Base Station Location Aware Optimization Model of the Lifetime of Wireless Sensor Networks

Mobile Netw Appl DOI 10.1007/s11036-015-0614-3 Base Station Location -Aware Optimization Model of the Lifetime of Wireless Sensor Networks Nguyen Thanh Tung & Huynh Thi Thanh Binh # Springer Science+Business Media New York 2015 Abstract Recently, wireless sensor networks (WSNs) have been progressively applied in various fields and areas However, its limited energy resources is indisputably one of the weakest point that strongly affects the network’s lifetime A WSN consists of a sensor node set and a base station The initial energy of each sensor node will be depleted continuously during data transmission to the base station either directly or through intermediate nodes, depending on the distance between sending and receiving nodes This paper consider determining an optimal base station location such that the energy consumption is kept lowest, maximizing the network’s lifetime and propose a nonlinear programming model for this optimizing problem Our proposed method for solving this problem is to combine methods mentioned in [1] respectively named the centroid, the smallest total distances, the smallest total squared distances and two greedy methods Then an improved greedy method using a LP tool provided in Gusek library is presented Finally, all of the above methods are compared with the optimized solution over 30 randomly created data sets The experimental results show that a relevant location for the base station is essential Keywords Base station location Wireless sensor network Routing Non-linear programming * Nguyen Thanh Tung tungnt@isvnu.vn Huynh Thi Thanh Binh binhht@soict.hust.edu.vn International School, Vietnam National University, Hanoi, Vietnam Hanoi University of Science and Technology, Hanoi, Vietnam Introduction Being invented from the purposes in the army, wireless sensor networks (WSN) appears more and more popularly in most areas and fields of the humanity life Network nodes in a WSN are sensors having capability of collecting information around their locations then sending to the base station without physical links Hence, WSNs are easily deployed in dangerous or badly situated places to provide human with requisite information This information can be humidity, temperature, concentration of pesticides, noise and so on; which makes WSN applicable to many fields such as environment, heath, military, industry, agriculture, etc However, one disadvantage of WSNs is that sensor nodes are operated by not frequently rechargeable and/ or limited energy resources such as batteries These energy resources will be depleted gradually Then the energy source of a sensor node runs out, this node dies, which means it can no longer collect, exchange as well as send information to the base station Therefore, the WSN will not be able to complete its mission The duration since the WSN began operating until the first sensor node runs out of its energy is called the network lifetime and is considered as one of the most important measures to evaluate the quality of WSNs Namely, the longer the network lifetime is, the better the WSN is So, the quality of WSNs depends on speed of energy consumption of sensor nodes This brings out a problem is how to use sensor nodes’ energy effectively, in other words, to maximize the lifetime of WSNs that is considered in this paper There are many ways as well as methods to maximize the lifetime of WSNs In general, the authors approach this Mobile Netw Appl problem in the way to find effective routing methods in data transmission with the given random location of sensor nodes and the base station However, the fact shows that the base station location needs to be optimized, which is our approach for the problem of maximizing the lifetime of WSN Specifically, we consider the model in which all sensor nodes in the network are responsible for sending data to the base station in every specified period When a sensor node sends data, its consumed energy is directly proportional to the square of distance between it and the node which receives data An optimal location of the base station needs to be found such that the network lifetime is maximized We modeled this problem as a nonlinear programming Also, five methods, the centroid, the smallest total distances, the smallest total squared distances, the greedy and the integrated greedy method, are presented to specify the optical base station location Then, the nonlinear programming model is used to evaluate our proposed methods over 30 randomly created data sets The experimental results show that a relevant location for the base station is essential, which proves our correct research way The rest of this paper is organized as follows: Section describes the related works Mathematical model for this problem is introduced in Section Four methods for specifying the base station location is showed in Section Section proposes an improved greedy method Section gives our experiments as well as computational and comparative results The paper concludes with discussions and future works in Section node i should not directly send data to node j if j ≥ i+2 because communication over long links is not desirable Their greedy scheme offered an optimal placement strategies that is