Binary Tree Routing for Parallel Data Gathering in Sensor Networks of Smart Home

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1 Binary Tree Routing for Parallel Data Gathering in Sensor etworks of Smart Home Guangyan Huang and Xiaowei Li Jing He Advanced Test Technology Lab. Chinese Academy of Sciences Research Center on Data Institute of Computing Technology, Technology and Knowledge conomy Chinese Academy of Sciences 18 Beijing, China 18 Beijing, China {huanggy, Abstract With advances in consumer electronics and wireless communications, wireless sensors will be placed everywhere in future s smart home to provide the safety and convenience for consumers. A PC connected with a Base Station (BS) will work as a control center for gathering and handling the data sensed from physic environment in the home. Because of the network area of approximately 2m 2m in the home, transmitting distance is no longer important. Directly transmitting data to BS consumes less energy than any other energy-efficient protocols. However, high delay is one of the most important problems produced by direct transmitting. This paper proposes Binary Tree Routing Protocol (BTRP) to reduce delay in the networks of smart home. BTRP is proved to be the optimal tree routing protocol by evaluating the performance of the networks with energy delay metric. Simulation results show BTRP outperforms traditional direct routing and two-hop routing in terms of lifetime/delay metric. I. ITRODUCTIO With advances in consumer electronics and wireless communications, wireless sensors will be placed everywhere in future s smart home [1]. For example, sensors are deployed for hazards detection [2] such as fire-detection, intruder-detection, etc., and for automation control [1] such as collecting information of temperature, humidity and light for related electronic devices. A PC connected with a Base Station (BS) will work as a control centre for gathering and handling the data messages sensed from physic environment in the home. The sensor networks of smart home show a kind of network scenario with a very high density of sensors deployed in a small area of approximately 2m 2m. Directly transmitting data to BS consumes less energy than any other energy-efficient protocols. However, several issues such as high delay and interference [3] produced by direct routing must be resolved. To reduce delay costs, parallel data gathering can be achieved for time efficiency by organizing sensors as a tree with many hops to transmit data to BS instead of one hop transmitting in direct routing. To alleviate interference, good transmitting scheduling must be adopted. However, multi-hop schemes would incur more energy dissipation than direct routing in the networks of smart home. Because handling 1-bit data on MCU dissipates far less energy than transmitting 1-bit data on radio module [4], reducing the amount of data transmitted between sensor nodes and BS by combining one or more packets to produce a same-size resultant packet may be a good solution for energy efficiency [5]. This means source data messages such as temperature, light, the quantity of smoke, etc. sensed by wireless sensors can be aggregated partly and be gotten rid of redundancy or compressed to a small number. Although they have only limited computing ability, wireless sensors can do the above computing jobs to get maximum network efficiency. This paper proposes Binary Tree Routing Protocol (BTRP) for the networks of smart home. Proofs are given to demonstrate that BTRP is the best one among all n-tree multihop routings. An algorithm of generating binary tree and an algorithm of parallel tree scheduling are given. The energy delay metric [5] is captured to balance the energy dissipation and delay cost for parallel data gathering in BTRP. Simulation also shows BTRP outperforms traditional direct routing and two-hop routing. The rest of this paper is organized as follows. Section II introduces backgrounds. Section III applies simple two-hop routing to the networks of smart home. Section IV provides general n-tree multi-hop routing schemes and proves binary tree is one of the optimal tree routing protocols. Section V simulates the results of BTRP in the networks of smart home and shows the better lifetime/delay metric in BTRP than in direct and two-hop routing. Section VI concludes that BTRP is the elegant solution for the networks of smart home. II. BACKGROUDS In this paper, using the same first order radio model as discussed in [6], a radio dissipates elec = 5nJ / bit to run the 2 transmitter or receiver circuitry and ε FS = 1 pj / bit / m for the transmitter amplifier, the energy dissipation, T ( k, d), of transmitting k-bit data between two nodes separated by a distance of d meters is given as follows: T 2 ( k, d) = k( + ε d ). (1) elec FS And the energy cost, R (k), incurred in the receiver of the destination sensor node is given as follows: ( k) =. (2) R k elec In the networks of smart home ( d < 2 2 = 28. 8m ) the energy spent in the electronics part is nearly 6 times more than the maximum energy spent in the amplifier part. Therefore, multi-hop can spend far more energy than direct transmitting on receiving and mid-transmitting data. A simple scheme is one hop routing or direct routing (Direct) which lets each sensor directly send source data message to BS. As the above energy analysis, the farthest sensors drain their energy resource at almost the same time as

