed EBDC mechanism mainly consists of three phases: Initialization, Energy Estimation, and Trajectory Construction Phases. The Initialization Phase evaluates the number of sensors |S_i| in each track k_i while the Energy Estimation Phase derives the energy consumption required for each sensor when mobile sink traverses any track for one sweep repetition. Eventually, the Trajectory Construction Phase schedules the movement trajectory J min E B − T for mobile sink. When mobile sink completes the movement of trajectory J min E B − T in each round, the data-relaying workloads can be totally shared by all sensors. That is to say, the energy consumptions of all sensors can be balanced. Theoretical analysis and performance evaluation reveal that the proposed EBDC mechanism outperforms existing approaches in terms of network lifetime and the degree of energy balancing achieved.