more efficient than a commonly used uniform placement scheme In [5] proposed a network model for heterogeneous networks, a set of Ns sensors is deployed in a region in order to monitor some physical phenomenon The complete set of sensors that has been deployed can be referred as S = {s1…… sN} Sensor i generates traffic at a rate of ri bps All of the data that is generated must eventually reach a single data sink, labeled s0 Let qi,j be traffic on the link (i,j) during the time T The network scenario parameters also include the traffic generation rate ri for each sensor The power model in [5–9], is used, where the amount of energy to transmit a bit can be represented as: The total transmission energy of a message of k bits in sensor networks is calculated by: E t ẳ E elec ỵ FS d and the reception energy is calculated by: E r ¼ Eelec where Eelec represents the electronics energy, ε FS is determined by the transmitter amplifier’s efficiency and the channel conditions, d represents the distance over which data is being communicated Maximize: T Subject to: N X Related works Until now, the problem of maximizing the lifetime of WSNs has received a huge interest of the researchers According to [2], there have two different approaches for maximizing the network lifetime One is the indirect approach aiming to minimize energy consumption, while the other one directly aims to maximize network lifetime With the indirect approach, the authors [3] gave a method to calculate energy consumption in WSNs depending on the number of information packets sent or the number of nodes Then they proposed the optimal transmission range between nodes to minimize total amount of consumed energy With this method, the total energy consumption is reduced by 15 to 38 % Cheng et al formulated a constrained multivariable nonlinear programming problem to specify both the locations of the sensor nodes and data transmission patterns [4] The authors proposed a greedy placement scheme in which all nodes run out of energy at the same time The greed of this scheme is that each node tries to take the best advantage of its energy resource, prolonging the network lifetime They reason that q j;i þ ri T ¼ j¼1 N X À N X qi; j : iẵ1N 1ị jẳ0 X Eelec þ ε FS d qi; j þ E elec q j;i < ẳ E i : iẵ1N 2ị jẳ0 qi; j >ẳ : i; jẵ1n N jẳ1 3ị Problem formulation of maximizing the lifetime of wireless sensor networks with the base station location A sensor network is modeled as a complete undirected graph G = (V, L) where V is the set of nodes including the base station (denoted as node 0) and L be the set of links between the nodes The size of V is N The link between node i and node j shows that node i can send data to node j and vice versa Each node i has the initial battery energy of Ei Let Qi be the amount of traffic generated or sank at node i Let dij be the distance between node i and node j Let T be the time until the first sensor node runs out of energy Let qij be the traffic on the link Mobile Netw Appl L(ij) during the time T The problem of maximizing the lifetime of the wireless sensor networks with the base station is formulated as follows [10–14]: Maximize: T Subject to: N X q ji ỵ QT ẳ jẳ1 N X qi j : ∀i∈½1…N Š one By using a tool to find the lifetime of WSN, we can evaluate quality of this base station location as well as that of these methods Four methods are as follows: The centroid method: defines the base station location as the centroid of all sensor nodes This location is calculated by (8) N X 4ị jẳ0 h i X 2 qi j d i j ỵ qi0 xi x0 ị ỵ yi y0 ị < ẳ E i : iẵ1N 5ị x0 ẳ N jẳ1 N X qi0 ẳ Q0 6ị iẳ1 qi j >ẳ : i; jẵ0N 7ị x0 ; y0 ; T : V ariable In which, (xi, yi) is coordinate of node i in the twodimensional space Four methods for specifying the base station location To maximizing the lifetime of WSNs, the base station location not only is close, but also balances distances with as many sensor nodes as possible This guarantees that sensor nodes not consume too much energy in transmitting data to the base station and no sensor node depletes its energy much faster than other nodes The center of network seems to be in accord with this requirement However, there are many definitions for the center of network, each definition gives different locations So this paper proposes four methods corresponding to four different “center” definitions to specify the center of network that is also the base station location These four methods are named respectively as the centroid, the smallest total distances, the smallest total squared distances and the greedy methods After this base station location is determined, the model in Section becomes a linear optimal Fig Illustration of the greedy method N X xi i¼1 N −1 ; y0 ¼ yi i¼1 N −1 ð8Þ The smallest total distances method: the base station location is a point such that the Euclidean distance summation from it to all sensor nodes is the smallest one This point satisfies (9) With this definition, easily seen, the base station location should be a point in the convex hull of all sensor nodes However, for the sake of simplicity, this location is found in the smallest rectangle surrounding all sensor nodes M in : N q X xi x0 ị2 ỵ yi y0 ị2 9ị iẳ1 The smallest total squared distances method: it is similar to the smallest total distances one, but the base