2 the nearest sensors do. Therefore, energy efficiency of routing scheme is less important in the networks of smart home than in larger wireless sensor networks. However, one BS for receiving the data of all sensors serially makes high delay. We assume that the delay is one unit for a packet message transmitted [5]. In one hop routing, the value of delay metric is the number of sensors in the networks of smart home. For example, on a 2Mbps link, a 2,-bit message can be transmitted in 1ms, and suppose 2 sensors deployed in the networks of smart home and each has a packet of 2,-bit to be transmitted in each round, the delay time is 2s. Therefore, some sensors should help to handle or fuse some sensed data for reducing the delay of BS. One of the two-hop routing protocols is provided by Low nergy Adaptive Clustering Hierarchy (LACH) [6], which chooses some sensors as Cluster Heads (CHs) to help fuse data. In LACH, several nodes are randomly chosen as CHs dynamically in each round, then the remaining nodes are affiliated to the nearest CHs based on received signal strength by a distributed algorithm, and at last CHs transmit all data message to BS. Applying LACH to the networks of smart home, BS is within the network area and thus no optimal number of CHs for energy efficiency. The main purpose of using LACH is to reduce delay. III. TWO-HOP LOW DLAY ROUTIG PROTOCOL The routing scheme adopted in the networks of smart home must be useful to get less delay costs and to evenly distributing the energy dissipation. Improved LACH for the networks of smart home named Two-Hop Low Delay routing protocol (THLD) is provided in this paper. THLD is a simple routing scheme to reduce delay of the networks but to introduce small extra energy dissipation. Firstly, THLD makes parallel communication possible and thus reduces the delay costs. Moreover, THLD distributes data to be handled by different CHs in different round, and thus evenly distributes the energy dissipation among all sensors. A. Delay Analysis in THLD THLD provided by this paper adopts the club-club twohop topology. However, THLD minimizes delay in the networks of smart home networks. Suppose the number of sensors is and all sensors are grouped into CH clusters, the delay cost, C, will be given as follows: CH delay C delay = + CH. (3) We can find the optimum number of clusters by setting the derivative of C delay with respect to CH to zero as follows: opt. (4) CH = Moreover, the number of sensors in each cluster is also. Thus the minimal delay cost of THLD is as follows: C delay = 2. (5) B. venly Distributing of nergy Dissipation Two-hop brings the problem that some sensors as the midtransmitters die long before the others. In one hop routing, the i-th sensor dissipates energy of transmitting k-bit data, T ( k, d i ). In two-hop routing, the j-th CH dissipates energy of CH = k + 1) elec + FS d 2 j ) + k1 bit (( ε (6) where 1 bit is the energy dissipation of fusing 1-bit data. Given 1 bit = 5nJ / bit, =1, and neglecting energy spent in the amplifier part, CHs consume approximately 11 times more energy than non-ch sensors. Therefore, positions of CHs should be evenly distributed into all the sensors. The average energy dissipation of electronics part for k-bit data can be given as follows: 1 ) total elec = k( 2 elec. (7) df The average energy dissipation of data fusion for k-bit is = k1. (8) bit BS is placed in the centre of the smart home. The average transmitting distance between sensors and their CHs is also non-significant. Fig. 1 plots that the average energy dissipation of amplifier part on each node during each round can be neglected, because the energy dissipation of electronics part is nearly several hundreds times of it. Therefore, all the two hoprouting schemes for energy efficiency in the networks of smart home are not better than direct routing. Average nergy Dissipation of Amplifier Part (nj) Direct THLD Fig. 1. Average energy dissipation of amplifier part on transmission of 1-bit data. Compared with the energy spent in the electronics part for 1-bit data, 5 nj in Direct and approximately 1 nj in THLD, the energy dissipation on amplifier part is far less and thus can be neglected. Suppose all the sensors have the same initial energy resource. The algorithm of evenly distributing energy dissipation in THLD is given as follows: Step 1. Choose sensors with maximum energy resource as CHs. If p sensors have the same energy resources and q sensors have been chosen, then x sensors are randomly chosen as CHs, where x p. If p + q, then x = p, else x = q.

