Energy Conservation in Progressive Decentralized ... - IEEE Xplore

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Energy Conservation in Progressive Decentralized Single-Hop Wireless Sensor Networks for Pervasive Computing Environment Chen Yu, Dezhong Yao, Laurence T. Yang, Member, IEEE, and Hai Jin, Senior Member, IEEE

Abstract—In the pervasive computing environment, energy efficiency is very important in terms of prolonging the lifetime of the communication. As a practical application in pervasive computing environment, wireless sensor networks consist of many sensors and several access points that make them work cooperatively to monitor/measure certain areas. Since the deployment of sensors in unknown sites impedes their recharging, thus exhausting their energy quite quickly, energy conservation becomes a critical issue. Unavoidably, the lavishness of both single- and multihop modes on energy conservation declines the system’s life span severely. Therefore, a progressive decentralized single-hop method is conceived. This mechanism works with several phases, in each of which sensors may act in single- or multihop mode. The wellbalanced energy consumption rate results in the extension of the system’s life span. The method also adapts in general cases and has been proven by mathematical demonstration to totally balance the energy consumption. In addition, the method is very easy to implement. According to the simulation results, it attains most of the original aims of energy conservation. Index Terms—Energy balanced, energy conservation, progressive decentralized single hop (PDSH), system lifetime, wireless sensor networks (WSNs).

I. I NTRODUCTION

T

HE pervasive computing is a novel paradigm in the field of communication and computing, where many intelligent equipment are involved in gathering information, sharing information, and making collaborative decision. To prolong the lifetime of the whole pervasive communication, the energy efficiency must be considered [27]–[29]. As a practical application of pervasive computing environment, wireless sensor network (WSN) need be optimized for energy conservation. WSN amasses many scattered autonomous sensors, working collaboratively to monitor certain sites for physical phenomena [1]. Sensors are deployed in monitoring areas so that they collect Manuscript received May 12, 2014; revised June 14, 2014; accepted June 20, 2014. The work is partly supported by NSFC (No. 61003220) and Technology Innovation Fund of Huazhong University of Science and Technology (No. CXY13Q018). C. Yu, D. Yao, and H. Jin are with the Services Computing Technology and System Laboratory and the Cluster and Grid Computing Laboratory, School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: [email protected]; dyao@hust. edu.cn; [email protected]). L. T. Yang is with School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China, and also with the Department of Computer Science, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada (e-mail: [email protected]). Digital Object Identifier 10.1109/JSYST.2014.2339311

environmental data and try to send the data to the sink [7]. An access point, which is also called a sink, is capable of holding a large computational burden and acts like a brain gathering all the data to analyze them. Normally, sensors and sinks constitute a WSN, which are often multihop networks: nodes function as forwarders relaying data to the sink. The energy is the scarcest resource in WSN. Experimental measurements have shown that data aggregation do not consume as much energy as data transmission and receipt. The energy cost for transmitting single-bit data is nearly the same as that of processing 1000 commands in a typical sensor device [8], [9]. In this paper, we focus on the energy efficiency of sensors in data transmission and receiving. The networks are divided into equivalent clusters, in each of which a sink gathers the data from sensors. Hence, if one cluster is energy efficient, the others are, too. There are two basic methods to deliver data from sensors to a sink: single hop and multihop, as shown in Fig. 1. In single hop, each sensor gives its best effort to reach the sink directly. As the same amount of data has to be sent, a farther sensor node has to work harder than the nearer one over the greater communication distance. This apparently leads to faster energy exhaustion, and the whole system ends up with an unexpected earlier dead time, with much energy remaining in the nodes adjacent to the sink. A similar problem happens in multihop. When sensors send data hop by hop, sensors not only work as originators but also as forwarders, and it is obvious that the sensors nearer to the sink have to accomplish more forwarding jobs than the ones farther away. There are many studies to solve the problem. Low-Energy Adaptive Clustering Hierarchy (LEACH) selects some nodes as heads, to gather and relay the data for sensors nearby [10]. While the energy consumption is well balanced and efficient, the network has to execute a head election step over and over. Another strategy is deployment control [18], which adjusts the node density in specific areas, in order to alleviate the remaining energy problem. However, it is impractical to deploy a large amount of sensors manually, particularly in unknown places. Moreover, a hybrid of single hop and multihop can partially solve the problem [19]–[25]. We propose a progressive decentralized single-hop (PDSH) method that neither requires the node to do any extra energy intensive jobs nor places the nodes in any kind of distribution constraints. Single hop drains outer nodes faster, whereas multihop drains inner ones faster. Hybrid is a strategy the combines the two methods to make

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Fig. 1. Basic data collection methods in WSNs. (a) Single-hop network. (b) Multihop network.

energy consumption even. Our method, which is grounded on Hybrid, splits the progress into many phases, in which the network has a unique mode of gathering data, and between which the series of sensor nodes changes their modes between single hop and multihop. In one or more combinations of the phases, the system appears to transform its nodes’ working modes from multihop to single hop progressively, from interior to exterior, and that is why we call this the PDSH method. We will testify to it in theoretical proof and in simulations. The rest of this paper is organized as follows. We briefly describe related studies in Section II, and in Section III, the system models are built. In Section IV, our method is shown in detail, with the mathematical demonstration. Section V shows the results and analysis of the simulations. II. R ELATED W ORK The Hybrid data gathering protocol is first proposed in [19], where all sensor nodes alternate periodically between singlehop mode and multihop mode, to prolong the system’s life span. To implement this protocol, the cluster head is supposed to broadcast a switch-over message periodically, or each sensor would have a timer to indicate when to switch over. The key point would be choosing the best time portion for each of the two modes. It needs a near-optimal method to solve this, although it does not make the energy burden completely uniform among all these nodes. The study in [23] proposes an optimal mixed data gathering algorithm, which is based on calculating the nodes’ residual energy periodically, and proves that hybrid data gathering approaches perform better than centralized multihop algorithms from an energy-saving perspective. In [20], the sensor nodes run on single-hop mode sometimes and multihop mode sometimes. Unlike in [19], not all the nodes switch their mode to single hop or multihop at the same time. Hence, the network works in two modes simultaneously. To balance the energy consumption of each node, a node should decide whether to use single-hop mode or multihop mode, according to the information it received from the previous-hop node and the next-hop node, which tells the node how much energy remains in the previous-hop and next-hop nodes, as well as how much energy has been consumed by its neighbor node per minute. These communications for status inquiring should be scheduled periodically, so that the node can choose the right mode to run and the network will be well energy balanced. The studies in [21] designed a probabilistic data gathering strategy,

