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An energy-efficient path determination strategy for mobile data collectors in wireless sensor network
Computers and Electrical Engineering xxx (2015) xxx–xxx
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Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
An energy-efficient path determination strategy for mobile data collectors in wireless sensor network q Nimisha Ghosh ⇑, Indrajit Banerjee Department of Information Technology, Indian Institute of Engineering Science and Technology (Formerly BESUS), Shibpur, Howrah, West Bengal 711103, India
a r t i c l e
i n f o
Article history: Received 17 April 2015 Received in revised form 3 September 2015 Accepted 3 September 2015 Available online xxxx Keywords: Wireless Sensor Network (WSN) Mobile collector Sojourn points (SPs) Data collection Obstacles
a b s t r a c t In wireless sensor networks, introduction of mobility has been considered to be a good strategy to greatly reduce the energy dissipation of the static sensor nodes. This task is achieved by considering the path in which the mobile data collectors move to collect data from the sensors. In this work a data gathering approach is proposed in which some mobile collectors visit only certain sojourn points (SPs) or data collection points in place of all sensor nodes. The mobile collectors start out on their journey after gathering information about the network from the sink, gather data from the sensors and transfer the data to the sink. To address this problem, an algorithm named Mobile Collector Path Planning (MCPP) is proposed. MCPP schema is validated via computer simulation considering both obstacle free and obstacle-resisting network and based on metrics like energy consumption by the static sensor nodes and network life time. The simulation results show a reduction of about 12% in energy consumption and 15% improvement in network lifetime as compared with existing algorithms. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Wireless Sensor Networks (WSNs) are a popular source of data-collecting and sensing mechanism for a wide range of applications, such as military, agriculture, environment monitoring, smart transportation, and health [1]. Each sensor node collects data from the environment and forwards this sensed data to one or more sink nodes via a wireless link in either single-hop or multi-hop manner. This data-gathering and forwarding property of the sensor nodes dominate the main energy consumption factor of a network. These sensor nodes being equipped with low power batteries which may be difficult to replace, making it a major research area to design energy-efficient protocols [1]. Energy management in Wireless Sensor Networks (WSNs) is of paramount importance for the remotely deployed energy stringent sensor nodes [2]. Now, in multi-hop communications due to heavy overload of relaying messages, the nodes which are near a sink tend to die earlier than those which are farther away. This leads to the formation of energy hole in the network [3] resulting in the Hot-Spot problem [4,5]. As a result the sink loses connection with other nodes.
q
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⇑ Corresponding author. Tel.: +91 9874041577.
E-mail addresses: [email protected] (N. Ghosh), [email protected] (I. Banerjee). http://dx.doi.org/10.1016/j.compeleceng.2015.09.004 0045-7906/Ó 2015 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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To mitigate this problem, the concepts of mobile sink and mobile data collector were introduced. Luo and Hubaux [3] employs one or more mobile sinks to collect data directly from the sensor nodes. The mobile sinks move along the periphery thereby maximising the network lifetime. There are many ways in WSNs in which a mobile sink goes about collecting data from the sensor nodes. Ghafoor et al. [6] uses Hilbert Space Filling Curve to determine the trajectory of the mobile sink. One method is to visit each sensor node individually to collect the sensed data. This is the well-known travelling salesman problem (TSP). Kumar et al. models the tour of a mobile data collector (MDC) based on TSP and use Range Constrained Clustering to determine the stop points of the mobile collectors [7]. In this work, we have presented a new mechanism wherein some mobile collectors collect data from the static sensors based on the buffer overflow time of the sensors. Somasundara et al. [8] also uses sensors buffer overflow time to schedule the visit of a mobile element where single nodes are visited depending on the strictness of the deadline of the nodes as opposed to this work where the mobile collectors visit a cluster to collect the data from the sensors. This work presents some mobile collectors (which are equipped with powerful transceiver, battery and large memory) go around the network to collect data from the static sensor nodes by stopping at specific stop points in the network. The aim is to minimise the number of stop or sojourn points, while ensuring that all the sensors are covered. The mobile collectors start from the static data sink and ultimately transfer the data to the sink via a wireless link using either 802.15.4 or 802.11. E.g., 802.11n provides about 74–300 Mbps, with ranges of about 70–250 m [7]. A path is determined for each of the mobile collectors in which they will traverse. The buffer size of the sensors is the main contributing factor for determining this path. Based on the buffer overflow time of the sensors, the mobile collectors collect data from them. The novelty of this work lies in the fact that other than sensing, transmission and receiving of data in single-hop communication, the sensors are not involved in the determination of either the sojourn points or the obstacle avoiding path of the mobile collectors. This way the energy utilisation of the sensors are minimised. To the best of our knowledge none of the previous works have used this concept of energy optimisation in their work. Also, using sensor buffer to determine the trajectory of a mobile collector in the presence of obstacles is an area which is yet to be fully explored. The paper is thus summarised as follows: At first, some data collection points (sojourn points (SPs)) are determined where the mobile collector will stop during its journey to collect data. The motivation is to conserve energy which is lost due to multi-hop transmission of data from the sensors to the collector. The procedure is described later in Section 4. After the determination of the collection points, Mobile Collector Path Planning (MCPP) algorithm based on the buffer size of the sensors and the data collection capacity of the mobile collectors is proposed. More than one mobile collectors are employed for the data collection purpose. The path determination algorithm is considered for both obstacle-free and obstacle-resisting environment. Extensive simulations are carried out to verify the effectiveness of our proposed algorithm by comparing with other data-gathering algorithms. The rest of the paper is organised as follows: Section 2 discusses the related works done so far in this area. Section 3 gives the problem formulation for the proposed model. MCPP is presented in Section 4 along with the sojourn point determination. The simulation results are given Section 5. Finally, Section 6 concludes the paper.
2. Related study Mobility patterns can be categorised into the following [9]: (i) Random mobility, (ii) predictable mobility and (iii) controlled mobility. The different categories of mobility patterns indicate the variety of data collection protocols used in each case. Animal-based nodes are used in [10] to collect data in wild environment. This is an example of a random mobility pattern. In such a model it is extremely hard to control and predict the movement of the nodes. In [11] a predictable mobility model is introduced wherein sensor nodes know the path that will be used by the mobile sink and thus to save energy the nodes go into sleep mode until the predicted time for data transfer. After that, the sensor nodes regain their active mode and transfer data to the mobile sink. Gao et al. [12] use controlled mobility to propose a data collection scheme called the Maximum Amount Shortest Path (MASP) to improve the network lifetime by optimising the assignment of sensor nodes. Somasundara et al. [8] have also used controlled mobility. Based on the assumption that a mobile element visits each sensor node, a path planning for a mobile sink was formulated as the mobile element scheduling (MES) problem. The main drawback where a mobile element visits each sensor node to collect data is the increased delay in the data collection process as the mobile sink has to be within the transmission range of each sensor to collect data. [13] use a set of rendezvous points (RPs) to address this issue. These RPs buffer data from the static sensors and transfer them to the mobile element when they come in the RPs vicinity. An algorithm RD-VT is proposed in [14] with the objective that the travelling path of a mobile sink will be shorter in duration than that of the packet delivery time. Weighted Rendezvous Planning (WRP) is proposed in [13] to find a near-optimal trajectory path of
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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a sink node which minimises the energy consumption of sensor nodes. A cluster-based (CB) approach is proposed in [15] which uses binary search procedure to select RPs. Bi et al. [16] proposes an autonomous moving strategy wherein a mobile sink approaches the sensors with the highest residual energy and coaxes them to forward data from other nodes. Liu et al. [17] uses mobility-assisted data collection (MADC) schemes to collect data from the sensors. The behaviour of the mobile sinks is analysed based on throughput capacity and lifetime. In this model before the data is forwarded, each sensor determines a nearest rendezvous point (RP) and then selects a cache node which is at one-hop distance from the RP. Ma et al. [18] uses a mobile data collector, called M-collector, to gather data from the network. This M-collector starts on its journey from a static sink and polls each sensor while within its transmission range. Then it collects data from the sensors in a single-hop and finally forwards the data to the static sink. The paper focuses on minimising the trajectory of the mobile sink by formulating a single-hop data-gathering (SHDGP) problem. The authors in [19] use quad-tree based approach to divide the network for data collection by the mobile sinks. The path detection strategy by the mobile sinks detects all kinds of obstacles and create a path for the movement of the mobile sinks avoiding those obstacles. From the above discussions, we can see that to increase network lifetime it is necessary to use a mobile sink or mobile data collector in the network. Thus, in our work we have incorporated the concept of controlled mobility to determine the trajectory of a mobile collector. 3. Problem formulation A WSN is considered in which some mobile collectors will roam around the network to collect data from the static sensor nodes only when they reach the SPs. For instance let us take Fig. 1 which shows some feasible SPs of a mobile collector in an example WSN. The objective of this work is to determine the set of SPs and the way in which the mobile collectors will move to visit these SPs within a given time frame. This time frame will be the buffer overflow time (bot) of the static sensor nodes. The movement path of the mobile collectors will be calculated both in the presence and absence of obstacles. 3.1. Assumptions Before delving deep into the problem, we first outline some assumptions. 1. Each mobile collector has sufficient capacity to store all collected data. 2. The mobile collectors are aware of the location of each SP as they start on their journey after gathering the network information from the base station. 3. The mobile collectors move at a fixed speed v m . 4. The mobile collectors follow controlled mobility. 5. The sensor nodes are randomly deployed in a G G field and their location coordinates are known a priori. 6. Each sensor node produces one data packet with the length of b bits in a specific time interval. After each packet generation the sensors wait for a predetermined time period p before it generates its next round of data. 7. The sensor nodes have a specific buffer size bs. 8. The paths of the mobile collectors have been determined for the worst-case scenario. Thus, it is assumed that initially the buffer for all sensor nodes have already overflown.
