Network Science Approach for Device Discovery in Mobile Device-to ...

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by over 15%, compared to the existing best wakeup techniques without considering ... data services including social networking applications, mul- tiplayer gaming ..... [t1,t2] to perform the adaptive wakeup scheduling for node. A, and thus for ...

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Network Science Approach for Device Discovery in Mobile Device-to-Device Communications Bentao Zhang, Yong Li, Member, IEEE, Depeng Jin, Member, IEEE, and Zhu Han Fellow, IEEE.

Abstract—With emerging demands for local area services, mobile device-to-device (D2D) communication is conceived as a vital component for the next-generation wireless networks to improve spectral reuse, bring hop gains and enhance system capacity. In mobile D2D networks, energy-efficient probing schemes are vital to prolong the limited battery life of mobile devices. Current solutions mainly focus on optimizing the probing interval during contacts by assumption of exponential distributed contact. However, studies in the area of network science have shown the contact interval follows a power-law distribution, which indicates the current solutions to be not optimal while on the other hand dramatically increases the difficulty to analyze this problem. In this paper, we propose a network science approach for adaptive wakeup schedule based on power-law distributed contacts. Our approach requires nodes stay asleep when a contact is unlikely to happen and wake up only when the possibility that it successfully contacts another node is relatively high. By predicting node contacts in the future based on network science, our approach significantly reduces energy consumption without degrading the performance of opportunistic networks. Extensive simulations with real-life human and vehicular traces demonstrate the outstanding performance of our approach. The results show that our scheme saves 30% energy while keeping the same performance in most scenarios, and it enhances the performance in terms of average delivery ratio and delivery delay by over 15%, compared to the existing best wakeup techniques without considering network science. Index Terms—Device discovery, device-to-device communication, wakeup scheduling, network science.

I. I NTRODUCTION Mobile Internet access is getting ever-increasingly popular and it provides various services and applications, including audios, images and videos. On one hand, a huge portion of the total mobile data traffics delivered by mobile service providers, such as weather forecasts, multimedia newspapers, stock information, movie trailers, etc., are typically delivered or broadcasted to a large number of mobile users. On the other hand, with the ever-increasing number of vehicles on roads [1] aiming at partly alleviating serious problems of traffic jams and accidents, recently there is an increasing B. Zhang, Y. Li, and D. Jin are with Tsinghua National Laboratory for Information Science and Technology (TNLIST), Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (E-mails: [email protected]). B. Zhang is also with the Department of Electrical and Computer Engineering, University of California, San Diego. Z. Han is with the Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004 USA. This work is supported by National Basic Research Program of China (973 Program) (No. 2013CB329105) and National Nature Science Foundation of China (No. 61301080, No. 61171065 and No. 61273214, No. 91338203, and No. 91338102), and National High Technology Research and Development Program (No. 2013AA013501 and No. 2013AA013505). Part of this work was presented at IEEE ICC 2014, Sydney, Australia.

interest in developing vehicular networks that enable wireless communications among vehicles to obtain information and content from Internet. Currently, the simple way for providing such communication is through cellular networks, like 3G and 4G. From the data of the last two years, Cisco forecasts that mobile traffic will be growing at an annual rate of 131% between 2008 and 2014, and will reach over 3.6 exabytes per month in 2014 [2]. Among this traffic, about 66% will be mobile video data [2]. With the increase of mobile services and user demands, however, mobile networks will very likely be overloaded and congested in the near future. Especially during peak time and in urban areas, mobile communication for both personal and vehicular networks will face significant challenges in terms of low network bandwidth, missed calls, and unreliable coverage. As one of the next generation wireless communication systems, Third generation partnership project (3GPP) Long Term Evolution (LTE) is committed to provide technologies for high-data-rate transmission system, and LTE-Advanced (LTEA) is defined to support new components for LTE to enable higher-rate communication and mobile content downloading demands [3]. Combined with the emerging demands for local area services of popular content downloading, Device-toDevice (D2D) communication is proposed as one key component for LTE-A, which enables devices to communicate directly, and it is an underlay to the cellular network for increasing the spectral efficiency [4]–[8]. Moreover, D2D communication enables LTE to become a competitive broadband communication technology for public safety networks [9] used by first responders [10]. Compared to the commercial networks which evolve rapidly towards LTE, public safety networks currently focus on old 2G technologies like Project 25 (P25) and terrestrial trunked radio (TETRA) [11], and have much more strict requirements on reliability and security and also need direct communication between devices, especially when cellular assistance fails or is not available [9]–[11]. Besides, D2D communication is also motivated by various usage cases, which can also be classified into two wide categories [7], [10], [13]. The first category is the peer to peer case, including proximity-based services, such as local voice services, local data services including social networking applications, multiplayer gaming, context sharing, etc. Here devices exchange data as sources and destinations. The second category is the relay case, such as devices as the gateway to sensor networks and cooperative relay. One of the communicating D2D devices is supposed to relay the exchanged information to the base station, and then the base station forwards the data to the destination device. Because of direct communication, D2D