to balance the different energy consumption among nodes. In [22], the authors separated the network topology into several coronas and balanced the node’s energy consumption inside coronas and intercoronas. This makes every node select the next hop intelligently, to balance the variance of energy dissipation between nodes in the same coronas. Then, it separates the data flows of each node into forwarding flows and direct-hopping flows. If the equation with an amount of forwarding data, directhopping data, and receiving data and the equation of energy consumption of each node on one path are satisfied, this path of the network should be totally energy balanced. However, these conditions may not be always satisfied in some network parameters, such as node deployment density, the minimum fixed multihop transmission range, or even radio transmission loss. Moreover, authors in [24] tried to find a better network division for balancing energy consumption, and authors in [25] proposed an algorithm to compute the optimal parameters of a probabilistic data propagation algorithm in WSNs. In [30], the researchers deployed a weighted grid to reduce the energy consumption for different grid. The work [31] introduced an approach for robust scalable network coding in dynamic environments. III. S YSTEM M ODELS A sensor cluster has a number of sensors densely deployed with one sink. The sensor, which is energy limited and not able to recharge, senses the environmental phenomena and generates the sensing data. The sink, which may have a power supply, or larger batteries and looser constraints on size or price, is able to conduct heavier computational and communicational tasks (gathering and congregating all those sensing data in specific areas). This method works for balancing the energy consumption of the sensor nodes inside the cluster and maximizes the life span. A. Network Models Plenty of sensors are uniformly distributed in a round cluster area C of radius R, with a constant distribution density w. The sink is located at the center of the cluster, gathering all the data from the sensors. We denote the maximum transmission range of a sensor as rmax -trans , which is larger than R, which makes each sensor able to send data to the sink directly. If rmax -trans ≤ R in some cases, this method can be also achieved

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Proof: Since the nodes are uniformly deployed in the cluster with distribution density ρ, the number of the nodes Nk in Rk would beρ times the areas of Rk , 1 ≤ k ≤ n, i.e., Nk = ρ × π × (r × k)2 − π × (r × (k − 1))2 .

Fig. 2.

Network division (n = 5).

by placing several stronger nodes to form subclusters, which have similar responsibility as a cluster. Like the model in [20], C is divided into n rings with the same width r, where it is easy to see that R = n × r, n ≥ 1, 0 < r ≤ R. These rings are denoted by R1 , R2 , R3 , . . . , Rn−1 , Rn from inner to outer, as shown in Fig. 2. When a node works in the multihop mode, it has to send the data to the node in the next inner ring with a fixed transmission range rmulti-hop . To communicate with the next-hop node in the next inner ring, rmulti-hop should be larger than r, but smaller than 2r. When a node works in the singlehop mode, it has to directly communicate with the sink with the data transmission range rsingle-hop . Since rsingle-hop is only related to the distance from the sensor to the sink, if the node is in Rk (1 ≤ k ≤ n), we can compute it as rsingle-hop = k × r. B. Traffic Models We assume that the network works in rounds as in [10]. The sensing data are generated at the same rate in every place of the cluster, which means that each sensor constantly produces ls bits per round. The traffic sent out by a node in ring k is denoted by lk . We first consider the pure single-hop case and the multihop case. Since each sensor sends data directly to the central sink in the single-hop mode, no sensor has to receive any data and only has to transmit ls traffic per round. Thus, lk = ls , 1 ≤ k ≤ n, in the single-hop mode. Traffic model in the multihop case is not the same as that in the single-hop case at all, since the data have to be forwarded hop by hop. A sensor node also produces ls bits per round on its own, but sends them to the nodes in the next ring. Thus, each sensor has to receive the data from the sensors in the previous outer ring, except for the node in the outermost ring, which means that ln = ls . Generally, a node in ring k − 1 should receive data from several nodes in ring k and produce ls -bit data and then send both to some node in ring k − 2. When we know that the data sent from nodes in ring k are all going into the nodes in ring k − 1, and assuming that each node in ring k − 1 averagely receives the traffic flowing out from ring k, we can obtain the relationships of the node’s traffic between neighbor rings as in Lemma 1. Lemma 1: In the pure multihop mode, the traffic relationship between a node in Rk−1 and a node in Rk would be lk−1 =

2k − 1 × l k + ls 2k − 3

where 2 ≤ k ≤ n, and ln = ls .

(1)

Since nodes in Rk−1 averagely receive the data from Rk , the ratio of the amount of data received by the nodes in ring k − 1 to that sent by the nodes in ring k is equal to the ratio of the number of the nodes in ring k to that in ring k − 1. Additionally, each node also has to produce ls -bit data by itself. Thus, a node in Rk−1 gets lk−1 bits of data to transmit totally, where 2 ≤ k ≤ n, and ln = ls , i.e., Nk lk−1 = × lk + ls Nk−1 ρ× π×(r×k)2 −π×(r×(k−1))2 × lk + ls = ρ× π×(r×(k−1))2 −π×(r×(k−2))2 2k − 1 × l k + ls . = 2k − 3 The recurrence formula about the amount of data that has to be sent out by a node in ring k − 1 to the next hop in ring k − 2 has been shown above. The general formula is given out in the following. Theorem 1: In the pure multihop mode, the traffic of the nodes in ring k should be 2 n − (k − 1)2 × ls (2) lk = 2k − 1 where 1 ≤ k ≤ n. Proof: When k = n, ln = [n2 − (n − 1)2 ] × ls /(2n − 1) = ls is true. In addition, when 1 ≤ k ≤ n − 1, we iterate the formula in Lemma 1 and can get 2·k+1 × lk+1 + ls lk = 2·k−1 2·k+3 2·k+1 × × lk+2 + ls + ls = 2·k−1 2·k+1 .. . n−k

ls × (2 · k − 1 + 2 · i) 2 · k − 1 i=0 2 n − (k − 1)2 × ls . = 2·k−1

=

As shown in the previous section, the nodes are farther from the sink and send less data than the nearer ones. Theorem 2: The node in Rk−1 sends out more data than that in Rk , where 2 ≤ k ≤ n, i.e., lk−1 > lk ,

2 ≤ k ≤ n.

(3)

Proof: From Lemma 1, we can easily obtain 2 × l k + ls lk−1 − lk = 2·k−3 because lk > 0 and k > 2, lk−1 − lk > 0, lk−1 > lk , where 2 ≤ k ≤ n.