Fig. 1. Example showing a mobile collector performing data collection in WSN.
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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3.2. Time bound movement path A mobile collector moves at a fixed speed v m and its total movement time is mct . The amount of time a mobile collector waits at a sojourn point to collect the entire data sensed by the sensors in that cluster is dct . Let sp and ep respectively be the start and end points of the travel path of the mobile collector. Thus the path L (v m mct ) that a mobile collector will cover is P P subjected to the conditions that sp ¼ ep and ni¼1 dcti þ ni¼1 mcti <¼ bot, where ‘n’ is the number of sojourn points visited by a mobile collector. To address the above problem, we need to consider the data collection and storage properties of sensors and mobile collector. Now the sensors collect data at regular intervals. After a sensor has sensed data, in each round it takes about T time for 1 byte of data to be written into EEPROM (Electrically Erasable Programmable Read Only Memory) [20]. Then it waits for p amount of time for its next round of data collection. So, the buffer overflow time (bot) of a sensor node is:
bot ¼ ðT þ pÞ bs
ð1Þ
Thus, this will be the buffer overflow time for all the sensors in the network. A mobile collector can move in any of the eight possible directions (i.e. North, South, East, West, North–East, North–West, South–East and South–West) from its current position. Now, the RF data rate between a static sensor node and a mobile collector is very high. So data receipt time from a sensor is considered to be negligible. But the controller has a certain baud rate which is equal to its bit rate (Dt ) (there being one bit per symbol). Then to collect 1 data packet from the sensor and store in its buffer, the mobile collector would require a time of Dbt , where b is the size of a data packet. Thus if a mobile collector wants to collect the entire data from all the sensors (ns ) (assuming their buffer is full) belonging to a particular sojourn point, the time required would be
dct ¼
b bs ns Dt b
ð2Þ
bs ns Dt
ð3Þ
which gives
dct ¼
Once a mobile collector reaches a sojourn point, it sends a signal to wake up the transceiver of the sensors in its transmission range (by using passive RFID device), gather data from them and once it leave the cluster puts them into sleep again. It is assumed that the sensors are equipped with passive radio frequency identification (RFID) device which get energy from the outside RF signal [18]. Considering all these parameters henceforth, in the following section we propose a novel approach to determine the movement path of the mobile collectors to collect data from the static sensor nodes. 4. Proposed algorithm The proposed algorithm is divided into two parts: (i) A network without obstacles and (ii) A network with obstacles. For both the aforementioned parts, sojourn point determination and mobile collector movement strategy are considered. 4.1. Network without obstacles 4.1.1. Sojourn point determination The determination of the collection or the sojourn points (SPs) is of major concern in a mobile collector environment. The motivation is to identify a set of points so that the sensor nodes in a cluster are within the transmission range of the SP and all the nodes in a network are covered by the mobile collectors. The determination of the SP is based on finding a circle that best fits a set of points [21]. The whole network is divided into triangles and the circumcenter of these triangles are taken to be the sojourn points for the mobile collectors. The sides of the triangles are calculated based on the transmission range of the sensors which is equal to the radius of the circumcircle as given in Fig. 2 according to
SideðSÞ ¼ Radius of circumcircleðRÞ
pffiffiffi 3
ð4Þ
The point O is the circumcenter or the sojourn point (SP). The main steps of the SP calculation are presented in Algorithm 1. Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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Algorithm 1. Sojourn point and the corresponding cluster determination.
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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Fig. 2. Calculation for determination of SP.
In Algorithm 1, xcðm; nÞ and ycðm; nÞ are the arrays to store the circumcenter (or the SPs) of the circles. Based on the circumcenters and circumradius, the circles are created. This circumradius gives the transmission range of a sensor. Then in lines 38–47 the sensors are assigned to the sojourn points. If a sensor has been already assigned to one sojourn point, it will not be considered for joining another SP (line 44). The number of sojourn points is dependent only on the network size G and not on the number of nodes. So, for the same network size even if the number of nodes are increased, the number of SP will remain the same. After the circumcenters or the sojourn points are determined the distance of each SP to each sensor is calculated according to the formula
di ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxsp xs Þ2 þ ðysp ys Þ2
ð5Þ
where xsp and ysp are the x-coordinate and y-coordinate respectively for the sojourn points, whereas xs and ys are the xcoordinate and y-coordinate, respectively for the sensor nodes. The number of sensors that are covered by a MC from a SP is considered to be a cluster and is determined by the count array (line 40). Fig. 3(a) shows the steps in the determination of the sojourn points produced by Algorithm 1. The examples show a 300 300 field with 200 randomly deployed nodes. To determine the SPs, in each row the circumcircles for every alternate triangle is taken. In this way all the sensors belong to some SPs or the other with minimal overlapping. As shown in Fig. 3(b) some sojourn points (marked in red1) fall outside the boundary of the grid. They are adjusted as in Fig. 3(c) and we get the final list of sojourn points and create the clusters accordingly based on transmission range of the sensors as given in Fig. 3(d). Once the sojourn point are determined and the clusters are formed, they are numbered in chronological fashion (as given in Fig. 3(d)). All the above mentioned procedures for cluster formation take place at the base station. The mobile collectors gather the cluster-id information from the base station and they send the respective cluster ids to the sensors when they visit the SPs to collect data. The sojourn point calculation takes OðG2 Þ time, where G is the grid size. To estimate the number of sensors belonging to each sojourn point, both number of sojourn points and the number of nodes have to be considered. This has been carried out in lines 38–46 which eventually take Oðno of sojourn points NÞ amount of time, where N is the number of sensor nodes. So, the overall complexity of Algorithm 1 is OðG2 Þ þ Oðno of sojourn points NÞ. 4.1.2. Mobile Collector Path Planning (MCPP) The path planning of a mobile collector will be based on the Eqs. (1) and (2) and the conditions sp ¼ ep and Pn Pn i¼1 dc t i þ i¼1 mct i <¼ bot. To determine a path for itself a mobile collector will initially follow a greedy approach. This is over, considering both the data collection and the movement time from approach will be followed till half of bot i.e. ðTþpÞbs 2 one SP to another. After this, a mobile collector will try to come back to its starting position without repeating any of the already traversed sojourn points. This should be done considering the fact that the overall bot is not exceeded. This is 1
For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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Fig. 3. Steps in the formation of cluster.
achieved by following depth first search. The final path thus formed represents a simple cycle. Once the path is determined using MCPP (Algorithm 2), a mobile collector will follow this path throughout the network lifetime.
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Algorithm 2. Mobile Collector Path Planning (MCPP).
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The algorithm shows how MCPP works. Initially, as input we need to provide the total buffer overflow time of the sensors and their buffer size. We also need to take the starting position id or the cluster ID of the mobile collector. From its current position a mobile collector can move to any of the eight possible directions. As the clusters are numbered, the direction values from the present cluster(cur pos id) in line 13 can be denoted by the following:
East ¼ cur pos id þ 1
ð6Þ
West ¼ cur pos id þ ð1Þ
ð7Þ
North ¼ cur pos id þ
G pffiffiffi 2 þ 1 R 3
G pffiffiffi 2 þ 1 South ¼ cur pos id þ R 3 North—East ¼ cur pos id þ
G pffiffiffi þ 1 R 3
North—West ¼ cur pos id þ
G pffiffiffi R 3
ð8Þ
ð9Þ
ð10Þ
ð11Þ
G pffiffiffi South—East ¼ cur pos id þ R 3
ð12Þ
G pffiffiffi þ 1 South—West ¼ cur pos id þ ð R 3
ð13Þ
Special considerations: 1. For the clusters on the left boundary, the value for the cluster number (cluster no) for the West direction is always set to 0. Otherwise it will give the last cluster number in the previous row. Similarly, for the clusters on 3(d), there is no cluster in the West direction for cluster no 14. Thus, if we use Eq. (7), the resultant cluster no will be 13 which is incorrect. l m l m G ffiffi G ffiffi p p þ 1 þ ðn 1Þ 2 þ 1 , where n ¼ 1; 2; . . . ; n, the cluster no in the 2. For the cluster numbered R 3 R 3 North—West and South—West directions are set to 0 for similar reasons. l m G ffiffi p 2 þ 1 , where n ¼ 1; 2; . . . ; n, the cluster no for North—East and South—East are 3. For the cluster numbered n R 3 also set to 0. For the cluster no thus found, the mobile collector moves towards the direction of that cluster which has the maximum number of sensors. During this journey the corresponding data collection time and the collector movement time also get calculated. Lines 8–27 in Algorithm 2 show this greedy approach calculation. This approach will continue till bot crosses 50% (line 28). The collector will then trace back to the point (xp ; yp ) where the bot was 650%. From this point the collector will make an attempt to move towards the starting position from where it embarked on its journey. To go back to the starting point (xp ; yp ) is thus taken as the source. From (xp ; yp ) a number of paths will lead to the starting point. The vertices on this path will be the neighbouring sojourn points of those sojourn points that were covered during the greedy approach. The data collection time and the collector movement time are assessed for each of these paths (similar to lines 11–12) and stored in path tot. Then the maximum path tot value which is less than or equal to left (Buffer overflow time – the amount of time spent in collection of data and mobile collector movement during greedy approach) is taken. The corresponding path with this value is considered to be the movement path of the mobile collector. So Algorithm 2 in its entirety gives the movement path of a mobile collector. Once all the sojourn points from one cluster to another is decided, the mobile collector will follow the following angle measurements for its movement:
hi ¼ 0
if xiþ1 > xi ; yiþ1 ¼ yi
hi ¼ 180
if xiþ1 < xi ; yiþ1 ¼ yi
hi ¼ 90
if xiþ1 ¼ xi ; yiþ1 > yi
hi ¼ 90
if xiþ1 ¼ xi ; yiþ1 < yi
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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Fig. 4. Mobile collector path planning with sensor buffer size = 2 KB.