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users may enjoy high data rates, low delays, improved energy efficiency and alleviated congestion [10], [12]. Now we introduce the relationship between the proposal in this work and 3GPP LTE standard. In fact, prior to establishing direct D2D communication, a user equipment first needs to discover the presence of nearby devices and identify whether the D2D pairs require to communicate with each other, which is called device discovery or peer discovery. Thus, energyefficient device discovery is critical to the performance of D2D communication. Usually there are two techniques for device discovery. The first one is out-of-coverage approach, where the discovery is made by the devices themselves through sending a known synchronization or reference signal sequence. The second one is the network-controlled approach, by which the network utilizes paging or other signalings to mediate discovery process by recognizing D2D candidates and potential services. In this approach, the network coordinates time and frequency of device discovery. This approach provides huge benefits in various aspects, such as synchronization, session setup, resource allocation, routing, but the out-of-coverage scenario function is rudimentary, especially in public safety networks [9], [11]. In 3GPP TR 28.303, both general use cases and public safety use cases are proposed, and all the use cases include the out-of-coverage scenario. In this paper, we focus on the out-of-coverage cases. There are two widely used outof-coverage modes: clusterhead and ad-hoc. The clusterhead mode requires a clustering scheme, places significant burden on the master user equipment and may cause resistance. Thus, in this work, we investigate the ad-hoc mode. However, different from the ad hoc mode in the Mobile Ad Hoc Network (MANET), the device discovery process in this work requires information gathered by the base station, which facilitates the accuracy and efficiency of discovery. Compared to the location-based discovery [14], the devices do not frequently communicate with base stations and avoid inefficient use of radio resources. Since out-of-coverage scenario is considered, we utilize direct discovery instead of EPC-level discovery [15], and asynchronous discovery. In terms of the discovery signal, sequence-based signal is preferred to packet-based signal due to complexity and synchronization consideration. Besides, the devices communicate under outband D2D mode in order to avoid interference with cellular network [16], [17]. WiFi-direct is adopted in this mode. However, device discovery is not a simple problem. Device discovery without network assistance is usually time and energy consuming. The devices are continuously sending probing messages to the possible nearby devices to avoid missing communication possibilities. Consequently, devices are probing during most of their lifetime, and turn into the data transmission state only when the contacts between devices are detected [18]. A contact is defined as the event when two devices are within the communication range of each other. Thus, it is not surprising that contact probing is rather energyconsuming, which is substantiated by experimental results [19], [20]. How to schedule contact probing determines the energy consumption of the mobile devices significantly. Previous works propose mechanisms to optimize the probing intervals [21] or utilize low-duty-cycle methods [20]. Researches in

[22]–[24] allow nodes to stay asleep and only wake up at scheduled contact periods. These works do not take intercontact time into consideration, which is much longer than contact duration [25]. In [26], the authors schedule the wakeup periods of mobile devices adaptively and assume exponentially distributed contacts. On the other hand, in D2D communications, the handheld communication devices are carried by human beings by walking or in vehicles, which form social networks that exhibit certain stable social structures and phenomenons [27], [28], and social-aware solutions are proposed to solve related technical problems [29]–[32]. Network science [33], [34], emerging as an interdisciplinary academic field that studies complex networks of telecommunication networks, social networks, etc., recently reveals some significant break points about human behaviors and corresponding social structures [35]–[37]. For example, studies on large-scale online social networks report that the network structures formed by people also confirm sociological theories such as “Small World” [38], which can be modeled precisely with the power-law distribution in terms of node degree and network size [39], [40]. More recently studies [37], [41], [42] find that the human mobility trajectories are characterized by power-law distributions of jump sizes and waiting times. Especially, extensive experimental works reveal the contact interval among human also follows the powerlaw distribution [25], [43]–[47], in terms of both the vehicular mobility and human mobility. A natural question here to ask is “can we leverage the discovered properties in network science to assist the contact detection in mobile D2D communication in order to enhance the probing performance?’’ Based on this insight, in this paper, we investigate the adaptive wakeup schedule via a network science approach. Specially, we investigate the optimal beacon probing and wakeup schedule under the condition that D2D contact intervals among mobile nodes follow the power-law distribution discovered by network science. Our proposal is to decide when a node can sleep if a contact is unlikely to happen and when a node should wake up if it can contact with another node with high probability, thereby avoiding unnecessary probing during intercontact time to save energy. We predict next contact duration statistically according to former contacts of mobile nodes and characteristics of networks. The contributions of this work can be summarized as follows: •



We propose an adaptive device discovery scheme for out-of-coverage D2D communication, whereas most of existing discovery schemes focus on discovery with network assistance. We establish a theoretical framework to analyze the device discovery problem via a new paradigm of network science approach. In this framework, we lay the theoretical base to characterize the trade-off between the energy consumption and system performance with power-law distributed contacts for the beacon probing and wakeup schedule. We optimize the energy consumption of mobile nodes during inter-contact time with the fact that inter-contact time follows a power-law distribution. Through theoretical analysis, we give precise mathematical solution to

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II. S YSTEM OVERVIEW

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the problem, which is calculated by solving an explicit equation. • We carry out extensive simulations with several reallife human and vehicular mobility traces to evaluate our scheme. Simulation results demonstrate that it significantly reduces energy consumption while ensuring performance, and outperforms previous wakeup scheduling methods. The rest of this paper is structured as follows. We overview the system in Section II. The basic idea and implementation of our approach are presented in Section III. In Section IV, we evaluate the performance of our proposed approach through extensive simulations. After reviewing the related work in Section V, we conclude the paper in Section VI.

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A. Motivation Mobile D2D communications have been driven by the phenomenon that mobile devices, such as smartphones, are becoming increasingly powerful in aspects of computation, storage and radio interfaces. Smartphones are playing more and more important roles in communications because of their advanced capability of processing media contents. However, the conflict between limited battery capacity of smartphones and high energy consumption of D2D communication needs to be solved. Device discovery, the first and critical step of D2D communication, is usually time and energy consuming. The devices are continuously sending probing messages to the possible nearby devices to avoid missing communication possibilities. Consequently, devices are probing during most of their lifetime, and turn into the data transmission state only when the contacts between devices are detected. Thus, it is not surprising that contact probing is rather energy-consuming, which is substantiated by experimental results [15], [16]. Besides, ref. [26] experimentally examines the energy consumption of Samsung Nexus S smartphone with different tasks during 5 minutes, and the obtained results suggest that contact probing via Bluetooth or WiFi consumes as much energy as that of playing videos or making phone calls. Therefore, we are able to reduce energy consumption significantly if we could avoid unnecessary contact probing, which further enhances the performance of D2D communication and the network. Existing techniques optimize probing interval to reduce energy consumption during contacts [21]–[23]. However, these methods cannot entirely meet the demands of energy-efficient opportunistic communication since lots of unnecessary beacons are wasted during inter-contact time. Our basic solution to address this insufficiency is to predict future contacts statistically by a network science approach. A node sleeps during inter-contact times and stays awake during the predicted contact durations. Instead of using exponential contact intervals, our prediction is based on power-law distribution found in network science, and thus, describes mobile D2D communications more precisely.