3 Step 2. Sensors with lower energy resource will firstly be affiliated into a nearest CH and just sensors are in each cluster. The number of sensors in the last cluster may be less than. Fig. 2 shows the average energy dissipation in THLD is approximately two times of that in direct routing. However, energy delay metric in THLD is reduced greatly compared with direct routing. Using (5), delay of THLD reduces to 16, 2, 26, 3, 32, 36, 38, 4, 44 and 46 in networks varying from 5 to 5 sensors by the costs of consuming approximately one time more energy. Thus, the values of energy delay in THLD are reduced to approximately 64%, 4%, 34.7%, 3%, 25.6%, 24%, 21.7%, 2%, 19.6% and 18.4% of direct routing respectively. Average nergy Dissipation of etwork (nj) Direct THLD Fig. 2. Average energy dissipation of networks in each round. THLD provides the improvement direction of routing protocols in the networks of smart home. Because energy dissipations of amplifier part are far less than electronic part in the networks of smart home and also data fusion reduces the amount of data greatly, the key problem of energy efficiency is changed into not only reduce the total energy dissipation of the networks but also evenly distribute the energy to all the nodes. Distance is not as important in home networks as in outdoor networks with long transmitting distance. IV. OPTIMAL TR ROUTIG PROTOCOLS General n-tree should be analyzed by using energy delay metric for finding the optimal one with the lowest energy dissipation and lowest delay of the whole sensor networks. Also, sensors with the lowest energy resource should be the key pivots to distribute the energy dissipation. A. Optimal Delay Analysis Suppose sensors deployed in the networks of smart home. Optimal delay can be obtained by connecting sensors with suitable depth, h, and suitable number of divarication, n, of the tree topology. In a binary-tree, namely n=2, firstly half of the leaf nodes can send their data by parallel transmission in each round, then the leaf of the remaining tree (excluding the latest leaf nodes) send data and repeat until all the nodes except the root have sent their data. In an n-tree, 1/n of the leaf nodes can send their data simultaneously in each round and the remaining operations are finished by the same method as the binary-tree. Suppose the first level of the tree is connected directly to the root, the leaf nodes are at the h-th level, n delay would be made by each level s transmission and n i sensors can send data by parallel transmission at the i-th level. Thus, the total delay of an n-tree is given as follows: C delay = h n. (9) is given as follows: = 1+ n + n n h h+ 1 Using (9) and (1), the delay is as follows: n 1 = 1. (1) n 1 ln( n + n) C delay = ( 1) n. (11) ln n Some examples of (11) are shown in Fig. 3. Delay =1 =5 =4 =3 = n -tree Fig. 3. Delay varies with general n-tree by setting =1, 2, 3, 4, 5, and the minimal delays are 12, 14, 15, 16 and 16 respectively with n=2 or 3. B. Analysis of energy delay Metric Generally, the total energy dissipation of the networks is given as follows: network = T ( k, d ) + n( leaf ) ( n + 1)( ) ( k) leaf df R ( k) + (12) where d is the average transmitting distance of each sensors and is the number of leaf nodes in the n-tree. leaf h n n + n h 1 leaf = + n = + 1 n. (13) n Using (1), we give the depth of the n-tree as follows: ln( n + n) h = 1. (14) ln n Using (11)-(14), we calculate the value of energy delay metric as follows:

4 f ( n, ) = C delay nk(ln( n + n) / ln network = n 1)((15 + (15) + 5 / n) 55n 5) where is the average energy dissipation of amplifier part varying with in Fig. 1. If is given, the minimal value of f ( n, ) is determined by both and n for the routing problem in the networks of smart home. Fig. 4 shows the energy dissipations are changed slightly with the value of n. However, Fig. 3 plots the optimal delay costs are achieved with n=2 or 3. Average nergy Dissipation of ach Round n -tree =5 =4 =3 =2 =1 Fig. 4. Average energy dissipation varies with n-tree. Using (12)-(14), average energy dissipation of networks in each round with k=1 bit is plotted and is only affected by n slightly. Fig. 5 plots the value of energy delay metric varies with n. It shows that binary tree is the best solution for =2, 4 and 5 and 3-tree is the best solution for =1 and 3. Because the performances of both binary tree and 3-tree are nearly the same, we adopt binary tree routing in this paper. energy delay n -tree Fig. 5. Metric of energy delay varies with general n-tree. =5 =4 =3 =2 =1 C. Binary Tree Routing Protocol (1) Build Binary Tree for venly Distributing the nergy Dissipation In Binary Tree Routing Protocol (BTRP), suppose BS knows the energy resource of all sensors in each round and n=2. This paper gives the algorithm of generating n-tree by BS with the following steps. This is a general algorithm and n can be an arbitrary integer greater than 1. Step 1. Choose leaf sensors with minimal energy resource as leaf nodes of the tree. Step 2. Given n leaf nodes with the 2-dimensional coordinates as (x 1, y 1 ), (x 2, y 2 ), (x n, y n ), let x1 + x xn y1 + y yn x = and y =. The father n n node of the n leaf nodes is the sensor whose coordinate is closest to ( x, y ). h ( n 1) n + n Step 3. Find F = father sensors of the n( n 1) h -th level of the tree by using the method in Step 2, and let i = h 1. Step 4. Find n i father nodes of the nodes at the i-th level of the tree by using the method in Step 2. Step 5. Let i = i 1, repeat Step 4 until i = 1, and then stop. (2) Parallel Transmission Scheduling of Binary Tree Routing Suppose all nodes use CDMA [7] to avoid collisions. Thus some nodes in a cluster can transmit data simultaneously. Thus parallel transmission scheduling of BTRP offers advantages of reducing delay and interference. This paper provides binary tree routing scheduling algorithm to generate the parallel transmission sets of sensors as follows. Step 1. Let i = h. The initial operation set is L = leaf nodes in the i-th level of the binary tree. Step 2. Place L nodes into set R. Split R into R1 and R2 by satisfying that both x1 and x2 have the same father and at the same time they are in the different sets, where both x1 and x2 are arbitrary different elements in R. Step 3. All nodes in R1 (or R2) transmit their data simultaneously. Thus it costs 2 delays to transmit data in R. Step 4. If i >, the operation set is L = n nodes of the (i- 1)-th level in the binary tree. Then let i = i 1 and go to Step 2. Otherwise, stop. Sensors in the same sets can send data to their father simultaneously. The main idea of this algorithm is to place the sensors, who have no more data needed be collected on their sons (if they have any) in the current round and never have the same father, into the same parallel transmission set. V. PRFORMAC OF BTRP xperiments are done to evaluate the performance of BTRP. Parameters of energy dissipation for radio and data fusion are given in Section II and III. One packet includes 2, bits. etwork area is given as 2m 2m. The coordinate of BS is (1m, 1m). The precision of distance between any two sensors is given as decimeter (dm) because of the short distance in the networks of smart home. etwork lifetime is defined as the Time or rounds before the First sensor odes Dies (TFD). A new metric of lifetime/delay is used to clearly evaluate the total performance of the three routing protocols. Another new metric of the Ratio of TFD and TAD (RTT) is given to evaluate the evenly distributing of i

5 energy dissipation, where TAD is the Time or rounds before All sensor odes Die. Fig. 6 shows RTT metrics of Direct, THLD and BTRP vary with the number of sensors. BTRP performs well to evenly distribute the energy dissipation with RTT of more than 99%. Because BTRP chooses the sensors with less energy resource as leaf nodes of the binary tree, which consumes less energy for only transmitting data once in each round. THLD adopts another distributing scheme of choosing sensors with more energy resource as CHs to do the tasks that consume more energy. RTT even in Direct is reasonable in the networks of smart home. Both BTRP and THLD outperform Direct. And BTRP excels THLD in terms of RTT. RTT (%) Fig. 6. RTT for evaluating evenly distributing of energy dissipation. Simulations of the network lifetime (number of rounds) and delay of the three routing protocols show in Fig. 7 and Fig. 8 respectively. Fig. 8 shows both BTRP and THLD outperform Direct in terms of delay by introducing more energy dissipation costs shown in Fig. 7. Fig. 7 plots the lifetime of BTRP is not better than THLD. However, Fig. 8 shows BTRP performs better than THLD in terms of delay. example, the lifetime/delay metric in BTRP is 17.6%, 43.4% and 68.9% greater than that in THLD as well as 127%, and 431% greater than that in Direct in networks with 5, 1 and 15 sensors respectively. Delay lifetime / delay Fig. 8. Delay of each round Fig. 9. Metric of lifetime/delay varies with number of sensors. umber of Rounds VI. COCLUSIOS In the networks of smart home with area of 2m 2m, the routing protocols are provided for two goals: evenly distributing energy dissipation and reducing delay. This paper firstly applies THLD routing protocols to the networks of smart home. Then general n-tree multi-hop routing schemes are analyzed theoretically. Binary tree is proved to be the optimal tree routing by evaluating with energy delay metric. At last, RTT and lifetime/delay are used to evaluate the two goals above. xperiments shows BTRP outperforms the traditional Direct and THLD routing in terms of RTT and lifetime/delay. In a word, BTRP is an elegant solution for the networks of smart home. Fig. 7. etwork lifetime varies with the number of sensors. The total performance of the three routing protocols can be shown in Fig. 9 by the metric of lifetime/delay, which is the greater the better, because lifetime is the longer the better and delay is the shorter the better. Fig. 9 clearly plots BTRP excels both Direct and THLD in terms of lifetime/delay metric. For ACKOWLDGMT This work was supported in part by the ational Basic Research Program of China (o.25cb32164) and the ational atural Science Foundation of China (o.9272).

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