yiþ1 yi xiþ1 xi y yi hi ¼ 180 arctan iþ1 xiþ1 xi yiþ1 yi hi ¼ 360 arctan xiþ1 xi yiþ1 yi hi ¼ 180 þ arctan xiþ1 xi hi ¼ arctan
if xiþ1 > xi ; yiþ1 > yi if xiþ1 < xi ; yiþ1 > yi if xiþ1 > xi ; yiþ1 < yi if xiþ1 < xi ; yiþ1 < yi
The angle of rotation is xi given by:
xi ¼ hi hi1
ð14Þ
where hi is the mobile collector’s next orientation, hi1 is the mobile collector’s present orientation, (xiþ1 ; yiþ1 ) is the next location of the sojourn point where the mobile collector will move, (xi ; yi ) is the current sojourn point of the mobile collector. Fig. 4 gives an instance of the MCPP algorithm. Now, a single mobile collector is not enough to achieve this goal. So, we require a specific number of mobile collectors. Lemma 1. If the number of sojourn points is n, then the number of mobile collectors is a function of the tour length of a mobile collector. Proof. Let the number of sojourn points be n. A mobile collector starts its journey from a corner sojourn point in the network. After the completion of its journey according to MCPP, its tour length (Lt ), in terms of hop count, is taken. Then, the number of mobile collectors will be equal to
Number of Mobile CollctorsðSn Þ ¼
n Lt
ð15Þ
While deciding on the number of mobile collectors, the four corner sojourn points of the network area are taken to be the initial starting points. Else, some corner points may remain unattended. Once these collectors complete their movement paths, to cover the rest of the network more collectors are employed starting along the periphery. This strategy is followed for the entire network. h 4.1.3. Analysis The time complexity of MCPP algorithm is mainly dictated by the greedy approach followed during the forward movement and the path created to go back to the starting position. The while loop for the forward movement condition is executed for fm times resulting in a time complexity of OðfmÞ. To find the cluster having the highest number of sensors, all the possible directions for the mobile collector movement have to be considered. This operation has a complexity of Oðnumber of directionsÞ. The number of directions in this case is 8. So, the overall time complexity for the forward movement Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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is Oðfm number of directionsÞ. To go back to the starting point using optimal path, depth first search is used amongst the neighbouring SPs of the initial paths to find out the possible paths. This operation takes OðV þ EÞ time where V is the number of sojourn points and E is the connecting edges between the sojourn points. Calculating the data collection time and movement time takes a total of OðcountÞ time. Finding the optimal path again takes a time of OðcountÞ. Thus, the total time complexity of MCPP algorithm is Oðfm number of directionsÞ þ OðV þ EÞ þ OðcountÞ þ OðcountÞ. But as the value of count is negligible as compared to the other parameters, so the time complexity amounts to Oðfm number of directionsÞ þ OðV þ EÞ. 4.2. Network with obstacles In a realistic environment, obstacles may be present in the sensing field and thus obstruct the motion of a collector. So, trajectory for a mobile collector in the presence of obstacles has been proposed in the following sections. 4.2.1. Sojourn point determination The procedure for the determination of sojourn point will remain the same. But if an obstacle falls on the circumcenter of an alternate triangle, the next triangle is taken such that all the sensors fall in some cluster as given in Fig. 5. 4.2.2. Mobile collector path planning The movement strategy of the mobile collector will be the same as that when there are no obstacles present in the network. But for planning its tour in the presence of obstacles, a mobile collector needs to know the position of obstacles. For this purpose, a mobile anchor node is introduced. The anchor node moves throughout the network according to [22]. Even though the position of an obstacle is known, there can be more than one obstacle in the network area. So, while deciding upon its movement, every time a mobile collector has to confirm which obstacle falls within its tour path. This can be done according to Eq. (16):
y y1 y1 y2 ¼ x x1 x1 x2
ð16Þ
Fig. 5. Sojourn point determination in the presence of obstacles.
Fig. 6. Obstacle detection calculation.
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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Here, ðx1 ; y1 Þ is the current position of the mobile collector, and ðx2 ; y2 Þ is the next SP where the collector will move. As the four corner coordinates of an obstacle are known, they are assigned to the ðx; yÞ variable to check if an obstacle falls within the movement path of a mobile collector. The Algorithm for obstacle avoidance is given in Algorithm 3. The description for Algorithm 3 is illustrated below with an example. In Fig. 6, the current position of mobile collector (cp mc) is (51.96, 175.37) and its next position (np mc) is (12.99, 181.86) which has been deduced according to Algorithm 2. The four coordinates (obs coord) of the obstacle are (17, 155), (42, 155), (42, 185) and (17, 185), respectively. So, to check if the obstacle falls within the point (C) and (D), the values of x; x1 ; y1 ; x2 ; y2 are assigned to Eq. (16) where x ¼ 42. The value of y evaluates to 177 which lies within 155 and 185, the two y coordinates of the obstacle. So it can be deduced that the obstacle falls within (C) and (D). Similarly, the other values are also assigned to check the position of the obstacle. If a straight line is drawn from (C) to (D), then it will meet the obstacle at the points (A) and (B) which have the values (17, 181.9) and (42, 177) thus confirming that the obstacle falls within (C) and (D). Now, to bypass the obstacle, the concepts of graph formation and Dijkstra’s shortest path algorithm are applied. The edges of the graph (G obs) are created by joining cp mc, the obstacle coordinates and np mc (they being the vertices of the graph) as given in Fig. 7. The diagonals of the obstacles are not considered as the mobile collectors cannot pass through an obstacle. Also, the edges which will not be a natural choice for the shortest path are also not taken into consideration. For example, in Fig. 7(b), the edge from vertex a to vertex h is not considered as either it will pass through the obstacle, or it will create a path which will not be a part during shortest path consideration. cp mc and np mc are connected to their nearby obstacle coordinates. The weights assigned to the edges of the graph are the Euclidean distances between the corresponding vertices. For more than one obstacle, their vertices are also connected to create G obs. After the formation of G obs, Dijkstra’s shortest path algorithm, which is an optimal greedy approach, is applied on the graph to determine the detour path of the mobile collector as shown in Fig. 8. So, whenever an obstacle will be found, a mobile collector will bypass it according to Algorithm 3. Algorithm 3 works well even if there are more than one obstacle in the path of a mobile collector. Algorithm 3. Obstacle avoidance for mobile collector.
The final tour of the mobile collectors is depicted in Fig. 9.
Fig. 7. Graph for obstacle avoidance.
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Theorem 2. The algorithm for obstacle avoidance has a time complexity of Oðm2 Þ, where m is the number of obstacles. Proof. In line 2 of Algorithm 3, drawing a straight line from the current position to the destination takes constant amount of time. Thus, the operation is executed in Oð1Þ time. To ensure the presence of obstacles, their four coordinates (4 m) have to be checked according to Eq. (16), which takes OðmÞ time. In line 9, the graph constructed for obstacle avoidance in the worst case will have nðn1Þ edges, where n is the number of vertices of the graph. Now, the number of vertices in Gobs is 4m þ 2 as is 2 can be rewritten as ð4mþ2Þð4mþ1Þ . Thus, construction of graph takes Oðm2 Þ time. Running Dijkstra’s evident from Fig. 8. So, nðn1Þ 2 2 shortest path algorithm on a graph with (4m + 2) vertices takes Oðð4m þ 2Þ2 Þ time which is equivalent to Oðm2 Þ. So, the overall complexity of the Algorithm is Oðm2 Þ. h 5. Performance evaluation Performance evaluation of the proposed schema has been carried out for both obstacle-free and obstacle-resisting environments. We consider a network area where sensor nodes are placed uniformly in a field of size 300 300 m2. As shown in Fig. 9, two obstacles of size 25 30 m2 are placed in the sensing field. To measure the network lifetime, it has been assumed that all sensor nodes have a fully charged battery with 6300V 0 J of energy, which corresponds to a standard rechargeable battery with a capacity of 1750 mA h [17]. Here, V 0 is the voltage of the battery. The experiments have been performed with a data transmission rate of 250 Kbps and assuming a periodicity (p) of 95 ms. The rate of storing data in micro-controller is 9600 bps. The sensors are assumed to hold 2 KB of data. The speed of mobile collector is 2 m/s. The current consumption is 23 mA at both the transmitter and the receiver. The current consumption in the sleep mode is 1 lA. All the parameters are in accordance with the datasheet of TelosB [23]. 5.1. Performance in obstacle-free environment Simulation results for the number of mobile collectors for a transmission range of 30 m is depicted in Fig. 10. The number of nodes are set to 200, 400 and 600. The area of the sensing field varies from 100 100 m to 500 500 m. As
Fig. 8. Detour path of mobile collector based on shortest-path.
Fig. 9. Mobile collector path planning in the presence of obstacles.
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Fig. 10. Number of mobile collectors.
Fig. 11. Average energy consumption during sleep and data transmission phases.
Fig. 12. Comparison for network energy consumption.