where t0 is the time when last contact ends, p1 (t) can be a constant or a linear function or others, α > 1 indicating the power-law characteristic, tm > 0, and a is a positive normalizing constant. Actually, in real systems, the contact between two nodes often cannot support a valid fitting because the number of contacts between two nodes is usually small. But if we observe the contacts between one nodes and all the other nodes, the number of contacts is usually large enough for good fitting. So in order to operate in real systems, p(t) denotes the intercontact time between a specific node and all the other nodes it has contacted. Fig. 1 is a histogram of inter-contact time of mobile node in a real mobile mobility trace [49]. From the figure we can observe that the distribution of inter-contact time is not always power-law, but dichotomous. Before the threshold tm , it increases sharply, and usually it is an approximate straight line. After the threshold tm , it decays with a power law. There are considerable numbers of contacts shorter than tm , which play important role when optimizing probing intervals and cannot be ignored. Thus, this result illustrates that our assumption about p1 (t) is valid. Specific characteristics of p1 (t) should be summarized from inter-contact time of mobile nodes and then applied in the optimization.

B. Network Model We consider a mobile D2D communication system composed of mobile nodes V = {1, 2, ..., N }. The inter-contact

C. Problem Description We describe the process of device discovery to show how our proposed approach works. Consider a specific node A in

Fig. 1. Histogram of inter-contact time of a mobile node in a real mobile trace of human mobility.

time between nodes i and j follows a power-law distribution with parameter αij . According to previous work, our assumption about power law is reasonable [25], [43]–[47]. But the probability density function of inter-contact time p(t) is not always power-law because it has to be convergent near t = 0. Therefore, we assume that ( p1 (t), t0 < t 6 t0 + tm , p(t) = (1) at−α , t > t0 + tm ,

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the network. Assume node A and node B contacted each other during the last contact duration [tL , t0 ], p(t) is the pdf of intercontact time between A and all other nodes, our basic idea is to keep node A asleep for a moment after t0 to save energy. According to the prediction, if node A wakes up at time t1 and stays awake during [t1 , t2 ], then node A can sleep during [t0 , t1 ], which means it does not consume any energy during [t0 , t1 ] at all. If the prediction is accurate, the probability that node A contacts with another node during [t1 , t2 ] is high. In this way can we save energy while providing considerable performance at the same time. The prediction is carried out based on the characteristics of inter-contact time distribution and the last contact time between two mobile nodes, which is further illustrated in Fig. 2. Now, we introduce the goal of system optimization. We define Energy Factor, denoted by θ, as follows, t2 − t1 , 0 < θ 6 1, θ= t2 − t0 where θ denotes the fraction of awake duration of node A, i.e., the awake duration over the total time duration of a prediction cycle. Since we are dealing with wakeup-sleep scheduling, the probing strategy during awake duration is beyond our consideration, it is reasonable to assume that the energy a mobile node consumes for device discovery is proportional to the time during which it is awake. Although the contact characteristic of a mobile node is time-varying in D2D communication, if we observe a time duration on the basis that we have no knowledge of the specific probing strategy, the above assumption is reasonable. So we further conclude that θ denotes the energy consumption of the algorithm which will be proposed in Section III over the energy consumption without that algorithm. Because we can choose t1 and t2 , θ can be an arbitrary value between 0 and 1. In this way, energy consumption is strictly controlled by θ. On the other hand, the performance of D2D communications is represented by the probability that node A contacts another node during the predicted contact duration [t1 , t2 ], i.e., P(t1 − t0 6 tA 6 t2 − t0 ), where tA denotes the inter-contact time between A and any other node, more specifically, the time that takes A to come within the range of another node again from the last time, denoted as t0 , when A and B were moving out of the range of each other. Our goal is to find the optimal [t1 , t2 ] so that the predicted contact happens with the maximum probability. By balancing the energy consumption of mobile nodes and the performance of D2D communications, we determine the duration [t1 , t2 ] during which node A should stay awake. If the prediction is successful, which means node A contacts another node in [t1 , t2 ], we update tL and t0 as t1 and t2 according to the happened contact, and predict the next awake duration, which is showing in Fig. 2 (a). Otherwise, an error handling mechanism will be utilized to determine the next awake period, which is showing in Fig. 2 (b). III. A DAPTIVE WAKEUP S CHEDULING A. Optimization Given an energy consumption requirement specified by 1 Energy Factor θ = tt22 −t −t0 , we focus on maximizing P(t1 −t0 6

Fig. 2. Illustration of the adaptive wakeup scheduling scheme for pair of nodes A and B under the cases of (a) successful wakeup prediction and (b) error handling.