C. Energy Consumption Models Sensors consume energy for computation, environment sensing, data transmission, and data receipt. Computational energy consumption is so little that it is not taken into account. As every sensor consumes the same amount of energy for environment sensing and sensors are uniformly deployed in the network, this method has the same resolution, whether considering the energy consumption for environment sensing or not. Hence, energy consumption for environment sensing is not considered, for simplicity of the deducing process. The energy consumption models for data transmission and receiving are similar to the models in [10]. The radio transmitter dissipates energy to run the radio electronics and the power amplifier, and the receiver consumes power to run the radio electronics. If the distance between transmitter and receiver is smaller than the distance threshold d0 , free-space fading channel models are used, in which the fading factor ω is 2. Otherwise, the multipath fading models are used, with w = 4. Consequentially, in order to transmit l-bit message, a transmitter would use energy of

Eelec × l + εfs × l × d2 , d < d0 (4) Etx (l, d) = Eelec × l + emp × l × d4 , d ≥ d0 where d is the distance from transmitter to receiver; electronics energy, i.e., Eelec , depends on the attributes of electronics; and εfs and εmp are the amplification coefficients for the freespace fading channel model and the multipath fading model, respectively. To receive this message, a receiver would expend Erx (l) = Eelec × l.

(5)

We now go back to our case. When the network environment has been set up, the energy consumption of a sensor would be dependent on the transmission range d, the amount of the data received, and the amount of data that it is going to send out. Definition 1: α = 2 × Eelec ,

β = εamp ,

2 ≤ k ≤ n.

(7)

However, in the multihop mode, a node in ring k − 1 dissipates more energy than a node in ring k, where 2 ≤ k ≤ n, i.e., Ek−1 > Ek ,

2 ≤ k ≤ n.

(8)

Proof: In the single-hop mode, a node in ring k has to transmit data with a range of d = rsingle-hop = k × r, where 1 ≤ k ≤ n. Each sensor sends out the same amount of data, i.e., lk = ls . Using Lemma 2 to compute ϕ, which is the energy difference between node in rings k and k − 1, where 2 ≤ k ≤ n, i.e., ϕ = Ek (ls , r × k) − Ek−1 (ls , r × (k − 1)) =[γ + (α + β × (r × k)ω × ls ] − [γ + (α + β × (r × (k − 1))ω × ls ] = β × rω × ls × [k ω − (k − 1)ω ] > 0. In addition, in the multihop mode, each node has the same fixed transmission range of rmulti-hop . From Lemma 2 and Theorem 2, we obtain ϕ = Ek (lk , rmulti-hop ) − Ek−1 (lk−1 , rmulti-hop ) ω = γ + (α + β × rmulti -hop × lk ω − γ + (α + β × rmulti hop × lk−1 ω = α + β × rmulti -hop × [lk − lk−1 ] < 0 where 2 ≤ k ≤ n. Furthermore, each node is assumed to have the same initial energy store as E0 .

A. Approach Illustration

Lemma 2: In single- or multihop mode, the energy consumption of a node in ring k is 1≤k≤n

Ek−1 < Ek ,

IV. PDSH A PPROACH

γ = −Eelec × ls .

Ek (lk , d) = γ + (α + β × dw ) × lk ,

Theorem 3: In the single-hop mode, a node in ring k − 1 dissipates less energy than a node in ring k, where 2 ≤ k ≤ n, i.e.,

(6)

where d is the transmission range of that node. Proof: In the single-hop mode, sensors do not have to receive any data; thus, lk is equal to ls , where 1 ≤ k ≤ n. From (4), sensors in ring k would use Ek (lk , d) = Etx (lk , d) = Eelec × ls + εamp × ls × dω = γ + (α + β × dω ) × lk . From (4) and (5), in multihop mode, the sensor in ring k would expend Ek (lk , d) = Etx (lk − ls ) + Etx (lk , d) = Eelec ×(lk − ls ) + Eelec × lk + εamp × lk × dω = γ + (α + β × dω ) × lk .

The network starts with a multihop mode, where all the nodes send the data they both received and produced to the node in the next inner ring. We call this phase 1, which lasts t1 rounds. When this mode is working, nodes in the inner rings have to carry heavier traffic, as we proved in Theorem 2; thus, they dissipate more energy, as we proved in Theorem 3. To balance the energy consumption between nodes in the first ring and the second ring, the nodes in the second ring start sending their data directly to the sink at time t1 , and nodes in the other rings continue to work as they did in phase 1. We call this phase 2, which lasts t2 rounds. In this phase, the nodes in the second ring bear the biggest energy dissipation, because they transmit more traffic than the nodes in all the other rings and have the longest transmission range at this time, compared with the nodes in the other rings. At the time of t1 + t2 , the network moves into phase 3, where the third ring’s nodes start to invert the transmission mode to single hop, which lasts t3 rounds. Then, the network working mode would be as follows: first, the ring’s nodes use single hop; second, the ring’s nodes use single hop; third, the ring’s nodes use single hop; and the other


nodes use multihop. Since the energy consumption of the third ring’s nodes is biggest in this phase and it is less than that of the second ring’s nodes in phases 1 and 2, the energy consumption balancing between the second ring’s and third ring’s nodes can be achieved by setting appropriate periods of t1 , t2 , t3 , and so forth. Going through k − 1 phases, the network comes into phase k, 1 ≤ k ≤ n, which lasts tk rounds. The nodes in ring k start to apply single-hop mode, whereas the other nodes do not change mode. The network would be like the nodes outside more than ring k apply the multihop mode, and nodes inside more than ring k apply the single-hop mode. Nodes in ring k would have the fastest energy consumption velocity in this phase. Theorem 4: In phase k, where 1 ≤ k ≤ n, nodes in ring k consume energy faster than those of all the other rings, and all the nodes in more inner rings follow the energy consumption model as the single-hop case, and all the nodes in the more outer rings follow the energy consumption model as the multihop case, i.e., Ek,1 < Ek,2 < · · · < Ek,k−1 < Ek,k Ek,k > Ek,k+1 > · · · > Ek,n−1 > Ek,n .