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the transmission range is fixed, the number of mobile collectors depend on the monitoring area and the number of sensors in each cluster. This is a determining factor for the final tour length of each mobile collector. The number of mobile collectors may increase or decrease with increasing area of the network based on the number of sensors falling in each cluster. The average energy consumption during sleep and data transmission phase is depicted in Fig. 11. The amount of energy consumed during sleep phase (Es ) of the sensors is much less as compared to when they are transmitting data (Et ) to the mobile collectors. This is because a sensor consumes only 1 lA of energy during sleep cycle. For this result, we have considered the worst case scenario of buffer overflow. As the paths for the mobile collectors have been determined based on the assumption that all the sensors are sensing data, so even if one node runs out of energy then the path will get altered. So, in this work Network lifetime is defined as the number of rounds till the first node in the network runs out of energy. As mobile sinks and mobile data collectors behave in a similar way, we have compared our work with other those who have considered mobile sinks for data collection. Fig. 12 shows the energy consumption comparison of our proposed algorithm (MCPP) with weighted rendezvous planning (WRP) [13], Cluter-based (CB) [15], rendezvous design for variable tracks (RD-VT) [14] and rendezvous planning utility-based greedy (RP-UG) [24] algorithms. The network parameters are according to [13]. RD-VT has the highest amount of energy consumption due to the fact that it has long data forwarding paths from the sensor nodes to the rendezvous points (RP). CB shows better performance than RD-VT because it replaces the selected RP in each cluster with a node closer to the cluster head. This is done to reduce the number of multi-hop transmissions showing a 28% reduction in the amount of energy consumption. WRP considers node density and hop counts when selecting RPs. This
Fig. 13. Comparison for network lifetime.
Fig. 14. Comparison for network lifetime.
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causes a 10% reduction in energy consumption when compared to CB. As compared to WRP, MCPP achieves almost 12% reduction in energy consumption due to the fact that MCPP does not involve multi-hop transmission of data. Energy loss is attributed to only single-hop transmission of data. In sleep mode, the consume very meagre amount of energy. All the experiments have been conducted with a confidence interval of 95% and taking a sample size of 30. Fig. 13 shows the network lifetime comparison of MCPP with WRP, CB, RD-VT and RP-UG. MCPP improves network lifetime by 15% as compared to WRP. CB causes non-uniform energy consumption due to random cluster-head selection process. In RD-VT, long forwarding paths get created from the static sensor nodes to the RPs resulting in non-uniform energy consumption. Thus compared to CB, it has a 25% reduction in lifetime. In Fig. 14, comparison of network lifetime is performed with some other popular methods of sink movement. The network parameters are based on [16]. The result shows an improvement of about 18% when compared to half-quadrant-based moving strategy (HUMS) [16]. With the increase in the density of the sensor nodes, the network lifetime decreases. This is quite expected as more number of sensors will result in faster energy depletion of the network. But all the algorithms with sink mobility fare better than that with a stationary sink. Network lifetime comparison for Path Discovery for Sinks Mobility (PDSM) [19], Maximum Amount Shortest Path (MASP) [12], Static Sink and MCPP is given in Fig. 15. An improvement of 25% is noted because of the single-hop transmission of data and the incorporated duty-cycle. Thus much less amount of energy gets consumed. The number of mobile collectors do not have any effect on the energy consumption of the sensor nodes in our algorithm because it has been assumed that the mobile collectors have infinite power supply.
Fig. 15. Network life time in obstacle free environment.
Fig. 16. Path length comparison in the presence and absence of obstacles.
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5.2. Performance in obstacle-resisting environment Two obstacles of size 25 m 30 m are placed at random positions in the network for the simulation and comparison purposes. However, the algorithm will work for obstacles of any size. Fig. 16 shows the maximum path length (in metre) of a mobile collector in an obstacle-free and resisting environment. There are more than one mobile collector involved in our proposed algorithm. The figure depicts the maximum path length amongst all the travel distances for all mobile collectors involved. The path length depends on the number of sensors in each cluster and the time taken to travel between each cluster, so the change in the tour length is not proportional to the increasing number of sensors. As can be seen from the figure, in some cases maximum tour length on obstacle-free and obstacle-resisting environment are the same. This is attributed to the fact an obstacle may not fall in the path taken by a mobile collector, thus keeping the tour length same. As in obstacle-free environment, the amount of energy consumed during sleep phase (Es ) of the sensors is much less as compared to when they are transmitting data (Et ) to the mobile collectors as given in Fig. 17. But as can be observed from the figure, though Et values are same for both obstacle-free and obstacle-resisting cases, but Es is a bit higher in the latter case. This is because due to the presence of obstacles in some scenarios, the mobile collectors have to make a detour to reach a sojourn point. So, some sensors will be in a longer sleep cycle than the others. Fig. 18 shows the average latency of the mobile collectors in an obstacle-free and resisting environment. The mobile collectors when move at a faster speed it can cover the sojourn points faster resulting in lower latency. As expected, the average
Fig. 17. Average energy consumption during sleep and data transmission phases.
Fig. 18. Average latency of mobile collectors in obstacle-free and obstacle-resisting environment.
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Fig. 19. Network life time in obstacle resisting environment.
latency is a bit higher for obstacle resisting environment. For 0.5 m/s the latency evaluates to almost 126 s for obstacle-free environment and 129 s for obstacle resisting environment. These are acceptable latency for detection of forest fire [25]. One may argue that the latency can be reduced by considering multi-hop communication. But in that case energy depletion will be much faster. This work shows a trade-off between latency and energy consumption by considering multiple mobile sinks. Network lifetime and energy consumption comparison between our proposed scheme and other mobile collector based data collection schemes in obstacle resisting environment are illustrated in Fig. 19. Our algorithm performs well because of the fact that the sensors are not involved in the obstacle detection or avoidance scheme in any way, thus enhancing the network lifetime. Thus both in the presence and in the absence of obstacles, the performance of MCPP is almost similar except for the fact the energy consumed during sleep phase is a bit more than that in obstacle-free environment. 6. Conclusion This paper presents MCPP which is used for controlling mobile collector movement in WSN. By introducing a mobile collector, data collection becomes more flexible and adaptable to the unexpected changes in the network. The paper determines the path of certain mobile collectors so that the full network is covered while ensuring data is collected before the sensors’ buffer overflow. Some stop points are calculated where the mobile collectors waits to collect data from the sensors. The determination of these points has a time complexity of OðG2 Þ þ Oðno of sojourn points NÞ, where N is the total number of random deployed sensors. To create the paths an obstacle-free environment is initially considered. We have shown that the time needed to execute the algorithm is Oðfm number of directionsÞ þ OðV þ EÞ. Angle of rotation has also been calculated to show how a mobile collector will actually move to reach its next position. As the mobile collectors collect data from the sensors in a single-hop, significant amount of energy is conserved. Preservation of energy is further aided by the dutycycling scheme adopted by the sensors. The simulation results corroborates this claim and shows an improvement of about 15% in network lifetime. Furthermore, for a more realistic scenario, an obstacle-resisting approach is also used in this work. A very simple obstacle-avoidance method for path determination has been proposed with a time complexity of Oðm2 Þ; m being the number of obstacles. As with obstacle-free network, this environment also shows a noteworthy improvement in network lifetime. Acknowledgment This work has been supported by UGC project, order no:F.No: 42-146/2013(SR). We would like to thank Prof. Sajal K. Das, Department of Computer Science, Missouri University of Science and Technology, Rolla, USA for his immense help and support in this work. References [1] Akyildiz IF, Su Weilian, Sankarasubramaniam Y, Cayirci E. A survey on sensor networks. IEEE Commun Mag 2002;40(8):102–14. [2] Khan Junaid Ahmed, Qureshi Hassaan Khaliq, Iqbal Adnan. Energy management in wireless sensor networks: a survey. Comput Electr Eng 2015;41:159–76.