tA 6 t2 − t0 ), which indicates the probability that the next contact between A and another node falls into the predicted wakeup period. In this way, we predict the wakeup period [t1 , t2 ] to perform the adaptive wakeup scheduling for node A, and thus for every node in the network. In other words, we need to obtain the optimal solution for t1 and t2 , denoted by t∗1 and t∗2 , in maximizing P(t1 − t0 6 tA 6 t2 − t0 ). Since tL and t0 are known when predicting next contact time, without loss of generality, let t0 = 0. According to the network model and (1) with t0 = 0, the probability density function of inter-contact time between A and other nodes can be expressed as follows, ( p1 (t), 0 < t 6 tm , p(t) = (2) at−α , t > tm . According to the above defined inter-contact time distribution, we have the following Proposition. Proposition 1: If p1 (t) is nondecreasing, then t2 > tm . Proof: If t2 < tm , consider another solution t01 and 0 t2 , where t01 = t1 − t2 + tm and t02 = tm . Since p1 (t) is nondecreasing, we have Z t2 Z t02 0 0 p1 (t)dt > P(t1 6 tA 6 t2 ) = p1 (t)dt. P(t1 6 tA 6 t2 ) = t01

t1

(3) Meanwhile, since θ0 =

t02 − t01 t2 − t1 tm ; otherwise, the obtained t2 is not the optimal solution. Thus, we have that t2 > tm always exists in the optimal solution. Then, according to the maximization goal of P(t1 − t0 6 tA 6 t2 − t0 ), we have the following

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0.8 θ = 0.9 θ = 0.7 θ = 0.5

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Fig. 3. P(t1 − t0 6 tAB 6 t2 − t0 ) varies according to t1 . We need to find the optimal t∗1 to get the maximum probability.

Theorem, which obtains the optimal prediction for wakeup period for node A. Theorem 1: Under the condition that nodes A and B ended contact with each other at t0 = 0, the optimal wakeup period is [t∗1 , t∗2 ], where ( −p1 (t∗1 ) + a(1 − θ)α−1 t∗−α = 0; 1 (5) t∗ ∗ 1 t2 = 1−θ . Proof: Let P = P(t1 6 tA 6 t2 ) denote the probability that node A contacts another node during the predicted contact duration of [t1 , t2 ]. Since we need to maximize P, we first calculate the expressions for P under the different cases. When 0 < t 6 tm , we have the following derivations for P : Z tm a P = p1 (t)dt + (t−α+1 − t−α+1 ) 2 α−1 m t1 Z tm t1 −α+1 a (t−α+1 −( ) ). (6) = p1 (t)dt + m α−1 1−θ t1 On the other side, when t > tm , we have a a t1 −α+1 P = (t1−α+1 −t−α+1 )= (t−α+1 −( ) ). 2 1 α−1 α−1 1−θ (7) Since the adoptive wakeup scheme is to maximize P , the ∂P ∗ optimal solution t∗1 should fit the equation that ∂t |t = 0. 1 1 Thus, in the case of 0 < t 6 tm , we have ∂P = −p1 (t1 ) + a(1 − θ)α−1 t−α (8) 1 . ∂t1 While in the case of t > tm , we have ∂P = a[(1 − θ)α−1 − 1]t−α (9) 1 . ∂t1 ∂P Noticing the Energy Factor θ ∈ (0, 1), we have ∂t < 0 1 ∗ when t1 > tm , which means 0 6 t1 < tm . Therefore, the optimal value t∗1 can be found out by solving the following equation:

−p1 (t∗1 ) + a(1 − θ)α−1 t∗1 −α = 0.

(10)

After we obtain t∗1 by (10), t∗2 can be calculated by the following equation: t∗ t∗2 = 1 , (11) 1−θ which proves the Theorem. With t∗1 and t∗2 , we define the next wakeup period with the maximum probability when energy consumption is limited. We show some cases with different energy factor in Fig. 3, which demonstrate that we can always obtain the optimal solution of t∗1 , consequently t∗2 , for the adaptive wakeup scheme. At t0 , the last contact ending, a node predicts the next contact duration [t1 , t2 ] according to Theorem 1. This node sleeps during [t0 , t1 ] and probes continuously during [t1 , t2 ]. If the prediction is correct and there is a successful contact, t0 is set to the time when contact ends; if there is no successful contact, we will use the following mechanism to deal with this situation. B. Error Handling Our wakeup schedule provides the greatest possibility that a node can contact with other nodes during [t1 , t2 ]. However, due to the random behavior of mobile nodes, the prediction can be inaccurate. If a node has not contacted with any other node during [t1 , t2 ], our above method becomes invalid because the new wakeup cycle will be based on a residual inter-contact time. In this section, we discuss how to design the wakeup period when an error occurs. If there is no successful contact during [t1 , t2 ], the node is scheduled to stay awake during [t3 , t4 ], where t4 > t3 > t2 , which is showing in Fig. 2 (b). To keep the energy consumption unvaried, let t2 − t1 t4 − t3 = . (12) θ= t4 − t2 t2 − t0 Thus, we are still able to control the energy consumption when scheduling new wakeup periods. We intend to maximize the probability that the next contact happens during [t3 , t4 ]. Denoting the time of the next contact happens as t, we need to maximize the probability, denoted by Q, Q = P(t ∈ [t3 , t4 ] | t ∈ / [t1 , t2 ]). In the condition that the predicted contact in duration of [t1 , t2 ] does not happen, we have the following Theorem for the node pair to perform the next wakeup scheduling. Theorem 2: Under the condition that node A performed the predicted wakeup scheduling in [t1 , t2 ], during which no contact happened, the next optimal wakeup period is [t∗3 , t∗4 ], where ( ∂Q = 0; ∂t∗ 3 (13) t∗ θ ∗ 3 t4 = 1−θ − 1−θ t2 . Proof: There are two explanations for the inaccuracy of our prediction [t1 , t2 ]: the first one is the contact happened during [t0 , t1 ] and there is no contact during [t1 , t2 ], the second one is the contact has not happened before t2 and will happen after t2 . Since Q = P(t ∈ [t3 , t4 ] | t ∈ / [t1 , t2 ]). Then, we have P(t ∈ [t3 , t4 ], t ∈ [t0 , t1 ]) + P(t ∈ [t3 , t4 ], t ∈ / [t0 , t2 ]) Q= . P(t ∈ / [t1 , t2 ]) (14)