station location has to satisfy that the sum squared distances from it to all sensor nodes is the smallest M in : N X xi x0 ị2 ỵ yi y0 Þ2 ð10Þ i¼1 The greedy method: defines a sensor set includes sensor nodes and a delegate center If the set has only one sensor node, its delegate center is this own sensor node Also, we define the distance between two sensor sets is the distance between their two delegate centers The main idea of this method is that starting with one-sensor-node sets (Fig 1a), we merge two sets having the smallest distance (sensor node set S1 and S2 in Fig 1a) A new delegate center for the merged set (the red node in Fig 1b) is specified as follows: this center is on the line segment connecting two old delegate centers and splits this line into two segments with proportional by p The sensor sets is merged until only one set remains The delegate Mobile Netw Appl center of this last set is the base station location (The green node in Fig 1c) To improve the greedy method, the authors break the original algorithm into two sequential steps: finding two componential node sets and combining them into one node set with a new delegate center (let say finding and combining steps for short); and propose various methods for partially optimization.To be specific, the two steps was improved with respectively two and three changes in the algorithm, bringing in eight different output sets Since six of them return equallyhigh-quality results, the authors select two combinations that have the best qualified output to present The first optimized greedy method: Change algorithm in the combining step Step The first step is kept originally, which is accomplished by looking for two sets having the smallest distance (sensor node set S1 and S2 in Fig 1a) Step To improve the solution, the authors propose a change in the second step: looking for a new center on the line segment connecting two old sets’ center such that the average squared distance from it to two old centers is the smallest The average squared distance AveSD of set S having M internal nodes toward the assuming center c is calculated as follows:   AveSD ẳ M xS xc ị2 ỵ yS yc ị2 ð11Þ The second optimized greedy method: Change algorithm in both steps Step finding two componential nodes The authors improve the first step by searching for two sets having the smallest average squared distance between every pair of internal nodes of both sets If the set S1 has N internal nodes, and S2 has M internal nodes, the two chosen sets are the one having: 2 XXÀ Á2  xS i xS j ỵ yS i −yS j  N ÂM i¼1 j¼1 N M in : M Because of that, a new concept appears—number of transmission (denote as t)—a constant value representing the average times of data being sent through intermediate nodes/centers The Fig illustrates internal nodes inside node sets S1 and S2 transmit data through the sets’ center The value of t is a constant and is chose with the maximum value, conditioning that the network functions well To be specific, energy consumption for transmitting data should not over the remaining energy of the node set The combination process starts with two chosen sets, the new center is located at somewhere on the line segment connecting two old sets’ center such that energy remained at the new center is the greatest one With the assumption that the energy consumption is directly proportional to square of transmitting distance and the constant t is, the needed energy for the set S consisting of M internal nodes to send data to the considering center c is:   Average energy consumption ¼ M  t xS xc ị2 ỵ yS yc ị2 13ị Our proposed method for improving the current method of finding base station location Basically, the results derived by using [1] were nearly optimal, which was found out by manually checking random points that locate nearby the final optimal location Therefore, we propose an improving integrated method for finding the base station location, such that it somehow combines all four published methods and inherits the advantages but limit the disadvantages of those methods This method applies the “divide and conquer” methodology on the original set of sensors by continuously forming subsets of a random number of sensors, combining them and appending their delegate point to the initial set thereafter until only one delegate center remains The final result is then qualified by using an intergrated LP tool included in the Gusek ð12Þ Step 2: combining two sets into one new virtual set This improvement on the greedy method relates to the energy it takes to transmit data, which is to find the optimal location preserving as much energy as possible The basic idea of this method goes with the assumption that when two original sets are combined into a new one with a delegate center, the data transmitting flow will start from the internal nodes to the new center before continuing to reach the base station Fig Two times transmitting illustration Mobile Netw Appl Fig Illustration of the intergrated greedy method library, which returns the value of maximum tval—the total number of data transmission; the higher tval is, the better the solution is We called this Intergrated Greedy Method (IGM) IGM starts with the definition of the weight of a sensor node or set, which is defined in the original Greedy method