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[3] Luo Jun, Hubaux J-P. Joint mobility and routing for lifetime elongation in wireless sensor networks. In: INFOCOM 2005. 24th annual joint conference of the IEEE computer and communications societies. Proceedings IEEE. vol. 3; March 2005. p. 1735–46. [4] Ghosh N, Banerjee I, Samanta T. Energy efficient coverage of static sensor nodes deciding on mobile sink movements using game theory. In: Applications and Innovations in Mobile Computing (AIMoC), Feb 2014; 2014. p. 118–25. [5] Ghosh N, Roy SK, Samanta T, Banerjee I. Path determination algorithm of mobile sinks for energy efficient data collection and optimal coverage in wireless sensor network. In: International Conference on Information Technology (ICIT), Dec 2014; 2014. p. 76–81. [6] Ghafoor Saim, Rehmani Mubashir Husain, Cho Sunghyun, Park Sung-Han. An efficient trajectory design for mobile sink in a wireless sensor network. Comput Electr Eng 2014;40(7):2089–100. [7] Kumar AK, Sivalingam KM. Energy-efficient mobile data collection in wireless sensor networks with delay reduction using wireless communication. In: Second international conference on Communication Systems and Networks (COMSNETS), Jan 2010; 2010. p. 1–10. [8] Somasundara AA, Ramamoorthy A, Srivastava MB. Mobile element scheduling with dynamic deadlines. IEEE Trans Mob Comput 2007;6(4):395–410. [9] Chatzigiannakis Ioannis, Kinalis Athanasios, Nikoletseas Sotiris. Sink mobility protocols for data collection in wireless sensor networks. In: Proceedings of the 4th ACM international workshop on mobility management and wireless access, MobiWac ’06. New York (NY, USA): ACM; 2006. p. 52–9. [10] Juang Philo, Oki Hidekazu, Wang Yong, Martonosi Margaret, Peh Li Shiuan, Rubenstein Daniel. Energy-efficient computing for wildlife tracking: design tradeoffs and early experiences with Zebranet. In: Proceedings of the 10th international conference on architectural support for programming languages and operating systems, ASPLOS X. New York (NY, USA): ACM; 2002. p. 96–107. [11] Chakrabarti Arnab, Sabharwal Ashutosh, Aazhang Behnaam. Using predictable observer mobility for power efficient design of sensor networks. In: Proceedings of the 2nd international conference on information processing in sensor networks, IPSN’03. Berlin, Heidelberg: Springer-Verlag; 2003. p. 129–45. [12] Gao Shuai, Zhang Hongke, Das Sajal K. Efficient data collection in wireless sensor networks with path-constrained mobile sinks. IEEE Trans Mob Comput 2011;10(4):592–608. [13] Salarian H, Chin Kwan-Wu, Naghdy F. An energy-efficient mobile-sink path selection strategy for wireless sensor networks. IEEE Trans Veh Technol 2014;63(5):2407–19. [14] Xing Guoliang, Wang Tian, Jia Weijia, Li Minming. Rendezvous design algorithms for wireless sensor networks with a mobile base station. In: Proceedings of the 9th ACM international symposium on mobile ad hoc networking and computing, MobiHoc ’08. New York (NY, USA): ACM; 2008. p. 231–40. [15] Almi’ani K, Viglas A, Libman L. Energy-efficient data gathering with tour length-constrained mobile elements in wireless sensor networks. In: IEEE 35th conference on Local Computer Networks (LCN), Oct 2010; 2010. p. 582–9. [16] Bi Yanzhong, Sun Limin, Ma Jian, Li Na, Khan ImranAli, Chen Canfeng. Hums: an autonomous moving strategy for mobile sinks in data-gathering sensor networks. EURASIP J Wirel Commun Netw 2007;2007(1). [17] Liu Wang, Lu Kejie, Wang Jianping, Xing Guoliang, Huang Liusheng. Performance analysis of wireless sensor networks with mobile sinks. IEEE Trans Veh Technol 2012;61(6):2777–88. [18] Ma Ming, Yang Yuanyuan, Zhao Miao. Tour planning for mobile data-gathering mechanisms in wireless sensor networks. IEEE Trans Veh Technol 2013;62(4):1472–83. [19] Chanak Prasenjit, Banerjee Indrajit. Path discovery for sinks mobility in obstacle resisting wsns. In: Advanced computing, networking and informatics – volume 2. Smart Innov Syst Technol, vol. 28. Springer International Publishing; 2014. p. 39–50. [20] Datasheet for 1024 i2 ct m cmos serial eeprom. [21] Maisonobe L. Finding the circle that best fits a set of points; Oct 2007. Available from:
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Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
An energy-efficient path determination strategy for mobile data collectors in wireless sensor network q Nimisha Ghosh ⇑, Indrajit Banerjee Department of Information Technology, Indian Institute of Engineering Science and Technology (Formerly BESUS), Shibpur, Howrah, West Bengal 711103, India
a r t i c l e
i n f o
Article history: Received 17 April 2015 Received in revised form 3 September 2015 Accepted 3 September 2015 Available online xxxx Keywords: Wireless Sensor Network (WSN) Mobile collector Sojourn points (SPs) Data collection Obstacles
a b s t r a c t In wireless sensor networks, introduction of mobility has been considered to be a good strategy to greatly reduce the energy dissipation of the static sensor nodes. This task is achieved by considering the path in which the mobile data collectors move to collect data from the sensors. In this work a data gathering approach is proposed in which some mobile collectors visit only certain sojourn points (SPs) or data collection points in place of all sensor nodes. The mobile collectors start out on their journey after gathering information about the network from the sink, gather data from the sensors and transfer the data to the sink. To address this problem, an algorithm named Mobile Collector Path Planning (MCPP) is proposed. MCPP schema is validated via computer simulation considering both obstacle free and obstacle-resisting network and based on metrics like energy consumption by the static sensor nodes and network life time. The simulation results show a reduction of about 12% in energy consumption and 15% improvement in network lifetime as compared with existing algorithms. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Wireless Sensor Networks (WSNs) are a popular source of data-collecting and sensing mechanism for a wide range of applications, such as military, agriculture, environment monitoring, smart transportation, and health [1]. Each sensor node collects data from the environment and forwards this sensed data to one or more sink nodes via a wireless link in either single-hop or multi-hop manner. This data-gathering and forwarding property of the sensor nodes dominate the main energy consumption factor of a network. These sensor nodes being equipped with low power batteries which may be difficult to replace, making it a major research area to design energy-efficient protocols [1]. Energy management in Wireless Sensor Networks (WSNs) is of paramount importance for the remotely deployed energy stringent sensor nodes [2]. Now, in multi-hop communications due to heavy overload of relaying messages, the nodes which are near a sink tend to die earlier than those which are farther away. This leads to the formation of energy hole in the network [3] resulting in the Hot-Spot problem [4,5]. As a result the sink loses connection with other nodes.
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E-mail addresses: [email protected] (N. Ghosh), [email protected] (I. Banerjee). http://dx.doi.org/10.1016/j.compeleceng.2015.09.004 0045-7906/Ó 2015 Elsevier Ltd. All rights reserved.
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To mitigate this problem, the concepts of mobile sink and mobile data collector were introduced. Luo and Hubaux [3] employs one or more mobile sinks to collect data directly from the sensor nodes. The mobile sinks move along the periphery thereby maximising the network lifetime. There are many ways in WSNs in which a mobile sink goes about collecting data from the sensor nodes. Ghafoor et al. [6] uses Hilbert Space Filling Curve to determine the trajectory of the mobile sink. One method is to visit each sensor node individually to collect the sensed data. This is the well-known travelling salesman problem (TSP). Kumar et al. models the tour of a mobile data collector (MDC) based on TSP and use Range Constrained Clustering to determine the stop points of the mobile collectors [7]. In this work, we have presented a new mechanism wherein some mobile collectors collect data from the static sensors based on the buffer overflow time of the sensors. Somasundara et al. [8] also uses sensors buffer overflow time to schedule the visit of a mobile element where single nodes are visited depending on the strictness of the deadline of the nodes as opposed to this work where the mobile collectors visit a cluster to collect the data from the sensors. This work presents some mobile collectors (which are equipped with powerful transceiver, battery and large memory) go around the network to collect data from the static sensor nodes by stopping at specific stop points in the network. The aim is to minimise the number of stop or sojourn points, while ensuring that all the sensors are covered. The mobile collectors start from the static data sink and ultimately transfer the data to the sink via a wireless link using either 802.15.4 or 802.11. E.g., 802.11n provides about 74–300 Mbps, with ranges of about 70–250 m [7]. A path is determined for each of the mobile collectors in which they will traverse. The buffer size of the sensors is the main contributing factor for determining this path. Based on the buffer overflow time of the sensors, the mobile collectors collect data from them. The novelty of this work lies in the fact that other than sensing, transmission and receiving of data in single-hop communication, the sensors are not involved in the determination of either the sojourn points or the obstacle avoiding path of the mobile collectors. This way the energy utilisation of the sensors are minimised. To the best of our knowledge none of the previous works have used this concept of energy optimisation in their work. Also, using sensor buffer to determine the trajectory of a mobile collector in the presence of obstacles is an area which is yet to be fully explored. The paper is thus summarised as follows: At first, some data collection points (sojourn points (SPs)) are determined where the mobile collector will stop during its journey to collect data. The motivation is to conserve energy which is lost due to multi-hop transmission of data from the sensors to the collector. The procedure is described later in Section 4. After the determination of the collection points, Mobile Collector Path Planning (MCPP) algorithm based on the buffer size of the sensors and the data collection capacity of the mobile collectors is proposed. More than one mobile collectors are employed for the data collection purpose. The path determination algorithm is considered for both obstacle-free and obstacle-resisting environment. Extensive simulations are carried out to verify the effectiveness of our proposed algorithm by comparing with other data-gathering algorithms. The rest of the paper is organised as follows: Section 2 discusses the related works done so far in this area. Section 3 gives the problem formulation for the proposed model. MCPP is presented in Section 4 along with the sojourn point determination. The simulation results are given Section 5. Finally, Section 6 concludes the paper.