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Since t1 and t2 are known and fixed when scheduling t3 and t4 , the value of P(t ∈ / [t1 , t2 ]) is fixed. So we only need to maximize Q0 , where

When we have t∗3 , then t∗4 can be calculated by the following equation:

θ t∗3 − t2 , (22) Q = P(t ∈ [t3 , t4 ], t ∈ [t0 , t1 ]) + P(t ∈ [t3 , t4 ], t ∈ / [t0 , t2 ]). 1−θ 1−θ (15) which proves the Theorem. The optimal t3 and t4 ensure that a node could contact with Thus, we have other nodes with the maximum probability if previous pret 1 −α+1 −α+1 R a(t3 −t4 ) ∂[ p (s)(t − s 6 t 6 t − s)ds + ] diction was inaccurate while keeping the energy consumption 1 3 AB 4 α−1 ∂Q0 invariant at the same time. = 0 ∂t3 ∂t3 Zt1 p(t4 − s)∂t4 C. Scheme of Adaptive Wakeup Scheduling = p1 (s)[ − p(t3 − s)]ds + a[(1 − θ)α−1 − 1]t−α 3 ∂t3 Now, we summary the proposed adaptive wakeup schedul0 (16) ing for peer discovery in Algorithm 1. It is worth noticing that the parameters of distribution of inter-contact time are Zt1 p(t4 − s) sent by the base station and the calculation is done by the −α α−1 = p1 (s)[ − p(t3 − s)]ds + a[(1 − θ) − 1]t3 . devices. But the base station cannot only send the optimal 1−θ 0 wakeup scheduling results to the devices because if the devices t3 θ − 1−θ t2 ), we cannot connect to the base station, it is supposed to calculate When t3 < t1 + tm and t4 < t1 + tm (t4 = 1−θ have the optimal wakeup period by itself with the parameters of distribution of inter-contact time. In this algorithm, each node Zt1 p(t4 − s) p1 (s)[−p(t3 − s) + ]ds (17) performs Algorithm 1 until the all the system transmission 1−θ ends. In each cycle, if a node contacts another node, it updates 0 the contact history, and performs the next contact prediction t3Z−tm −α a(t4 − s) by by obtaining the next optimal wakeup period of [t∗1 , t∗2 ] −α ]ds = p1 (s)[−a(t3 − s) + according to Theorem 1. Otherwise, it performs the error 1−θ 0 handling by obtaining the next optimal wakeup period of t4Z−tm −α [t∗3 , t∗4 ] according to Theorem 2. In this way, the wakeup a(t4 − s) + ]ds (18) scheduling provides the greatest possibility that a node can p1 (s)[−p1 (t3 − s) + 1−θ contact other nodes during [t01 , t02 ], which further provides the t3 −tm t 1 optimal solution for the wakeup period. Z p1 (t4 − s) The advantage of the proposed algorithm is that it works in + p1 (s)[−p1 (t3 − s) + ]ds. 1−θ a energy-controlled way. The energy consumption of a mobile t4 −tm device is determined by θ. If the device aims to achieve the When t3 < t1 + tm and t4 > t1 + tm , we have best performance and does not care about energy, then set Zt1 θ = 1, so the device is awake all the time; if the device needs 1 p1 (s)[−p(t3 − s) + p(t4 − s) ]ds acceptable performance, then set θ as a value between 0 and 1−θ 1, such as 0.7, so the device is awake during 70% of time; if 0 t3Z−tm the device is running out of battery, then set θ as a small value −α −α 1 = p1 (s)[−a(t3 − s) + a(t4 − s) ]ds (19) and the device has a longer lifetime. On the other hand, in the 1−θ system p(t) is a prior information because of the presence of 0 base stations. If the number of mobile users changes, p(t) will Zt1 also change and the base station will update these updates to 1 −α + p1 (s)[−p1 (t3 − s) + a(t4 − s) ]ds. the mobile nodes with the communication capability provided 1−θ t3 −tm by the cellular networks. When t3 > t1 + tm , we have the following expressions Zt1 D. Complexity of Device Discovery 1 p1 (s)[−p(t3 − s) + p(t4 − s) ]ds The complexity of the proposed algorithm is in two folds: 1−θ 0 first, calculating the parameters of distribution of inter-contact Zt1 time; second, calculating the optimal wakeup period according 1 = p1 (s)[−a(t3 − s)−α + a(t4 − s)−α ]ds. (20) to Theorem 1 or 2. The distribution of inter-contact time can 1−θ be divided into two parts. The first part p1 (t) can be an 0 ∗ Similar with the above method, the optimal t3 could be found arbitrary function and should be summarized from past intercontact time of mobile nodes in the network. In terms of the out by solving the following equation: data we utilized in the simulation, linear fitting has achieved ∂Q0 = 0. (21) acceptable accuracy. The second part, which is power-law dis∂t∗3 tribution, can be linearly fitted on a log-log axis. So evaluating 0