(9)

Proof: Phase 1, where k = 1, is a pure multihop mode. In addition, from Theorem 3, E1,1 > E1,2 > · · · > E1,n−1 > E1,n . Phase n, where k = n, is a pure single-hop mode. In addition, from Theorem 3, En,1 < En,2 < · · · < En,n−1 < En,n . Commonly, three kinds of working modes of node exist in phase k, where 2 ≤ k ≤ n − 1. Nodes in ring p work in singlehop mode, where 1 ≤ p ≤ k − 1. Nodes in ring q work in multihop mode, where k + 1 ≤ q ≤ n. According to Theorem 3 Ek,1 < Ek,2 < · · · < Ek,k−2 < Ek,k−1 Ek,k+1 > Ek,k+2 > · · · > Ek,n−1 > Ek,n . Nodes in ring k during phase k are in special mode, where each gets data from ring k + 1, which follows the multihop mode in data traffic, but sends its data directly to the sink as single-hop mode in transmission. From (4), (5), and Definition 1, the energy consumption velocity of this node is Ek,k = γ + (α + β × (r × k)ω ) × lk Ek,k−1 = γ + (α + β × (r × (k − 1))ω ) × ls Ek,k+1 = γ + (α + β × (rmulti-hop )ω ) × lk+1 . Hence, Ek,k > Ek,k−1 , and from Theorem 2, Ek,k > Ek,k+1 . After going through n − 1 phases, the network comes into the final phase, i.e., phase n, which lasts tn rounds. The nodes in ring n start to perform single hop in this phase, and the network would be a pure single hop. All the phases in a four-hop case are concisely depicted in Fig. 3, where Node 1 means the node in ring 1. With some network condition constraints, such as R, ρ, ls , and εamp , the network may be energy balanced by building up an appropriate set of phase periods tk , 1 ≤ k ≤ n. This approach extends to general cases with these constraints removed in the following section, and we also will figure out how to compute the set of phase periods.

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Fig. 3. Phases of the network (n = 4).

B. General Case In this part, we are going to prove that our approach is available in general cases with no constraints, where the node deployment density ρ has to stay in a density interval, or the original data generation rate ls is bigger than some value. The network energy dissipation will be totally balanced without any energy remaining in any node, when the network’s life span is over. During the demonstration process, the problem of how to compute that set of phase periods is solved step by step. The whole proving process is complex; thus, we begin with the special ones. When n = 1, the network is just like a single-hop network, with a fixed transmission range for every node. This generates the same amount of traffic and uses the same range of transmission. According to Theorem 1 and Lemma 2, they consume energy at the same velocity. Hence, the energy consumption velocity of all the nodes is balanced. When n = 2, the network is divided into two rings with two phases. In phase 1, the network is a pure multihop network. According to Theorem 1 and Lemma 2, the energy consumption of nodes in each ring would be ω E1,1 = γ + α + β × rmulti -hop × 4ls ω E1,2 = γ + α + β × rmulti -hop × ls . In addition, in phase 2, the network is a pure single-hop network; thus, the energy consumption of nodes in each ring would be E2,1 = γ + (α + β × rω ) × ls E2,2 = γ + (α + β × (2r)ω ) × ls . To make the statement easy, we call the nodes in ring k node k. To balance the energy consumption difference between nodes 1 and 2, the amount of energy used by node 1 through both two phases should be equal to that used by node 2, as in E1,1 × t1 + E2,1 × t2 = E1,2 × t1 + E2,2 × t2 .

(10)

Theorem 5: The energy consumption will be balanced in a two-hop case, which means that (10) is true with positive values of t1 and t2 , only if t1 β · rw · (2w − 1) . = t2 w 3 · α + β · rmulti -hop

(11)



Proof: If (10) is true, we can have the equation shown at the bottom of the page, where α, β, and r are greater than 0, and ω = 2 or 4. In addition, the ratio of t1 to t2 is positive. Thus, if (11) is true, there are positive t1 and t2 to make (10) become true. The problem we confront would be finding out a set of phases’ lasting times, to make the nodes in every ring have the same energy consumption velocity through all those phases. In other words, (12) should be true with tk > 0, 1 ≤ k ≤ n, n ≥ 2, i.e., n

Ek,1 · tk =

k=1

n

Ek,2 · tk = · · ·

k=1

=

n

Ek,n−1 · tk =

k=1

n

Ek,n · tk .

(12)

k=1

Definition 2: When 1 ≤ i ≤ n, 1 ≤ j ≤ n − 1 ai,j = Ei,j − Ei,j+1

(13)

when substituting (13) into (12), we obtained another form of (12), as will be shown in (14). Since the cases of n = 1 and 2 have been solved, we focus mainly on the case of n ≥ 3 in the following statement. Theorem 6: If the linear equations group A(n−1)×n × t = 0, as in (14), has a set of positive solutions t, the energy consumption velocity difference between nodes can be eliminated, which means that (12) is true where n ≥ 2, i.e., ⎡ ⎤ t1 ⎡ a a2,1 ··· ··· an−1,1 an,1 ⎤⎢ t ⎥ 1,1 2 ⎥ a2,2 ··· ··· an−1,2 an,2 ⎥⎢ ⎢ a1,2 ⎢ .. ⎥ ⎢ . ⎥ ⎢ .. .. .. ⎥ . ⎥ = 0. .. .. ⎢ . . . .. ⎥ . . . ⎥⎢ ⎢ . ⎥ ⎣ ⎦⎢ ⎢ a1,n−2 a2,n−2 · · · · · · an−1,n−2 an,n−2 ⎣ . ⎥ ⎦ a1,n−1 a2,n−1 · · · · · · an−1,n−1 an,n−1 tn−1 tn (14) Proof: When 1 ≤ j ≤ n − 1, from (12), we can easily get n

k=1

Ek,j · tk =

n

k=1

Ek,j+1 · tk ⇔

n

ak,j · tk = 0.

k=1

There are some properties among the entries of the energy consumption velocity difference matrix A(n−1)×n . Theorem 7: In the coefficient matrix A(n−1)×n , if j ≥ i, the value of ai,j is positive, whereas if j < i, the value of ai,j is negative, i.e.,

ai,j > 0, j ≥ i (15) ai,j < 0, j < i where 1 ≤ i ≤ n, 1 ≤ j ≤ n − 1, n ≥ 2.