2. Related study Mobility patterns can be categorised into the following [9]: (i) Random mobility, (ii) predictable mobility and (iii) controlled mobility. The different categories of mobility patterns indicate the variety of data collection protocols used in each case. Animal-based nodes are used in [10] to collect data in wild environment. This is an example of a random mobility pattern. In such a model it is extremely hard to control and predict the movement of the nodes. In [11] a predictable mobility model is introduced wherein sensor nodes know the path that will be used by the mobile sink and thus to save energy the nodes go into sleep mode until the predicted time for data transfer. After that, the sensor nodes regain their active mode and transfer data to the mobile sink. Gao et al. [12] use controlled mobility to propose a data collection scheme called the Maximum Amount Shortest Path (MASP) to improve the network lifetime by optimising the assignment of sensor nodes. Somasundara et al. [8] have also used controlled mobility. Based on the assumption that a mobile element visits each sensor node, a path planning for a mobile sink was formulated as the mobile element scheduling (MES) problem. The main drawback where a mobile element visits each sensor node to collect data is the increased delay in the data collection process as the mobile sink has to be within the transmission range of each sensor to collect data. [13] use a set of rendezvous points (RPs) to address this issue. These RPs buffer data from the static sensors and transfer them to the mobile element when they come in the RPs vicinity. An algorithm RD-VT is proposed in [14] with the objective that the travelling path of a mobile sink will be shorter in duration than that of the packet delivery time. Weighted Rendezvous Planning (WRP) is proposed in [13] to find a near-optimal trajectory path of
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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a sink node which minimises the energy consumption of sensor nodes. A cluster-based (CB) approach is proposed in [15] which uses binary search procedure to select RPs. Bi et al. [16] proposes an autonomous moving strategy wherein a mobile sink approaches the sensors with the highest residual energy and coaxes them to forward data from other nodes. Liu et al. [17] uses mobility-assisted data collection (MADC) schemes to collect data from the sensors. The behaviour of the mobile sinks is analysed based on throughput capacity and lifetime. In this model before the data is forwarded, each sensor determines a nearest rendezvous point (RP) and then selects a cache node which is at one-hop distance from the RP. Ma et al. [18] uses a mobile data collector, called M-collector, to gather data from the network. This M-collector starts on its journey from a static sink and polls each sensor while within its transmission range. Then it collects data from the sensors in a single-hop and finally forwards the data to the static sink. The paper focuses on minimising the trajectory of the mobile sink by formulating a single-hop data-gathering (SHDGP) problem. The authors in [19] use quad-tree based approach to divide the network for data collection by the mobile sinks. The path detection strategy by the mobile sinks detects all kinds of obstacles and create a path for the movement of the mobile sinks avoiding those obstacles. From the above discussions, we can see that to increase network lifetime it is necessary to use a mobile sink or mobile data collector in the network. Thus, in our work we have incorporated the concept of controlled mobility to determine the trajectory of a mobile collector. 3. Problem formulation A WSN is considered in which some mobile collectors will roam around the network to collect data from the static sensor nodes only when they reach the SPs. For instance let us take Fig. 1 which shows some feasible SPs of a mobile collector in an example WSN. The objective of this work is to determine the set of SPs and the way in which the mobile collectors will move to visit these SPs within a given time frame. This time frame will be the buffer overflow time (bot) of the static sensor nodes. The movement path of the mobile collectors will be calculated both in the presence and absence of obstacles. 3.1. Assumptions Before delving deep into the problem, we first outline some assumptions. 1. Each mobile collector has sufficient capacity to store all collected data. 2. The mobile collectors are aware of the location of each SP as they start on their journey after gathering the network information from the base station. 3. The mobile collectors move at a fixed speed v m . 4. The mobile collectors follow controlled mobility. 5. The sensor nodes are randomly deployed in a G G field and their location coordinates are known a priori. 6. Each sensor node produces one data packet with the length of b bits in a specific time interval. After each packet generation the sensors wait for a predetermined time period p before it generates its next round of data. 7. The sensor nodes have a specific buffer size bs. 8. The paths of the mobile collectors have been determined for the worst-case scenario. Thus, it is assumed that initially the buffer for all sensor nodes have already overflown.
Fig. 1. Example showing a mobile collector performing data collection in WSN.
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3.2. Time bound movement path A mobile collector moves at a fixed speed v m and its total movement time is mct . The amount of time a mobile collector waits at a sojourn point to collect the entire data sensed by the sensors in that cluster is dct . Let sp and ep respectively be the start and end points of the travel path of the mobile collector. Thus the path L (v m mct ) that a mobile collector will cover is P P subjected to the conditions that sp ¼ ep and ni¼1 dcti þ ni¼1 mcti <¼ bot, where ‘n’ is the number of sojourn points visited by a mobile collector. To address the above problem, we need to consider the data collection and storage properties of sensors and mobile collector. Now the sensors collect data at regular intervals. After a sensor has sensed data, in each round it takes about T time for 1 byte of data to be written into EEPROM (Electrically Erasable Programmable Read Only Memory) [20]. Then it waits for p amount of time for its next round of data collection. So, the buffer overflow time (bot) of a sensor node is:
bot ¼ ðT þ pÞ bs
ð1Þ
Thus, this will be the buffer overflow time for all the sensors in the network. A mobile collector can move in any of the eight possible directions (i.e. North, South, East, West, North–East, North–West, South–East and South–West) from its current position. Now, the RF data rate between a static sensor node and a mobile collector is very high. So data receipt time from a sensor is considered to be negligible. But the controller has a certain baud rate which is equal to its bit rate (Dt ) (there being one bit per symbol). Then to collect 1 data packet from the sensor and store in its buffer, the mobile collector would require a time of Dbt , where b is the size of a data packet. Thus if a mobile collector wants to collect the entire data from all the sensors (ns ) (assuming their buffer is full) belonging to a particular sojourn point, the time required would be
dct ¼
b bs ns Dt b
ð2Þ
bs ns Dt
ð3Þ
which gives
dct ¼
Once a mobile collector reaches a sojourn point, it sends a signal to wake up the transceiver of the sensors in its transmission range (by using passive RFID device), gather data from them and once it leave the cluster puts them into sleep again. It is assumed that the sensors are equipped with passive radio frequency identification (RFID) device which get energy from the outside RF signal [18]. Considering all these parameters henceforth, in the following section we propose a novel approach to determine the movement path of the mobile collectors to collect data from the static sensor nodes. 4. Proposed algorithm The proposed algorithm is divided into two parts: (i) A network without obstacles and (ii) A network with obstacles. For both the aforementioned parts, sojourn point determination and mobile collector movement strategy are considered. 4.1. Network without obstacles 4.1.1. Sojourn point determination The determination of the collection or the sojourn points (SPs) is of major concern in a mobile collector environment. The motivation is to identify a set of points so that the sensor nodes in a cluster are within the transmission range of the SP and all the nodes in a network are covered by the mobile collectors. The determination of the SP is based on finding a circle that best fits a set of points [21]. The whole network is divided into triangles and the circumcenter of these triangles are taken to be the sojourn points for the mobile collectors. The sides of the triangles are calculated based on the transmission range of the sensors which is equal to the radius of the circumcircle as given in Fig. 2 according to
SideðSÞ ¼ Radius of circumcircleðRÞ
pffiffiffi 3
ð4Þ
The point O is the circumcenter or the sojourn point (SP). The main steps of the SP calculation are presented in Algorithm 1. Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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Algorithm 1. Sojourn point and the corresponding cluster determination.
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Fig. 2. Calculation for determination of SP.
In Algorithm 1, xcðm; nÞ and ycðm; nÞ are the arrays to store the circumcenter (or the SPs) of the circles. Based on the circumcenters and circumradius, the circles are created. This circumradius gives the transmission range of a sensor. Then in lines 38–47 the sensors are assigned to the sojourn points. If a sensor has been already assigned to one sojourn point, it will not be considered for joining another SP (line 44). The number of sojourn points is dependent only on the network size G and not on the number of nodes. So, for the same network size even if the number of nodes are increased, the number of SP will remain the same. After the circumcenters or the sojourn points are determined the distance of each SP to each sensor is calculated according to the formula
di ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxsp xs Þ2 þ ðysp ys Þ2
ð5Þ
where xsp and ysp are the x-coordinate and y-coordinate respectively for the sojourn points, whereas xs and ys are the xcoordinate and y-coordinate, respectively for the sensor nodes. The number of sensors that are covered by a MC from a SP is considered to be a cluster and is determined by the count array (line 40). Fig. 3(a) shows the steps in the determination of the sojourn points produced by Algorithm 1. The examples show a 300 300 field with 200 randomly deployed nodes. To determine the SPs, in each row the circumcircles for every alternate triangle is taken. In this way all the sensors belong to some SPs or the other with minimal overlapping. As shown in Fig. 3(b) some sojourn points (marked in red1) fall outside the boundary of the grid. They are adjusted as in Fig. 3(c) and we get the final list of sojourn points and create the clusters accordingly based on transmission range of the sensors as given in Fig. 3(d). Once the sojourn point are determined and the clusters are formed, they are numbered in chronological fashion (as given in Fig. 3(d)). All the above mentioned procedures for cluster formation take place at the base station. The mobile collectors gather the cluster-id information from the base station and they send the respective cluster ids to the sensors when they visit the SPs to collect data. The sojourn point calculation takes OðG2 Þ time, where G is the grid size. To estimate the number of sensors belonging to each sojourn point, both number of sojourn points and the number of nodes have to be considered. This has been carried out in lines 38–46 which eventually take Oðno of sojourn points NÞ amount of time, where N is the number of sensor nodes. So, the overall complexity of Algorithm 1 is OðG2 Þ þ Oðno of sojourn points NÞ. 4.1.2. Mobile Collector Path Planning (MCPP) The path planning of a mobile collector will be based on the Eqs. (1) and (2) and the conditions sp ¼ ep and Pn Pn i¼1 dc t i þ i¼1 mct i <¼ bot. To determine a path for itself a mobile collector will initially follow a greedy approach. This is over, considering both the data collection and the movement time from approach will be followed till half of bot i.e. ðTþpÞbs 2 one SP to another. After this, a mobile collector will try to come back to its starting position without repeating any of the already traversed sojourn points. This should be done considering the fact that the overall bot is not exceeded. This is 1
For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
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Fig. 3. Steps in the formation of cluster.
achieved by following depth first search. The final path thus formed represents a simple cycle. Once the path is determined using MCPP (Algorithm 2), a mobile collector will follow this path throughout the network lifetime.
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Algorithm 2. Mobile Collector Path Planning (MCPP).