t∗4 =

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the distribution of inter-contact time for one time does not consume much energy. Moreover, if the characteristic of the network or the contact behavior of the mobile nodes do not change rapidly, there is no need to calculate of distribution of inter-contact time frequently. The major concern of complexity comes from the calculation of Theorem 1 or 2. When a contact between mobile nodes ends, the nodes calculate the solution to Theorem 1, when a prediction error happens, the nodes calculate the solution to Theorem 2. Generally speaking, the frequency of calculation is lower than the contact rate between nodes, which is once per seconds or minutes. We notice that the calculation itself is not difficult since it is just looking for the solution to a simple equation. Thus, we conclude that the complexity of the proposed algorithm does not have much influence to an advanced mobile devices. The energy consumption of calculation is negligible compared to that of WiFi probing, which is as energy-consuming as making phone calls. Algorithm 1 The adaptive wakeup scheduling algorithm for node A to perform the peer discovery. 1: Record the last contact duration between A and another node as [tL , t0 ]; 2: Perform the contact prediction by obtaining the optimal wakeup period of [t∗1 , t∗2 ] according to Theorem 1, where t∗ ∗ α−1 ∗−α ∗ 1 −p1 (t1 ) + a(1 − θ) t1 = 0 and t2 = 1−θ ; 0 ∗ 3: Update t00 ← t0 , t01 ← t∗ 1 , and t2 ← t2 4: while All transmission ends do 5: Let A sleep during [t0 ,0 , t01 ], and wakeup during [t01 , t02 ] 6: if Contact happens during [t01 , t02 ] then 7: Update [tL , t0 ] by the happened contact; 8: Perform the contact prediction by obtaining the next optimal wakeup period of [t∗1 , t∗2 ] according to Theorem 1; 9: Update t00 ← t02 , t01 ← t∗1 , and t02 ← t∗2 ; 10: else 11: Perform the error handling by obtaining the next optimal wakeup period of [t∗3 , t∗4 ]∗according to Theorem t3 ∂Q θ ∗ 2, where ∂t ∗ = 0 and t4 = 1−θ − 1−θ t2 ; 3 0 0 0 ∗ 0 12: Update t0 ← t2 , t1 ← t3 , and t2 ← t∗4 . 13: end if 14: end while

IV. P ERFORMANCE E VALUATION In this section, we carry out extensive simulations to evaluate the performance of our proposed approach under various settings. The compared state-of-the-art schemes, evaluation methods and settings, evaluation results are, respectively, presented as following subsections. A. Algorithms in Comparison In this paper, we only focus on optimizing energy consumption during inter-contact time. We do not consider what routing strategy the node exploits when it is awake. In order to show the performance bound of our approach, we use the

flooding forward to make sure a node does not miss any transmission opportunities [48]. We compare our approach in different energy constraints with the primary flooding, where a node stays awake all the time [26]. We will also compare our scheme, which is based on power-law distribution, with three different kinds of wakeup scheduling methods, i.e., exponential distribution, fixed period, random probing. The distinction between the performance of our approach and that of exponential method is to demonstrate the performance improvement by our proposed network science approach. Utilizing the above mentioned wakeup scheduling schemes for mobile D2D communications as the benchmarks, we will perform an extensive simulation study to evaluate our proposed algorithm. B. Simulation Method and Settings We use four human mobility traces and two vehicular mobility traces. Among them, the four human mobility traces, Infocom05, Infocom06, Reality and Cambridge, are collected by Cambridge Haggle projects [49], which records the mobile device contacts of human carrying small devices (iMotes), in office environments, conference environments, and city environments. For the Intel trace, it records the contacts of 128 users for a duration of six days in Intel Research Cambridge Corporate Laboratory, while Infocom06 records 98 people’s contact during the Conference IEEE Infocom 2006. Shanghai trace is collected by SG project [50], where 2,019 operational vehicles continuously covered one month of February 2007 without any interruptions in Shanghai city. In this trace, a vehicle sends its position report by GPRS to the central database. In collecting Beijing trace, we use the mobility track logs obtained from 27,000 participating Beijing vehicles carrying GPS receivers during the whole May month in 2010. Among the vehicles, most of them are taxis. The reason for us to choose taxis as vehicular devices is that taxis are more sensitive to urban environments in terms of underlying road topology, traffic control and urban planning, and they have broader coverage in terms of space and operation time than buses and private cars. Specifically, we utilize the GPS devices to collect the vehicles’ locations and timestamps and GPRS modules to report the records. Beijing trace is the largest vehicular data trace available. The six data traces are summarised in Table I, where we observe that the chosen traces covered diverse D2D communication environments, from concentrated conference sites (Infocom05 and Infocom06), to dispersed university campus (Intel and Cambridge), and vehicular scenario covering a large city (Beijing and Shanghai), with the experiment period from a few days (Infocom05, Infocom06 and Cambridge), to a month (Beijing and Shanghai). Utilizing these traces recording the instances of mobile communication contacts in realistic and diverse environments guarantees the credibility of the performance evaluation. We evaluate the performance of data transmission in terms of data delivery ratio, number of nodes which own the information, delivery delay. In order to observe the performance of the proposed algorithm, we keep the θ for a node unchanged

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TABLE I T RACE S UMMARY Trace Mobility Device Number of devices Duration (days) Number of contacts Contact frequency (per day)

Infocom05 iMote 41 3 22,459 4.6

Infocom06 Intel Human iMote iMote 98 97 3 246 191,336 54,667 6.7 0.024

during its lifetime, so the total energy consumption during its lifetime over the total energy consumption without this scheme is specified by θ. And we evaluate the performance for different values of θ. We set θ to 0.7, 0.5, 0.3 to show the performance under different energy requirements. Besides, we also evaluate the minimum energy budget for a specific performance requirement. There are several kinds of nodes in human mobility traces, only mobile iMotes will be chosen as source nodes and destination nodes since they are carried by experimenters and are frequently contacted. External devices relay information in the networks. For the vehicular trace, we choose the source and destination node without any constraint. Each experiment is repeated 500 times with random data sources and destinations for statistical convergence. C. Simulation Results 1) Human Mobility: We conduct simulations with four groups of Cambridge Haggle traces to evaluate the performance of our algorithm in terms of average message delivery ratio and delivery delay. We also compare our scheme with four different kinds of wakeup scheduling methods, i.e., exponential distribution, fixed period, random probing and flooding. Energy consumption is specified by the Energy Factor θ. In each group, θ varies from 0.3 to 0.7. It is shown in Figs. 4(a)-(d) that I) our approach offers a balance between delivery ratio and energy consumption. Energy consumption can be reduced significantly while maintaining considerable performance. If θ = 0.7, we can save 30% energy while the average delivery ratio degradation is less than 5%; if θ = 0.5, the average delivery ratio degradation is 10% to 40%; while if θ = 0.3, the average delivery ratio degradation is 30% to 60%. II) θ = 0.7 can be a good choice in the simulation settings. If we set θ = 0.7, we can save 30% energy, but the performance degradation will be less than 5% in most cases. In practice, the value of θ should be adaptively determined according to performance and energy requirements. III) The performance of our approach is better in Intel, Cambridge, Infocom05 than in Infocom06 trace. The difference might be caused by the number of nodes in the network and the frequency of contacts. In Intel, there are 8 mobile iMotes and 128 devices in total; in Cambridge, there are 12 mobile iMotes and 223 devices; in Infocom05, there are 41 mobile iMotes and 274 devices; but in Infocom06, there are 78 mobile iMotes and 4724 devices. Also, the contacts in the first three traces are more frequent than in the last trace. Our approach will get a better performance if the contact is frequent because a node is more likely to contact again if it misses a chance.