Proof: From Theorem 4, we have

Ei,j < Ei,j+1 , j ≤ i − 1 Ei,j < Ei,j+1 , j ≥ i where 1 ≤ i ≤ n, 1 ≤ j ≤ n − 1, n ≥ 2. Lemma 3: The energy consumption velocity of node j in phase i would be ⎧ n2 −(j−1)2 ·l ( ) s w ⎪ ⎪ γ + α + β · r , j>i ⎨ multi-hop · 2·j−1 2 2 Ei,j = (n −(j−1) )·ls γ + (α + β · (j · r)w ) · , j=i ⎪ ⎪ 2·j−1 ⎩ j i, the nodes are still in multi-hop mode, waiting for their chance to change mode. These nodes all comply with the multihop traffic model in (2) and the energy model in (6). Ei,j can be expressed as 2 n − (j − 1)2 × ls ω . × Ei,j = γ + α + β × rmulti -hop 2j − 1 When j = i, the nodes are just at the phase of changing their mode to single hop. These nodes should burden the adverse effects of the long transmission range of single hop and the heavy traffic of multihop, which would expand 2 n − (j − 1)2 × ls ω . Ei,j = γ + (α + β × (jr) ) × 2j − 1 When j < i, these nodes have changed to single-hop mode and go on working in the rest of the phases. The nodes that work in single-hop mode would have the energy consumption velocity of Ei,j = γ + (α + β · (j · r)w ) · ls . From Lemma 3 and Definition 2, we can get the expression of the entries of the energy consumption velocity difference matrix A(n−1)×n . Theorem 8: The energy consumption velocity difference matrix A(n−1)×n is expressed as ⎧ 2·(n2 −j 2 ) w ⎪ α + β · r · 1 + · ls , j > i 2 ⎪ multi-hop 4·j −1 ⎪ ⎪ ⎪ 2 2 n −(j−1) ·l ⎪ ( ) s ⎪ (α + β · (j · r)w ) · ⎪ ⎪ 2·j−1 ⎨ (n2 −j 2 )·ls w − α + β · rmulti j=i ai,j = -hop · 2·j+1 , ⎪ ⎪ w ⎪ (α + β · (j · r) ) · ls ⎪ ⎪ ⎪ (n2 −j 2 )·ls w ⎪ ⎪ j = i−1 ⎪ ⎩ − (α + β · ((j + 1) · r) ) · 2·j+1 , j < i−1 β · rw · (j w −(j + 1)w ) · ls , (17) where 1 ≤ i ≤ n, 1 ≤ j ≤ n − 1. Proof: When we put (16) into (13), we get (17). From Theorem 8, more properties of matrix A(n−1)×n are shown in the following.

t1 E2,2 − E2,1 γ + (α + β · (2r)w ) · ls − (γ + (α + β · rw ) · ls ) β · rw · (2w + 1) = = = t2 E1,1 − E1,2 w w w · 4 · l · l γ + α + β · rmulti − γ + α + β · r 3 · α + β · r s s multi-hop multi-hop -hop


Theorem 9: The positive part of each column in matrix A(n−1)×n constitutes a monotonic decreasing sequence, whereas the negative part of that constitutes a monotonic decreasing sequence, too. Meanwhile, the positive entries, except for the rightmost positive one in a row of matrix A(n−1)×n , have the same values and are less than the rightmost positive one, i.e.,

ai,j > ai,j+1 , j ≥ i (18) ai,j > ai,j+1 , j < i − 1

i i, the differential coefficient of ai,j would be dai,j j = −4(α + β × rω ) × ls × (4n2 − 1) × dj (4j 2 − 1)2 because j > 1, ai,j < 0. When j > i, ai,j > ai,j+1 , and when j < i − 1, the differential coefficient of ai,j would be dai,j = β × rω × ls × ω × j ω−1 − (j + 1)ω−1 dj

A(n−1)×n ⎡

1 ⎢0 ⎢ ⎢ 0 =⎢ ⎢ ⎢ .. ⎣. 0

a2,2 a1,2 a2,3 a1,3

a2,1 a1,1

a2,1 a1,1 a2,1 a1,1

− − .. . a2,n−1 a1,n−1 −

a2,1 a1,1

a3,2 a1,2 a3,3 a1,3

a3,1 a1,1

a3,1 a1,1 a3,1 a1,1

− − .. . a3,n−1 a1,n−1 −

a3,1 a1,1

··· ··· ··· .. . ···

an,2 a1,2 an,3 a1,3

an,1 a1,1

⎤ ⎥ ⎥ ⎥ ⎥. ⎥ ⎥ ⎦

an,1 a1,1 an,1 a1,1

− − .. . an,n−1 a1,n−1 −

an,1 a1,1

(20) Lemma 4: If b1,1 > 0, b2,1 < 0, (21) has positive solutions, i.e., b1,1 · x1 + b2,1 · x2 = 0.

of (n + 1)-variables has a set of positive solutions, too, where n ≥ 2, 1 ≤ i ≤ n, 1 ≤ j ≤ n − 1, i.e., ⎡ ⎤ ⎤ x1 ⎡ b b · · · · · · b b 1,1 2,1 n−1,1 n,1 ⎢ x2 ⎥ ⎥ b2,2 ··· ··· bn−1,2 bn,2 ⎥⎢ ⎢ b1,2 ⎢ .. ⎥ ⎢ . ⎢ . ⎥ .. .. .. ⎥ .. .. ⎥ ⎢ . =0 . . .. ⎥ . . . ⎥⎢ ⎢ . ⎥ ⎦⎢ ⎣ . ⎢ ⎥ b1,n−2 b2,n−2 · · · · · · bn−1,n−2 bn,n−2 ⎣ ⎦ b1,n−1 b2,n−1 · · · · · · bn−1,n−1 bn,n−1 xn−1 xn

bi,j > 0, j ≥ i b < 0, j < i ⎧ i,j ⎨ bi,j = bi,j+1 , j > i bi,j > bi,j+1 , j = i (22) ⎩ bi,j > bi,j+1 , j < i − 1. Proof: Transforming Bn×(n+1) the coefficient matrix of that linear equations of (n + 1)-variables by row elemental transformation as the way of transforming matrix A(n−1)×n to like matrix A(n−1)×n , we get the transformed matrix Bn×(n+1) A(n−1)×n . When eliding the first row and the first column of Bn×(n+1) , we get an (n − 1) × n submatrix, which is sub B(n−1)×n ⎡ b2,2

where ω is 2 or 4. Thus, ai,j < 0, and ai,j > ai,j+1 , when j < i − 1. According to Theorem 8, ai,j = ai+1,j when i < j − 1, and ai,j < ai+1,j when i = j − 1, as well as when i = j, ai,j > ai−1,j > ai−1,j+1 = ai,j+1 , and a1,1 > a1,2 . Combin ing with the result above, ai,j > ai,j+1 when j ≥ i. When there are more than three rings in the network, i.e., n ≥ 3, matrix A(n−1)×n can be transformed to matrix A(n−1)×n by elemental row transformations, where each entry is divided by the first entry of its row; then each row, except for the first row, is subtracted by the first row. We get

(21)