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The algorithm shows how MCPP works. Initially, as input we need to provide the total buffer overflow time of the sensors and their buffer size. We also need to take the starting position id or the cluster ID of the mobile collector. From its current position a mobile collector can move to any of the eight possible directions. As the clusters are numbered, the direction values from the present cluster(cur pos id) in line 13 can be denoted by the following:
East ¼ cur pos id þ 1
ð6Þ
West ¼ cur pos id þ ð1Þ
ð7Þ
North ¼ cur pos id þ
G pffiffiffi 2 þ 1 R 3
G pffiffiffi 2 þ 1 South ¼ cur pos id þ R 3 North—East ¼ cur pos id þ
G pffiffiffi þ 1 R 3
North—West ¼ cur pos id þ
G pffiffiffi R 3
ð8Þ
ð9Þ
ð10Þ
ð11Þ
G pffiffiffi South—East ¼ cur pos id þ R 3
ð12Þ
G pffiffiffi þ 1 South—West ¼ cur pos id þ ð R 3
ð13Þ
Special considerations: 1. For the clusters on the left boundary, the value for the cluster number (cluster no) for the West direction is always set to 0. Otherwise it will give the last cluster number in the previous row. Similarly, for the clusters on 3(d), there is no cluster in the West direction for cluster no 14. Thus, if we use Eq. (7), the resultant cluster no will be 13 which is incorrect. l m l m G ffiffi G ffiffi p p þ 1 þ ðn 1Þ 2 þ 1 , where n ¼ 1; 2; . . . ; n, the cluster no in the 2. For the cluster numbered R 3 R 3 North—West and South—West directions are set to 0 for similar reasons. l m G ffiffi p 2 þ 1 , where n ¼ 1; 2; . . . ; n, the cluster no for North—East and South—East are 3. For the cluster numbered n R 3 also set to 0. For the cluster no thus found, the mobile collector moves towards the direction of that cluster which has the maximum number of sensors. During this journey the corresponding data collection time and the collector movement time also get calculated. Lines 8–27 in Algorithm 2 show this greedy approach calculation. This approach will continue till bot crosses 50% (line 28). The collector will then trace back to the point (xp ; yp ) where the bot was 650%. From this point the collector will make an attempt to move towards the starting position from where it embarked on its journey. To go back to the starting point (xp ; yp ) is thus taken as the source. From (xp ; yp ) a number of paths will lead to the starting point. The vertices on this path will be the neighbouring sojourn points of those sojourn points that were covered during the greedy approach. The data collection time and the collector movement time are assessed for each of these paths (similar to lines 11–12) and stored in path tot. Then the maximum path tot value which is less than or equal to left (Buffer overflow time – the amount of time spent in collection of data and mobile collector movement during greedy approach) is taken. The corresponding path with this value is considered to be the movement path of the mobile collector. So Algorithm 2 in its entirety gives the movement path of a mobile collector. Once all the sojourn points from one cluster to another is decided, the mobile collector will follow the following angle measurements for its movement:
hi ¼ 0
if xiþ1 > xi ; yiþ1 ¼ yi
hi ¼ 180
if xiþ1 < xi ; yiþ1 ¼ yi
hi ¼ 90
if xiþ1 ¼ xi ; yiþ1 > yi
hi ¼ 90
if xiþ1 ¼ xi ; yiþ1 < yi
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Fig. 4. Mobile collector path planning with sensor buffer size = 2 KB.
yiþ1 yi xiþ1 xi y yi hi ¼ 180 arctan iþ1 xiþ1 xi yiþ1 yi hi ¼ 360 arctan xiþ1 xi yiþ1 yi hi ¼ 180 þ arctan xiþ1 xi hi ¼ arctan
if xiþ1 > xi ; yiþ1 > yi if xiþ1 < xi ; yiþ1 > yi if xiþ1 > xi ; yiþ1 < yi if xiþ1 < xi ; yiþ1 < yi
The angle of rotation is xi given by:
xi ¼ hi hi1
ð14Þ
where hi is the mobile collector’s next orientation, hi1 is the mobile collector’s present orientation, (xiþ1 ; yiþ1 ) is the next location of the sojourn point where the mobile collector will move, (xi ; yi ) is the current sojourn point of the mobile collector. Fig. 4 gives an instance of the MCPP algorithm. Now, a single mobile collector is not enough to achieve this goal. So, we require a specific number of mobile collectors. Lemma 1. If the number of sojourn points is n, then the number of mobile collectors is a function of the tour length of a mobile collector. Proof. Let the number of sojourn points be n. A mobile collector starts its journey from a corner sojourn point in the network. After the completion of its journey according to MCPP, its tour length (Lt ), in terms of hop count, is taken. Then, the number of mobile collectors will be equal to
Number of Mobile CollctorsðSn Þ ¼
n Lt
ð15Þ
While deciding on the number of mobile collectors, the four corner sojourn points of the network area are taken to be the initial starting points. Else, some corner points may remain unattended. Once these collectors complete their movement paths, to cover the rest of the network more collectors are employed starting along the periphery. This strategy is followed for the entire network. h 4.1.3. Analysis The time complexity of MCPP algorithm is mainly dictated by the greedy approach followed during the forward movement and the path created to go back to the starting position. The while loop for the forward movement condition is executed for fm times resulting in a time complexity of OðfmÞ. To find the cluster having the highest number of sensors, all the possible directions for the mobile collector movement have to be considered. This operation has a complexity of Oðnumber of directionsÞ. The number of directions in this case is 8. So, the overall time complexity for the forward movement Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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is Oðfm number of directionsÞ. To go back to the starting point using optimal path, depth first search is used amongst the neighbouring SPs of the initial paths to find out the possible paths. This operation takes OðV þ EÞ time where V is the number of sojourn points and E is the connecting edges between the sojourn points. Calculating the data collection time and movement time takes a total of OðcountÞ time. Finding the optimal path again takes a time of OðcountÞ. Thus, the total time complexity of MCPP algorithm is Oðfm number of directionsÞ þ OðV þ EÞ þ OðcountÞ þ OðcountÞ. But as the value of count is negligible as compared to the other parameters, so the time complexity amounts to Oðfm number of directionsÞ þ OðV þ EÞ. 4.2. Network with obstacles In a realistic environment, obstacles may be present in the sensing field and thus obstruct the motion of a collector. So, trajectory for a mobile collector in the presence of obstacles has been proposed in the following sections. 4.2.1. Sojourn point determination The procedure for the determination of sojourn point will remain the same. But if an obstacle falls on the circumcenter of an alternate triangle, the next triangle is taken such that all the sensors fall in some cluster as given in Fig. 5. 4.2.2. Mobile collector path planning The movement strategy of the mobile collector will be the same as that when there are no obstacles present in the network. But for planning its tour in the presence of obstacles, a mobile collector needs to know the position of obstacles. For this purpose, a mobile anchor node is introduced. The anchor node moves throughout the network according to [22]. Even though the position of an obstacle is known, there can be more than one obstacle in the network area. So, while deciding upon its movement, every time a mobile collector has to confirm which obstacle falls within its tour path. This can be done according to Eq. (16):
y y1 y1 y2 ¼ x x1 x1 x2
ð16Þ
Fig. 5. Sojourn point determination in the presence of obstacles.
Fig. 6. Obstacle detection calculation.
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Here, ðx1 ; y1 Þ is the current position of the mobile collector, and ðx2 ; y2 Þ is the next SP where the collector will move. As the four corner coordinates of an obstacle are known, they are assigned to the ðx; yÞ variable to check if an obstacle falls within the movement path of a mobile collector. The Algorithm for obstacle avoidance is given in Algorithm 3. The description for Algorithm 3 is illustrated below with an example. In Fig. 6, the current position of mobile collector (cp mc) is (51.96, 175.37) and its next position (np mc) is (12.99, 181.86) which has been deduced according to Algorithm 2. The four coordinates (obs coord) of the obstacle are (17, 155), (42, 155), (42, 185) and (17, 185), respectively. So, to check if the obstacle falls within the point (C) and (D), the values of x; x1 ; y1 ; x2 ; y2 are assigned to Eq. (16) where x ¼ 42. The value of y evaluates to 177 which lies within 155 and 185, the two y coordinates of the obstacle. So it can be deduced that the obstacle falls within (C) and (D). Similarly, the other values are also assigned to check the position of the obstacle. If a straight line is drawn from (C) to (D), then it will meet the obstacle at the points (A) and (B) which have the values (17, 181.9) and (42, 177) thus confirming that the obstacle falls within (C) and (D). Now, to bypass the obstacle, the concepts of graph formation and Dijkstra’s shortest path algorithm are applied. The edges of the graph (G obs) are created by joining cp mc, the obstacle coordinates and np mc (they being the vertices of the graph) as given in Fig. 7. The diagonals of the obstacles are not considered as the mobile collectors cannot pass through an obstacle. Also, the edges which will not be a natural choice for the shortest path are also not taken into consideration. For example, in Fig. 7(b), the edge from vertex a to vertex h is not considered as either it will pass through the obstacle, or it will create a path which will not be a part during shortest path consideration. cp mc and np mc are connected to their nearby obstacle coordinates. The weights assigned to the edges of the graph are the Euclidean distances between the corresponding vertices. For more than one obstacle, their vertices are also connected to create G obs. After the formation of G obs, Dijkstra’s shortest path algorithm, which is an optimal greedy approach, is applied on the graph to determine the detour path of the mobile collector as shown in Fig. 8. So, whenever an obstacle will be found, a mobile collector will bypass it according to Algorithm 3. Algorithm 3 works well even if there are more than one obstacle in the path of a mobile collector. Algorithm 3. Obstacle avoidance for mobile collector.
The final tour of the mobile collectors is depicted in Fig. 9.
Fig. 7. Graph for obstacle avoidance.