Cambridge iMote 54 11 10,873 0.345

Shanghai Beijing Vehicular GPS GPS 2100 27,000 30 28 1,317,060 9,317,060 0.373 0.479

TABLE II MINIMUM ENERGY FACTOR θ Trace Intel Cambridge Infocom05 Infocom06

Power Law 0.50 0.50 0.50 0.50

Exponential 0.60 0.56 0.59 0.58

Fixed Period 0.63 0.68 0.77 0.85

Random 0.80 0.88 0.85 0.90

Next, we measure the message distribution of D2D communications using the number of nodes which own the message to evaluate the performance for different scenarios. Figs. 5(a)-(d) show that I) the larger θ we have, the greater number of nodes will receive the message. II) if we set θ = 0.7, the number of nodes which own the message is close to that of flooding method, which means that θ = 0.7 offers a considerable performance while saving 30 percent energy. Then, we compare our scheme, which is based on powerlaw distribution, with four aforementioned different kinds of wakeup scheduling methods. In the simulation, we set θ = 0.7, which has been proven to be a good choice considering both network performance and energy consumption. Figs. 6(a)-(c) show the average delivery ratio varying with data lifetime. From the results, we observe that our approach is superior to exponential analysis and performs much better than the fixed period or random probing method. The average delivery ratio of our approach is 6 to 12% larger than that of exponential analysis, and 15% to 40% larger than that of fixed period or random probing. Average delivery delay is shown in Figs. 6(d)(f). Compared to the exponential method, the gain of our algorithm is 7% to 15%. We outperform other techniques because of our precise description and modeling about the characteristics of inter-contact time. Finally, we compare the minimum energy factor θ for a specific performance requirement. Let the energy factor of the proposed power-law algorithm be 0.5, and compare the energy factor of other algorithms in order to generate the same data delivery ratio. Results in Table II show that compared to the exponential method, the gain of our algorithm is 10% to 17%. 2) Vehicular Mobility: The same as human mobility, the system performance metrics are evaluated, in terms of delivery ratio, message distribution and comparison among different methods. We use the mobility trace of Beijing and Shanghai in our simulation and the results are shown in Figs. 7-9. Fig. 7 shows the average delivery ratio varying with data lifetime. With the increase of data lifetime, we observe that the average delivery ratio increases, as illustrated in Figs. 7(a) and (b). The average delivery ratio also increases with Energy Factor θ. In Beijing trace, when θ = 0.7, the delivery ratio loss

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TABLE III MINIMUM ENERGY FACTOR θ Trace Beijing Shanghai

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is less than 5%, which is negligible compared with the 30% energy consumption saved. In Shanghai trace, when θ = 0.7, the delivery ratio loss is about 30%, which offers a linear energy-performance balance. Regarding the message distribution as shown in Fig. 8, we observe that the number of nodes which own the message increases with data lifetime and θ. In these two traces, when θ = 0.7, the reduced message propagation is about 5% and 13%, respectively. Since the number of nodes that receive the message reflects the flooding strategy’s performance on propagation, our algorithm can spread messages further with limited time and energy. The same as human mobility, we also compare our algorithm with the four different kinds of wakeup scheduling methods, and set θ = 0.7 because the above experiments have proven that θ = 0.7 can provide similar performance as the primary flooding method while saving 30% energy. The average delivery ratio is shown in Figs. 9 (a) and (b). The delivery ratio increases with data lifetime. Our algo-

rithm outperforms all other wakeup scheduling methods. More specifically, compared with the exponential distribution, the average performance gain is about 15% in Beijing trace and 20% in Shanghai trace. With the increase of data lifetime, the discrepancy among different methods become smaller because almost all messages have been received by destination after a long time. Besides delivery ratio, we also evaluate average delivery delay and the results are shown in Figs. 9 (c) and (d). With the increase of Energy Factor, the delivery delay decreases. It is worth noticing that when θ is larger than 0.7, the delivery delay decreases slowly, which indicates that θ = 0.7 is a good choice as illustrated in Fig. 6 and 7. Compared with the exponential method, our algorithm offers a gain of 1.2× and 1.1× in Beijing and Shanghai traces, respectively. Since vehicular mobility can also be depicted by power-law characteristics as human mobility, our algorithm performs well in real vehicular mobility traces.

Finally, we compare the minimum energy factor θ for a specific performance requirement. Let the energy factor of the proposed power-law algorithm be 0.5, and compare the energy factor of other algorithms in order to generate the same data delivery ratio. Results in Table III show that compared to the exponential method, the gain of our algorithm is 17% to 23%.