Proof: When x1 = −(b2,1 /b1,1 ) · x2 , (21) is true, where x1 > 0, x2 > 0. Lemma 5: For the homogeneous linear equations group in the following, whose coefficient matrix is content with the conditions in (22), if every linear equations group of n-variables has a set of positive solutions, every linear equations group

7

⎢ ⎢ =⎢ ⎢ ⎣

b1,2 b2,3 b1,3

b2,n b1,n

− − .. . −

b2,1 b1,1 b2,1 b1,1

b3,2 b1,2 b3,3 b1,3

b2,1 b1,1

b3,n b1,n

− − .. . −

b3,1 b1,1 b3,1 b1,1

··· ··· .. . ···

b3,1 b1,1

bn+1,2 b1,2 bn+1,3 b1,3

bn+1,n b1,n

− − .. . −

bn+1,1 b1,1 bn+1,1 b1,1

⎤ ⎥ ⎥ ⎥. ⎥ ⎦

(23)

bn+1,1 b1,1

According to the properties that Bn×(n+1) is satisfied in (22), sub has the same properties as in (24) and (25), where B(n−1)×n 2 ≤ i ≤ n + 1, 2 ≤ j ≤ n, i.e., bi,j bi,1 b1,j − b1,1 > 0, j ≥ i (24) bi,j bi,1 b1,j − b1,1 > 0, j < i ⎧b bi,1 bi,j+1 bi,1 i,j ⎪ − b1,1 = b1,j+1 − b1,1 , j>i ⎪ ⎨ b1,j bi,j bi,1 bi,j+1 bi,1 (25) b1,j − b1,1 > b1,j+1 − b1,1 , j = i ⎪ ⎪ ⎩ bi,j − bi,1 > bi,j+1 − bi,1 , j < i − 1. b1,j

b1,1

b1,j+1

b1,1

sub Equations (24) and (25) denote that the submatrix B(n−1)×n is also content with the conditions in (22), since every linear equations group of n variables, which satisfied the conditions in (22), has a set of positive solutions. The linear equations group sub × X = 0 must have a set of positive solution, which B(n−1)×n is denoted by vector (m1 , m2 . . . mn−1 , mn )T . On account of b1,1 > 0 and bi,1 < 0, where 2 ≤ i ≤ n + 1, there must be a λ making the vector (λ, m1 , m2 . . . mn−1 , mn )T a set of positive solutions for linear equations Bn×(n+1) × X = 0, where λ=

n+1

i=2

bi,1 · mi−1 . b1,1

(26)

The other linear equations group with (n + 1)-variables has the same features as above; thus, each one of them has a set of positive solutions.



Theorem 10: If a linear equations group of n-variables is content with the conditions as in (22), those linear equations must have a set of positive solutions, where n ≥ 2. Proof: By Lemma 4, when n = 2, the linear equations group has a set of positive solutions. By Lemma 5, if every linear equations group with n-variables has a set of positive solutions, every linear equations group with (n + 1)-variables has a set of positive solutions. Using the principle of mathematical induction, if a coefficient matrix is content with the conditions in (22), that linear equations group of n-variables must have a set of positive solutions, where n ≥ 2. We go back to the submatrix of A(n−1)×n , which elided the first row and the first column from the transformed matrix sub A(n−1)×n denoted by Asub (n−2)×(n−1). The submatrix A(n−2)×(n−1) is proved in Theorem 11 to hold the same properties as (22). Theorem 11: The equations group A(n−1)×n × X = 0, as in (14), must have a set of positive solutions, where n ≥ 3. Proof: As we proved in Theorem 7 and Theorem 9, A(n−1)×n has the same properties as in (15), (18), and (19). Hence, the entries of the submatrix of Asub (n−2)×(n−1) follow the rules as in (24) and (25), where 2 ≤ i ≤ n, 2 ≤ j ≤ n − 1, n ≥ 3. According to Theorem 10, Asub (n−2)×(n−1) × X = 0 has a set of positive solutions, which is denoted by (v1 , v2 . . . vn−2 , vn−1 )T . Owing to a1,1 > 0 and ai,1 < 0, where 2 ≤ i ≤ n, there must be a positive variable λ = n+1 i=2 (ai,1 /a1,1 ) · vi−1 , making (λ, v1 , v2 . . . vn−2 , vn−1 )T to be a set of positive solutions for A(n−1)×n × X = 0. According to Theorem 6 and Theorem 11, when there are three or more rings in the network, the network can be totally energy balanced. To compute the exact phase periods, the calculation methods in Theorem 8, Theorem 11, and Lemma 5 can be applied. The coefficient matrix of linear equations group A(n−1)×n × t = 0 as in (14) can be row transformed to the matrix, as in (27), where the entries pi,j are positive when j = i, and pi,j is negative when j < i, and pi,j is zero when j > i, i.e., ⎤ ⎡ p11 p2,1 p3,1 · · · pn−2,1 pn−1,1 pn,1 ⎢ 0 p2,2 p3,2 · · · pn−2,2 pn−1,2 pn,2 ⎥ ⎥ ⎢ ⎢ 0 0 p3,3 · · · pn−2,3 pn−1,3 pn,3 ⎥ ⎢ . .. .. .. ⎥ .. .. .. ⎥. (27) ⎢ . . . . ⎢ . . . . ⎥ ⎥ ⎢ .. ⎣ 0 . pn−2,n−2 pn−1,n−2 pn,n−2 ⎦ 0 0 0 0 0 ··· 0 pn−1,n−1 pn,n−1 As we know, the row transformations do not change the solutions of linear equations; thus, with several more row transformations, we could get the transformed matrix, as in ⎡ ⎤ q1,1 0 0 ··· 0 0 qn,1 ⎢ 0 q2,2 0 · · · 0 0 qn,2 ⎥ ⎢ ⎥ ⎢ 0 0 q3,3 · · · 0 0 qn,3 ⎥ ⎢ . .. .. .. .. ⎥ .. .. ⎢ . ⎥. (28) . . ⎢ . . . . . ⎥ ⎢ ⎥ .. ⎣ 0 . qn−2,n−2 0 0 0 qn,n−2 ⎦ 0 0 0 ··· 0 qn−1,n−1 qn,n−1 Hence, the phase periods are ti = −

qn,i · tn , qi,i

1≤i≤n−1

(29)

TABLE I N ETWORK PARAMETERS

Fig. 4.