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Theorem 2. The algorithm for obstacle avoidance has a time complexity of Oðm2 Þ, where m is the number of obstacles. Proof. In line 2 of Algorithm 3, drawing a straight line from the current position to the destination takes constant amount of time. Thus, the operation is executed in Oð1Þ time. To ensure the presence of obstacles, their four coordinates (4 m) have to be checked according to Eq. (16), which takes OðmÞ time. In line 9, the graph constructed for obstacle avoidance in the worst case will have nðn1Þ edges, where n is the number of vertices of the graph. Now, the number of vertices in Gobs is 4m þ 2 as is 2 can be rewritten as ð4mþ2Þð4mþ1Þ . Thus, construction of graph takes Oðm2 Þ time. Running Dijkstra’s evident from Fig. 8. So, nðn1Þ 2 2 shortest path algorithm on a graph with (4m + 2) vertices takes Oðð4m þ 2Þ2 Þ time which is equivalent to Oðm2 Þ. So, the overall complexity of the Algorithm is Oðm2 Þ. h 5. Performance evaluation Performance evaluation of the proposed schema has been carried out for both obstacle-free and obstacle-resisting environments. We consider a network area where sensor nodes are placed uniformly in a field of size 300 300 m2. As shown in Fig. 9, two obstacles of size 25 30 m2 are placed in the sensing field. To measure the network lifetime, it has been assumed that all sensor nodes have a fully charged battery with 6300V 0 J of energy, which corresponds to a standard rechargeable battery with a capacity of 1750 mA h [17]. Here, V 0 is the voltage of the battery. The experiments have been performed with a data transmission rate of 250 Kbps and assuming a periodicity (p) of 95 ms. The rate of storing data in micro-controller is 9600 bps. The sensors are assumed to hold 2 KB of data. The speed of mobile collector is 2 m/s. The current consumption is 23 mA at both the transmitter and the receiver. The current consumption in the sleep mode is 1 lA. All the parameters are in accordance with the datasheet of TelosB [23]. 5.1. Performance in obstacle-free environment Simulation results for the number of mobile collectors for a transmission range of 30 m is depicted in Fig. 10. The number of nodes are set to 200, 400 and 600. The area of the sensing field varies from 100 100 m to 500 500 m. As
Fig. 8. Detour path of mobile collector based on shortest-path.
Fig. 9. Mobile collector path planning in the presence of obstacles.
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Fig. 10. Number of mobile collectors.
Fig. 11. Average energy consumption during sleep and data transmission phases.
Fig. 12. Comparison for network energy consumption.
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the transmission range is fixed, the number of mobile collectors depend on the monitoring area and the number of sensors in each cluster. This is a determining factor for the final tour length of each mobile collector. The number of mobile collectors may increase or decrease with increasing area of the network based on the number of sensors falling in each cluster. The average energy consumption during sleep and data transmission phase is depicted in Fig. 11. The amount of energy consumed during sleep phase (Es ) of the sensors is much less as compared to when they are transmitting data (Et ) to the mobile collectors. This is because a sensor consumes only 1 lA of energy during sleep cycle. For this result, we have considered the worst case scenario of buffer overflow. As the paths for the mobile collectors have been determined based on the assumption that all the sensors are sensing data, so even if one node runs out of energy then the path will get altered. So, in this work Network lifetime is defined as the number of rounds till the first node in the network runs out of energy. As mobile sinks and mobile data collectors behave in a similar way, we have compared our work with other those who have considered mobile sinks for data collection. Fig. 12 shows the energy consumption comparison of our proposed algorithm (MCPP) with weighted rendezvous planning (WRP) [13], Cluter-based (CB) [15], rendezvous design for variable tracks (RD-VT) [14] and rendezvous planning utility-based greedy (RP-UG) [24] algorithms. The network parameters are according to [13]. RD-VT has the highest amount of energy consumption due to the fact that it has long data forwarding paths from the sensor nodes to the rendezvous points (RP). CB shows better performance than RD-VT because it replaces the selected RP in each cluster with a node closer to the cluster head. This is done to reduce the number of multi-hop transmissions showing a 28% reduction in the amount of energy consumption. WRP considers node density and hop counts when selecting RPs. This
Fig. 13. Comparison for network lifetime.
Fig. 14. Comparison for network lifetime.
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causes a 10% reduction in energy consumption when compared to CB. As compared to WRP, MCPP achieves almost 12% reduction in energy consumption due to the fact that MCPP does not involve multi-hop transmission of data. Energy loss is attributed to only single-hop transmission of data. In sleep mode, the consume very meagre amount of energy. All the experiments have been conducted with a confidence interval of 95% and taking a sample size of 30. Fig. 13 shows the network lifetime comparison of MCPP with WRP, CB, RD-VT and RP-UG. MCPP improves network lifetime by 15% as compared to WRP. CB causes non-uniform energy consumption due to random cluster-head selection process. In RD-VT, long forwarding paths get created from the static sensor nodes to the RPs resulting in non-uniform energy consumption. Thus compared to CB, it has a 25% reduction in lifetime. In Fig. 14, comparison of network lifetime is performed with some other popular methods of sink movement. The network parameters are based on [16]. The result shows an improvement of about 18% when compared to half-quadrant-based moving strategy (HUMS) [16]. With the increase in the density of the sensor nodes, the network lifetime decreases. This is quite expected as more number of sensors will result in faster energy depletion of the network. But all the algorithms with sink mobility fare better than that with a stationary sink. Network lifetime comparison for Path Discovery for Sinks Mobility (PDSM) [19], Maximum Amount Shortest Path (MASP) [12], Static Sink and MCPP is given in Fig. 15. An improvement of 25% is noted because of the single-hop transmission of data and the incorporated duty-cycle. Thus much less amount of energy gets consumed. The number of mobile collectors do not have any effect on the energy consumption of the sensor nodes in our algorithm because it has been assumed that the mobile collectors have infinite power supply.
Fig. 15. Network life time in obstacle free environment.
Fig. 16. Path length comparison in the presence and absence of obstacles.
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5.2. Performance in obstacle-resisting environment Two obstacles of size 25 m 30 m are placed at random positions in the network for the simulation and comparison purposes. However, the algorithm will work for obstacles of any size. Fig. 16 shows the maximum path length (in metre) of a mobile collector in an obstacle-free and resisting environment. There are more than one mobile collector involved in our proposed algorithm. The figure depicts the maximum path length amongst all the travel distances for all mobile collectors involved. The path length depends on the number of sensors in each cluster and the time taken to travel between each cluster, so the change in the tour length is not proportional to the increasing number of sensors. As can be seen from the figure, in some cases maximum tour length on obstacle-free and obstacle-resisting environment are the same. This is attributed to the fact an obstacle may not fall in the path taken by a mobile collector, thus keeping the tour length same. As in obstacle-free environment, the amount of energy consumed during sleep phase (Es ) of the sensors is much less as compared to when they are transmitting data (Et ) to the mobile collectors as given in Fig. 17. But as can be observed from the figure, though Et values are same for both obstacle-free and obstacle-resisting cases, but Es is a bit higher in the latter case. This is because due to the presence of obstacles in some scenarios, the mobile collectors have to make a detour to reach a sojourn point. So, some sensors will be in a longer sleep cycle than the others. Fig. 18 shows the average latency of the mobile collectors in an obstacle-free and resisting environment. The mobile collectors when move at a faster speed it can cover the sojourn points faster resulting in lower latency. As expected, the average
Fig. 17. Average energy consumption during sleep and data transmission phases.
Fig. 18. Average latency of mobile collectors in obstacle-free and obstacle-resisting environment.
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Fig. 19. Network life time in obstacle resisting environment.
latency is a bit higher for obstacle resisting environment. For 0.5 m/s the latency evaluates to almost 126 s for obstacle-free environment and 129 s for obstacle resisting environment. These are acceptable latency for detection of forest fire [25]. One may argue that the latency can be reduced by considering multi-hop communication. But in that case energy depletion will be much faster. This work shows a trade-off between latency and energy consumption by considering multiple mobile sinks. Network lifetime and energy consumption comparison between our proposed scheme and other mobile collector based data collection schemes in obstacle resisting environment are illustrated in Fig. 19. Our algorithm performs well because of the fact that the sensors are not involved in the obstacle detection or avoidance scheme in any way, thus enhancing the network lifetime. Thus both in the presence and in the absence of obstacles, the performance of MCPP is almost similar except for the fact the energy consumed during sleep phase is a bit more than that in obstacle-free environment. 6. Conclusion This paper presents MCPP which is used for controlling mobile collector movement in WSN. By introducing a mobile collector, data collection becomes more flexible and adaptable to the unexpected changes in the network. The paper determines the path of certain mobile collectors so that the full network is covered while ensuring data is collected before the sensors’ buffer overflow. Some stop points are calculated where the mobile collectors waits to collect data from the sensors. The determination of these points has a time complexity of OðG2 Þ þ Oðno of sojourn points NÞ, where N is the total number of random deployed sensors. To create the paths an obstacle-free environment is initially considered. We have shown that the time needed to execute the algorithm is Oðfm number of directionsÞ þ OðV þ EÞ. Angle of rotation has also been calculated to show how a mobile collector will actually move to reach its next position. As the mobile collectors collect data from the sensors in a single-hop, significant amount of energy is conserved. Preservation of energy is further aided by the dutycycling scheme adopted by the sensors. The simulation results corroborates this claim and shows an improvement of about 15% in network lifetime. Furthermore, for a more realistic scenario, an obstacle-resisting approach is also used in this work. A very simple obstacle-avoidance method for path determination has been proposed with a time complexity of Oðm2 Þ; m being the number of obstacles. As with obstacle-free network, this environment also shows a noteworthy improvement in network lifetime. Acknowledgment This work has been supported by UGC project, order no:F.No: 42-146/2013(SR). We would like to thank Prof. Sajal K. Das, Department of Computer Science, Missouri University of Science and Technology, Rolla, USA for his immense help and support in this work. References [1] Akyildiz IF, Su Weilian, Sankarasubramaniam Y, Cayirci E. A survey on sensor networks. IEEE Commun Mag 2002;40(8):102–14. [2] Khan Junaid Ahmed, Qureshi Hassaan Khaliq, Iqbal Adnan. Energy management in wireless sensor networks: a survey. Comput Electr Eng 2015;41:159–76.
Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004
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Please cite this article in press as: Ghosh N, Banerjee I. An energy-efficient path determination strategy for mobile data collectors in wireless sensor network. Comput Electr Eng (2015), http://dx.doi.org/10.1016/j.compeleceng.2015.09.004