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V. R ELATED W ORK Device discovery is a critical function in both ad hoc networks and D2D communications. Various kinds of algorithms and schemes have been proposed to improve the performance of device discovery. In ad hoc networks, beaconing mechanism for detecting communication contacts is most widely used. Ref. [51] evaluates the importance of beaconing to the transmission capacity of the network. After [21] proves that period probing achieves the minimum number of missing contacts, some researches focus on adapting the probing frequency to improve network performance [24], [52]. Other work rely on synchronous [53], [54], [55] or asynchronous [22], [56] scheduling of probing time slots. Besides these methods which only require mobile devices’ probing, other kinds of strategies which need additional facilities are raised, e.g., secondary low-power, longrange radio [19], [57], [58] or home information [59]. Device discovery in D2D communication is divided by the criterion whether it is assisted by network or Base Station (BS). With network assistance, device discovery could reduce cost on extremely expensive procedures, such as synchronization, resource allocation. [60] evaluates the influence of degree of network assistance on the performance of device discovery. The authors in [61] propose a distributed peer discovery protocol for LTE-A networks, which requires user

devices to advertise their presence based on random access. In [62], devices can detect potential D2D partners by listening to cellular uplink transmissions. A centrally controlled device discovery scheme which consists of an application layer procedure and a set of access level enhancements is proposed in [63]. Device discovery algorithms of centralized fully networkdependent and semi centralized semi-network-dependent are devised and compared in [65]. Besides, social information is also utilized in D2D communication [64]. However, due to the distributed nature and out-of-coverage consideration, device discovery without network assistance are essential and should be improved. A grouping algorithm is proposed in [66], such that devices in a group will take turns to announce the existence of other devices in the same group. Different from these work, we study the network-science-guided device discovery problem for mobile D2D networks. Specially, we exploit the power law distribution to design optimal wakeup scheduling mechanisms. VI. C ONCLUSION In this paper, we propose a contact detection scheme to adaptively schedule wakeup periods for mobile device-todevice communications based on power-law distributed contacts via network science approach. Our approach reduces energy consumption during the inter-contact time by avoiding

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plenty of unnecessary contact probing. We mathematically analyze the problem and balance between energy consumption and performance requirement. Extensive simulations show that our approach significantly reduces the energy consumption while providing considerable performance. Specifically, the simulation results demonstrate that our scheme saves 30% energy while keeping the same performance in most scenarios, and it enhances the performance in terms of average delivery ratio and delivery delay by over 15%, compared to the existing best wakeup techniques without considering network science.

Thus, our network science approach avoids unnecessary probing so that mobile devices are able to consume much less energy to perform the peer discovery in the mobile deviceto-device communications. Our future work includes realistic scenarios where the nodes may exhibit selfish behaviors and implementation of the algorithm in 3GPP TS 23.303. R EFERENCES [1] M. Khabazian, S. Aissa, and M. Mehmet-Ali, “Performance modeling of message dissemination in vehicular ad hoc networks with priority,”

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Message distribution of different traces in Beijing and Shanghai trace, where energy consumption is specified by Energy Factor θ.

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Comparison among different wakeup scheduling methods in vehicular mobility traces.

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Bentao Zhang is a PhD student majoring in Electrical and Computer Engineering at University of California, San Diego. He received his B.S. degree from Tsinghua University, Beijing, China, in 2014 in Electronic Engineering. His research interests include wireless communication and networking.

Yong Li (M09) received the B.S. degree in electronics and information engineering from Huazhong University of Science and Technology, Wuhan, China, in 2007 and the Ph.D. degree in electronic engineering from Tsinghua University, Beijing, China, in 2012. During July to August 2012 and 2013, he was a Visiting Research Associate with Telekom Innovation Laboratories and The Hong Kong University of Science and Technology, respectively. During December 2013 to March 2014, he was a Visiting Scientist with the University of Miami, Coral Gables, FL, USA. He is currently a Faculty Member of the Department of Electronic Engineering, Tsinghua University. His research interests are in the areas of networking and communications, including mobile opportunistic networks, device-to-device communication, software-defined networks, network virtualization, and future Internet. Dr. Li has served as a Technical Program Committee (TPC) Chair for the WWW workshop of Simplex 2013 and the TPC for several international workshops and conferences. He is a Guest Editor of ACM/Springer Mobile Networks and Applications, Special Issue on Software-Defined and Virtualized Future Wireless Networks. He is currently the Associate Editor of EURASIP Journal on Wireless Communications and Networking. He was a recipient of the Outstanding Postdoctoral Researcher, Outstanding Ph.D. Graduates, and Outstanding Doctoral Thesis awards from Tsinghua University. His research is granted by the Young Scientist Fund of the Natural Science Foundation of China, the Postdoctoral Special Fund of China, and industry companies of Hitachi, ZET, etc.

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Depeng Jin received the B.S. and Ph.D. degrees from Tsinghua University, Beijing, China, in 1995 and 1999 respectively both in electronics engineering. He is an associate professor at Tsinghua University and vice chair of Department of Electronic Engineering. Dr. Jin was awarded National Scientific and Technological Innovation Prize (Second Class) in 2002. His research fields include telecommunications, high-speed networks, ASIC design and future Internet architecture.

Zhu Han (S’01-CM-’04-SM’09-F’14) received the B.S. degree in electronic engineering from Tsinghua University, in 1997, and the M.S. and Ph.D. degrees in electrical engineering from the University of Maryland, College Park, in 1999 and 2003, respectively. From 2000 to 2002, he was an R&D Engineer of JDSU, Germantown, Maryland. From 2003 to 2006, he was a Research Associate at the University of Maryland. From 2006 to 2008, he was an assistant professor in Boise State University, Idaho. Currently, he is an Associate Professor in Electrical and Computer Engineering Department at the University of Houston, Texas. His research interests include wireless resource allocation and management, wireless communications and networking, game theory, wireless multimedia, security, and smart grid communication. Dr. Han is an Associate Editor of IEEE Transactions on Wireless Communications since 2010. Dr. Han is the winner of IEEE Fred W. Ellersick Prize 2011. Dr. Han is an NSF CAREER award recipient 2010.

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