as the actual number of nodes that it contains From the initial 30-node-covered set, a subset of several sensors is created with the number of internal small-weighted nodes being limited to a specific value and needs to satisfy the condition that there is at least one sensor node remains In the chosen subset, we apply one method amongst four original methods introduced in [1] with regard to specific pre-defined ratios a and b For the sake of high quality results, we adjusted the ratio so that the Greedy method takes up the highest probability since it provided the best result so far, while others have inconsiderable probability of being chosen; which, guarantees that the final result to be at least as high as that of the Greedy method and the minor but important changes will improve the quality of the algorithm The new delegate center having a new higher weight is then appended to the subset, which means it has a low priority to be chosen After that, the process starts over again repeatedly until there is only one point remains Pseudo code for the algorithm, in which, take_out is the amount of sensor nodes contained in one set and ratio represent a way we classify the ratio into working variables Algorithm 1: Combinator Input: A set of sensor nodes S Output: Delegete center location (x, y) begin while size_of_subset > take_out = rand() if (take_out < threshold) switch (ratio) case 0–10 %: (x, y) = CentroidMethod() break case 10–2 %0: (x, y) = STDMethod() break case 20–30 %: (x, y) = STSDMethod() 10 break 11 case 30–100 %: (x, y) = GreendyMethods() 12 break 13 end switch 14 endif 15 add (x, y) into S 16 end while 17 return (x, y) end The principle of this method is illustrated in the Fig In the figures, black points represent sensor nodes that are not either combined or considered yet, meanwhile the gray one represent the one that has been combined at least once To evaluate the result derived by using this method, we included Gusek library and based on that to calculate the maxmimal, which represents the total number of data transmission in the WSN during its lifetime High tval value equals to good performance If the result is not as good as expected, we shall re-run the progress because the result will not be the same next time due to many random factors taking places in the main algorithm Hence, the next time you repeat the entire project, another result will be brought in and the qualification might also be different In addition, it is recommended that the code should be run k times and all data are kept in a structure file By that way, we can easily find the peak point in those gained from vairous earlier attempts and the avarage qualifying “tval” value for statistical purposes Mobile Netw Appl The experiment parameters Table Parameter Value The network size Number of sensor nodes - l Initial energy of each node - E Ratio p in method 100 m×100 m 30 1J pffiffiffi cx pffiffiffi with cx, cy is the number of sensor nodes in two old sensor sets cy Energy model Eelec = d2 where d is the distance between two sensor nodes Experimental results 6.1 Problem instances In our experiments, we created 30 random instances denoted as TPk in which k (k=1, 2, , 30) shows ordinal number of a instance Each instance consists of l lines Each line has two numbers representing coordinate of a sensor node in the twodimensional space 6.2 System setting The parameters in our experiments were set as follows Table 1: 6.3 Computational results To prove the efficiency of our above proposal, coordinate of the base station and the corresponding lifetime found by IGM are presented and compared to ones found by four methods in Table [1] Also, the optimal lifetime of each instance is presented to evaluate quality of proposal methods Table presents the base station location of the centroid, the smallest total distances, the smallest total squared distances, the greedy and the integrated greedy method in BS1, BS2, BS3, BS4 and BS5 column respectively This table shows that the centroid and the smallest total square distances method gave extremely close locations over all instances The difference between locations found by four methods in [1] for each instance is inconsiderable If with each instance, we choose the method giving the best lifetime among these four methods, then comparing its base station location to one found by IGM, we can see the difference between two locations is only focus on one coordinate axis, either x-coordinate or ycoordinate Namely, if x-coordinate of the base station locations found by the best method in four methods in [1] is near to one found by IGM, their y-coordinate is far from each other and vice versa These can prove two following things: fisrtly, all five methods have tendency of converging in one point that is very near to optimal location Secondly, despite having random factor, the IGM is extremely stable The base station location found by five methods for 30 instances y BS1 (x-y) BS2 (x-y) BS3 (x-y) BS4 (x-y) TP1 TP2 TP3 TP4 TP5 TP6 TP7 TP8 TP9 TP10 TP11 TP12 TP13 TP14 TP15 55.2–39.9 39.9–55.3 55.3–42.6 42.6–56.2 56.2–42.3 42.3–56.4 56.4–42.9 42.9–56.8 56.8–41.3 41.3–58.4 58.4–42.0 42.0–58.7 58.7–39.9 39.9–59.9 59.9–38.3 54–37 36–60 55–41 40–62 57–39 39–61 58–40 39–63 59–36 36–64 62–38 36–64 61–36 36–65 62–35 55–40 40–55 