Network lifetime in theory and simulation (ω = 2).

where tn > 0, qn,i < 0, and qi,i > 0. As the cases of one ring and two rings have been stated at the beginning of this section, this method has been proved that it can balance the network energy consumption velocity in every network division case. Without any other network parameter constraints, the network performed very energy efficiently, and the system’s life span was maximized. V. S IMULATION R ESULTS We show some simulation results and the analysis here. In the first part, we want to find the difference between the simulation and the theory. In the second part, we try to find the relationships among the network parameters. In the third part, the method is compared with the Hybrid data gathering scheme and LEACH, for two different aspects. A. Theoretical and Simulation Results In this part, the theoretical results matched with the simulation results. The basic network parameters are shown in Table I. The area radius ranged from 150 to 500 m. The nodes are deployed according to near-uniform distribution. The node density was 0.01 node/m2 . The node initial energy E0 was set as 1 J. Both the free-space fading and multipath fading channel models were adopted. The optimal multihop transmission range was figured out in [22], and according to our network environment, 1.5r was used as multihop transmission range rrelay . Each node sent to send 500-bit data every round. The networks were divided into 15 rings in this simulation. The simulation results are shown in Figs. 4 (the free-space fading channel model, w = 2) and 5 (the multipath fading channel model, w = 4). Obviously, the network lifetime of


Fig. 5.

Network lifetime in theory and simulation (ω = 4).

Fig. 6. Network lifetime in theory and simulation with best network division (ω = 2).

simulations run nearly as long as that of theory in both channel fading models. As in the free-space fading channel model case, the network with a 150-m radius lasts 8496 rounds before it runs out of power in theory. That network runs 8437 rounds in the simulation, approximately the same life span as in theory. With a 275-m network radius, the network runs 3676 rounds in theory, nearly the same as the life span in simulation, which runs 2628 rounds. With a 475-m network radius, the network runs 1700 rounds in theory and 1688 rounds in simulation. On the other hand, similar situations occur when the multipath fading model is applied. The network runs 5051 rounds in theory, when it utilizes the network radius of 150 m, whereas it runs 4990 rounds in simulation. With a radius of 325 m, it lasts 1122 rounds in theory and 1102 rounds in simulation. As a consequence, the networks in theory have nearly the same performance as the simulation, no matter what channel model is applied and no matter how large the network is. In PDSH, the network life span has nuances with the different network divisions. Hence, the following part shows the simulation results of the comparison between theory and simulation in the best network division. The parameters are same as in Table I, and the n ranges are from 2 to 20. The simulation results are shown in Figs. 6 (w = 2) and 7 (w = 4). In the best network divisions, the simulation results also have approximately the same network life span as the theoretical results. For one thing, the two have a similar life

9

Fig. 7. Network lifetime in theory and simulation with best network division (ω = 4).

span when the free-space fading channel model is applied. The network is supposed to last 9140 rounds in theory, in the optical network division case (n = 5), when w = 2 and radius is 150 m, whereas it runs 9094 rounds in simulation. It is expected to have a lifetime that lasts 2064 rounds in theory when the radius is 425 m, whereas the simulation results say it will perform 2043 rounds in its lifetime. In addition, the two have similar life spans when the multipath fading channel model is applied. As Fig. 7 illustrates (w = 4), the network lasts 6351 rounds in calculation as the network best divided (n = 5) when R = 150 m, whereas it lasts 6319 rounds in simulation with the same network division. When the network radius is 300 m, the calculation tells us the network could run 1518 rounds, whereas it runs 1502 rounds in simulation. In short, the theoretical results closely match the simulation results. Hence, we substitute our theoretical results for simulation results in the following simulations. B. Parameters That Affect the Network Lifetime Here, we figure out the parameters that affect the network life span through simulations. As we said, the divisions of the network affect the network lifetime somehow. Hence, the next simulation is involved in finding out the best divisions for some different network scales. We set the network radius as 100, 200, 400, and 800 m, respectively. Network divisions n are ranged from 2 to 20 rings. The other parameters in this simulation are the same as in Table I. Although we do not figure out the best division through math, the simulation provides the veiled orderliness. The simulation results are shown in Fig. 8 (w = 2), from which we can learn that the best division occurs in a medium value, neither too small nor too great. As the network divided into six rings runs 6205 rounds, the optimal network life span is in a 200-m radius case when the free-space model is applied. The network runs 2262 rounds when a 400-m-radius area is divided into nine rings. From another aspect, the network best division becomes greater and greater when the network becomes larger and larger. The network reaches its best life span of 14 913 rounds when it is divided into five rings with a 100-m radius. It gets its best lifetime of 6205 rounds in six-ring


Fig. 8. Best divisions in the different network scales (ω = 2).


Fig. 10.

Issues of the nodes’ densities (ω = 2).

Fig. 11.

Issues of the nodes’ densities (ω = 4).

Fig. 9. Best divisions in the different network scales (ω = 4).

network, when the radius is 200 m. It gets its best lifetime of 2262 rounds in nine-ring network, when the radius is 400 m. In addition, when the network radius is 800 m, its best lifespan situation occurs at 15 rings. Moreover, the networks have a similar characteristic when the multipath channel model is applied (see Fig. 9). Another parameter that affects the network lifetime would be the nodes’ density. Assume that the network tasks (ST ) are fixed, for example, 5 bits/m2 , which means that all the nodes in a square meter would collect 5-bit data altogether every round (ST = (ls • N )/A = ls • r. Note that N is the number of the nodes in the network, and A is the areas of the network). The node densities r are set as 0.005, 0.01, and 0.04, respectively. n is not fixed, but ranges from 2 to 20. We only choose the best n to show in the results. R is set from 50 to 700 m. The simulations are executed with the free-space model and the multipath model, separately. The simulation results are shown in Figs. 10 (w = 2) and 11 (w = 4). With greater node density comes a longer system life span. That is because each node in the low-density case can perform fewer tasks than that in the high-density case if the task is constant. For instance, the network runs 7456 rounds in the free-space channel model case when the radius is 100 m, and the nodes’ density is 0.005 node/m2 . The network could run 14 913 rounds when the density is 0.01 node/m2 , and the network could run 59 653 rounds when the density is 0.04 node/m2 . Similar situations happen in the multipath channel model case, as in Fig. 10.

C. Comparison With LEACH and Hybrid Here, the strategy PDSH is compared with LEACH [10] and Hybrid [19]. In the first part, the simulation shows the performance of the three strategies in different network radii, which range from 0 to 500 m. The node density is set as 0.01 node/m2 . Both the free-space model and the multipath model are simulated. Still, n is, if not settled, the best division in the specific case. The other network parameters are similar to those in Table I. Note that only one cluster is considered in this simulation for simplicity. When LEACH is utilized, the head is elected in setup phase, and the head use 10-bit message to notice the other nodes. Each node this time should use a fixed transmission range, which can send data to every node in this cluster. The simulation results are shown in Figs. 12 (w = 2) and 13 (w = 4). As Fig. 11 reveals, the PDSH strategy does indeed improve the network life span compared with Hybrid and LEACH. In small-scale networks, such as one with a 50-m radius, PDSH gains 27 181 rounds of lifetime, whereas Hybrid gains 24 869 rounds, and LEACH gains 26 653 rounds. On the other hand, in the larger scale networks, such as one with a 450-m radius, PDSH gains 1892 rounds of lifetime, whereas Hybrid gains 1255 rounds, and LEACH gains 965 rounds of lifetime. Fig. 12 demonstrates a similar situation when w = 4. Going back to this simulation, the scale of task (ST ) is a constant, for example, 5 bit/m2 • round. ST = (ls • N )/A = ls • ρ. ρ ranges from 0.005 to 0.04 node/m2 . Network radius is set to 300 m. The other parameters are the same as those in Table I.


Fig. 12. Strategies’ comparison on network scale aspect (ω = 2).

11

Fig. 15. Strategies’ comparison from the node density perspective (ω = 4).

almost 10% lifetime than the Hybird and LEACH methods. In another part, it is more scalable than the other methods. VI. C ONCLUSION

Fig. 13. Strategies’ comparison on network scale aspect (ω = 4).

The performance of WSN is severely influenced by an energy hole problem, which brings a different energy consumption velocity between different nodes and a large portion of energy wasting in these nodes. To solve this problem, PDSH data gathering method is proposed, which works in uniformly deployed sensor networks, and the main idea is to balance the energy consumption ratio between every neighboring ring. By obtaining a series of laws of the traffic model and the energy model of the network during phases, we proved that PDSH can be adaptive to general sensor network cases and can balance the energy consumption ratio of the network. The first simulation results (see Section V-A and B) show that this method is quite energy efficient in theory, although the performance is actually a little worse. From several more simulations, comparing PDSH with other similar type of data gathering method, it can improve the system’s life span to a considerable extent and balance the energy consumption burden of the network pretty well. The second simulation (see Section V-C) result shows that the system’s life span varies with the different network divisions in the same network phenomena, and finding the best network division would be an important job before implementing PDSH in a real sensor network. The better network division may be found through mathematical deduction, simulations, or real network tests.

Fig. 14. Strategies’ comparison from the node density perspective (ω = 2).

The simulation results were shown in Figs. 14 and 15. PDSH has distinct advantages when competing against Hybrid or LEACH, in both channel fading models. As Fig. 14 shows, PDSH runs 1693 rounds with a node density of 0.005 node/m2 , whereas Hybrid lasts 1311 rounds, and LEACH lasts 1052 rounds. When node density reaches 0.032 node/m2 , PDSH runs 11 109 rounds, whereas Hybrid lasts 8439 rounds, and LEACH runs 6736 rounds. In the multipath fading model, as shown in Fig. 14, the difference becomes even greater. PDSH runs 3036 rounds at 0.02 node/m2 density, whereas Hybrid runs 1296 rounds, and LEACH runs 378 rounds. In short, as we illustrated above, PDSH gains a longer life span on each two aspect of views. Our method can extend

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Chen Yu received the B.S. degree in mathematics and the M.S. degree in computer science from Wuhan University, Wuhan, China, in 1998 and 2002, respectively, and the Ph.D. degree in information science from Tohoku University, Sendai, Japan, in 2005. From 2005 to 2006, he was a Japan Science and Technology Agency Postdoctoral Researcher with the Japan Advanced Institute of Science and Technology. In 2006, he was a Japan Society for the Promotion of Science Postdoctoral Fellow with the Japan Advanced Institute of Science and Technology. Since 2008, he has been with the School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, where he is currently an Associate Professor and a Special Research Fellow, working in the areas of wireless sensor networks, ubiquitous computing, and green communications. Dr. Yu was a recipient of the Best Paper Award in the 2005 IEEE International Conference on Communication and the nominated Best Paper Award in the 11th IEEE International Symposium on Distributed Simulation and Real-Time Applications in 2007. Dezhong Yao received the B.S. degree in computer science from Huazhong University of Science and Technology (HUST), Wuhan, China, in 2006. He is currently working toward the Ph.D. degree in the Service Computing Technology and System Laboratory and the Cluster and Grid Laboratory, HUST. From 2010 to 2012, he was a Visiting Scholar under Anind’s guidance with the Human-Computer Interaction Institute, Carnegie Mellon University. His research interests include ubiquitous computing, context awareness, wireless networks, and data mining. Mr. Yao is a Student Member of the Association for Computing Machinery. Laurence T. Yang (M’97) received the B.E. degree in computer science and technology from Tsinghua University, Beijing, China, and the Ph.D. degree in computer science from the University of Victoria, Victoria, Canada. He is currently a Professor with the School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, China, and the Department of Computer Science, St. Francis Xavier University, Antigonish, Canada. He has authored or coauthored over 200 papers in peerreviewed international journals (around one third are on IEEE/ACM transactions and journals, and the others are mostly on Elsevier, Springer, and Wiley journals). His research interests include parallel and distributed computing, embedded and ubiquitous/pervasive computing, and big data. His research has been supported by the National Sciences and Engineering Research Council of Canada and the Canada Foundation for Innovation. Hai Jin (SM’06) received the Ph.D. degree in computer engineering from Huazhong University of Science and Technology (HUST), Wuhan, China, in 1994. In 1996, he was awarded a German Academic Exchange Service (DAAD) Fellowship for visiting the Technical University of Chemnitz in Germany. Between 1998 and 2000, he was with The University of Hong Kong and participated in the HKU Cluster project. Between 1999 and 2000, he was a Visiting Scholar with the University of Southern California. He is currently a Professor of computer science and engineering and the Dean of the School of Computer Science and Technology with HUST. He is the Chief Scientist of the largest grid computing project, i.e., ChinaGrid, in China, and the Director of Key Laboratory of Service Computing Technology and System, Ministry of Education. In addition, he is the Chief Scientist of the National 973 Basic Research Program, Basic Theory and Methodology of Virtualization Technology for Computing System. He has coauthored ten books and published over 200 research papers. His research interests include cluster computing and grid computing, peer-to-peer computing, network storage, network security, and virtualization technology.