55–43 43–56 56–42 42–56 56–43 43–57 57–41 41–58 58–42 42–59 59–40 40–60 60–38 53.1–50.5 40.6–54.8 52.6–53.0 42.1–55.1 52.1–53.4 41.8–55.0 53.3–54.6 44.7–53.6 54.1–53.7 45.9–54.5 54.5–53.5 46.1–54.9 57.4–43.3 46.1–48.9 58.1–41.9 BS5 (x-y) Ins BS1 (x-y) BS2 (x-y) BS3 (x-y) BS4 (x-y) BS5 (x-y) 59–42 55–61 63–43 41–65 62–42 21–56 63–42 26–51 58–43 34–50 57–41 33–50 60–30 TP16 TP17 TP18 TP19 TP20 TP21 TP22 TP23 TP24 TP25 TP26 TP27 TP28 TP29 TP30 38.3–59.9 59.9–38.5 38.5–61.2 61.2–40.5 40.5–59.6 59.6–40.3 40.3–58.2 58.2–39.0 39.0–55.9 55.9–39.4 39.4–54.6 54.6–41.5 41.5–53.2 53.2–39.4 39.4–50.5 36–64 62–35 35–66 64–37 36–64 62–37 36–64 60–34 35–63 58–35 36–59 56–38 39–55 54–35 37–51 38–60 60–39 39–61 61–41 41–60 60–40 40–58 58–39 39–56 56–39 39–55 55–42 42–53 53–39 39–51 38.5–54.2 58.1–42.3 38.9–55.0 52.1–40.2 47.0–58.4 57.6–43.4 47.0–57.7 56.8–43.1 45.9–56.3 53.9–44.3 46.2–55.0 53.6–45.5 47.3–54.0 53.9–45.6 45.9–52.6 32–51 60–30 32–51 53–44 34–50 54–39 34–49 55–40 41–49 55–38 46–52 56–39 47–52 54–40 46–50 Mobile Netw Appl Table The lifetime of WSNs with the corresponding base station locations in the Table and the optimal lifetime (Opt) Ins BS1 BS2 BS3 BS4 TP1 TP2 TP3 TP4 TP5 TP6 TP7 TP8 TP9 TP10 TP11 TP12 TP13 TP14 TP15 870 809 867 838 878 822 931 739 941 736 1044 777 1171 762 907 811 652 845 885 839 832 926 706 910 700 1041 722 1160 739 907 867 820 866 837 869 815 925 738 948 736 1044 777 1171 762 907 890 836 865 829 877 805 906 746 907 738 971 791 1171 797 907 BS5 911 886 971 874 991 781 1006 814 1044 846 1171 826 907 Opt Ins BS1 BS2 BS3 BS4 BS5 Opt 911 903 983 884 985 813 1025 836 1044 866 1171 891 907 TP16 TP17 TP18 TP19 TP20 TP21 TP22 TP23 TP24 TP25 TP26 TP27 TP28 TP29 TP30 762 907 746 893 751 1020 744 1056 695 1115 843 1040 838 988 817 739 907 726 870 695 935 682 943 587 997 741 1048 799 962 789 761 907 747 894 750 1003 745 1065 694 1116 838 1038 845 988 810 812 907 793 907 786 1130 794 1124 746 1010 893 977 862 952 861 842 907 945 907 853 1202 846 1168 808 1120 918 1068 884 988 875 952 907 946 907 879 1202 874 1178 809 1128 921 1068 884 988 884 The lifetime of 30 WSNs corresponding to 30 instances are showed in the Table These lifetime were found by using the tool with the found base station locations in the Table The optimal liftetime of each instance is also presented in the Table to easily evaluate quality of our proposal methods The maximum lifetime of each instance among five methods is traced with green The optimal values are traced with blue to show that there is at least one our method giving these optimal lifetime It is seen easily that IGM shows its superior to others when having he best lifetime over all 30 instances This method also give the optimal value over 10 instances On other instances, the lifetime with the base station location found by IGM is aproximate to the optimal, the gap between these two values is very small, less than %, especially on TP4, TP5, TP18, TP23, so on Comparing other methods, IGM give the better lifetime values so far Notably, with TP18, TP20, TP24, TP26, the disparity in the lifetime between four remain methods and IGM is up to from 15 to 27 % The centroid, the smallest total squared distances, the greedy method gave the optimal lifetime over four instances and the smallest total distances is over two instances The lifetime with the base station location of the centroid method and the smallest total squared distances method is about the same over all data sets, which can be explained by the relatively same coordinate of these base station locations So in general, the IGM is the best method in maximizing the network lifetime with the base station location in our proposal The centroid is the simplest method which is suitable to real-time or limited computing systems And again, the difference among the network lifetimes corresponding to the base station location gave by five methods over all instances shows that the location for the base station should be optimized as mentioned in the Section Conclusion This paper proposed a nonlinear programming model for maximizing the lifetime of wireless sensor networks with the base station location We presented our intergrated greedy method that compete with other four methods that are introduced in [1], which shows a significant improvement on the original greedy method, bringing in the results that is about 10% higher than that of the other four methods The new method is also very close to the optimal solution In this paper, our proposed method was experimented on 30 random data sets With the found base station locations, specific lifetime of WSNs was calculated by our model and not only offered a high reliability about the solution but also showed that a relevant 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Mobile Netw Appl L(ij) during the time T The problem of maximizing the lifetime of the wireless sensor networks with the base station is... formulation of maximizing the lifetime of wireless sensor networks with the base station location A sensor network is modeled as a complete undirected graph G = (V, L) where V is the set of nodes... find the lifetime of WSN, we can evaluate quality of this base station location as well as that of these methods Four methods are as follows: The centroid method: defines the base station location