Peer-Assisted Computation Offloading in Wireless Networks, Student Member, IEEE, and Guohong Cao, Fellow, IEEE

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1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY Peer-Assisted Computation Offoading in Wireess Networks Yei Geng, Student Member, IEEE, and Guohong Cao, Feow, IEEE Abstract Computation offoading has been widey used to aeviate the performance and energy imitations of smartphones by sending computationay intensive appications to the coud. However, mobie devices with poor ceuar service quaity may incur high communication atency and high energy consumption for offoading, which wi reduce the benefits of computation offoading. In this paper, we propose a peer-assisted computation offoading (PACO) framework to address this probem. In PACO, a cient experiencing poor service quaity can choose a neighbor with better service quaity to be the offoading proxy. Through peer to peer interface such as WiFi direct, the cient can offoad computation tasks to the proxy which further transmits them to the coud server through ceuar networks. We propose agorithms to decide which tasks shoud be offoaded to minimize the energy consumption. We have impemented PACO on Android and have impemented three computationay intensive appications to evauate its performance. Experimenta resuts and simuation resuts show that PACO makes it possibe for users with poor ceuar service quaity to benefit from computation offoading and PACO significanty reduces the deay and energy consumption compared to existing schemes. Index Terms Energy consumption, ceuar phones, computation offoading, wireess communication. I. INTRODUCTION AS MOBILE devices are becoming increasingy powerfu, computationay intensive mobie appications such as image or video processing, augmented reaity, and speech recognition have experienced exposive growth. However, these computationay intensive appications may quicky drain the battery of mobie devices. One popuar soution to conserve battery ife is to offoad these computation tasks from mobie devices to resource-rich servers, which is referred to as computation offoading [1]. Previous research on computation offoading has focused on buiding frameworks that enabe mobie computation offoading to software cones of smartphones in the coud [2] [4]. However, a these studies assume good network connectivity whie negecting rea-ife chaenges for offoading through ceuar networks. In ceuar networks such as 3G, 4G and LTE, some areas have good coverage whie others Manuscript received March 17, 2017; revised August 26, 2017 and January 19, 2018; accepted Apri 4, Date of pubication Apri 24, 2018; date of current version Juy 10, This work was supported by the Nationa Science Foundation under Grant CNS and Grant CNS The associate editor coordinating the review of this paper and approving it for pubication was K. Huang. (Corresponding author: Yei Geng.) The authors are with the Schoo of Eectrica Engineering and Computer Science, Pennsyvania State University, University Park, PA USA (e-mai: yzg5086@cse.psu.edu; gcao@cse.psu.edu). Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier /TWC may not because of practica depoyment issues. As a resut, the wireess signa strength of a mobie device varies based on its ocation. Mobie users experiencing weak signa strength usuay have ow data-rate connections. Moreover, the data throughput depends on the traffic oad in the area [5]. When the network connectivity is sow, it may incur higher communication atency and consume more energy to offoad computation to the coud. Therefore, mobie devices experiencing poor service quaity (in terms of signa strength and throughput) may not benefit from computation offoading. Some existing research has identified simiar chaenges for data transmission in ceuar networks. Many studies propose to offoad ceuar traffic to WiFi network to save energy [6], [7]. Schuman et a. [8] propose to defer data transmissions to coincide with periods of strong signa to save energy. In QATO [9], data traffic is offoaded from nodes with poor service quaity to neighboring nodes with better service quaity to save energy and reduce deay. However, a these works focus on traffic offoading rather than computation offoading, and computation offoading decisions have to consider the deay and energy consumption of both computation execution and data transmission. In this paper, we propose a Peer-Assisted Computation Offoading (PACO) framework to enabe computation offoading in wireess networks, which is especiay hepfu for mobie devices suffering from poor service quaity. In PACO, cients with poor service quaity can identify neighbors with better service quaity and choose one of them as the offoading proxy. Through peer to peer interfaces such as WiFi direct, cients can offoad computation tasks to the proxy which actuay handes the computation offoading to the server. Athough everaging nearby devices to reay traffic has been studied in prior work, using them for computation offoading in ceuar networks raises new chaenges which have not been addressed. One main chaenge is how to make offoading decisions, i.e., determining which tasks shoud be offoaded to minimize the energy consumption of the mobie devices. Existing research [2], [4] considers the trade-off between the energy saved by moving computation to the coud and the energy spent on offoading the computation. However, they did not consider the specia characteristics of ceuar networks when making offoading decisions. After a data transmission, the ceuar interface has to stay in the high-power state for some time which coud consume a significant amount of additiona energy (referred to as the ong tai probem) [10]. This ong tai probem makes it hard to decide whether to offoad the computation IEEE. Persona use is permitted, but repubication/redistribution requires IEEE permission. See for more information.

2 4566 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY 2018 We have impemented PACO on the Android patform. To evauate its performance, we have deveoped three computationa intensive appications. Experimenta and simuation resuts show that PACO can significanty reduce the energy and deay compared to other computation offoading approaches. The main contributions of this paper are as foows. We introduce the idea of everaging peers with better service quaity to enabe computation offoading in ceuar networks. We design a peer-assisted computation offoading framework to detect and utiize neighbors with better service quaity to save energy. We aso propose agorithms to determine whether a task shoud be offoaded or not. We have impemented the framework on the Android patform and have impemented three appications to vaidate its effectiveness. The remainder of this paper is organized as foows: In Section II, we present reated work. Section III provides background and motivation for peer-assisted computation offoading. We present a high-eve description of the PACO architecture in Section IV. We describe the design of PACO in more detais; i.e., the proxy seection mechanism in Section V, and the offoading decision agorithms in Section VI. Section VII evauates PACO s performance. Finay, Section VIII concudes the paper. II. RELATED WORK In this section, we review three categories of research reated to our work. A. Power Saving in Ceuar Networks In ceuar networks, the wireess interface wi stay in highpower states for a ong time (i.e., the ong tai probem) after a data transmission. Existing research [10], [11] has shown that a arge amount of energy can be wasted due to this probem. As a resut, many researchers proposed to defer data transmission [8] or to aggregate the network traffic to amortize the tai energy [10], [12]. B. Computation Offoading Computation offoading has received considerabe attention recenty. Some previous work has focused on buiding frameworks that enabe computation offoading to the remote coud, such as MAUI [2], ConeCoud [4] and ThinkAir [3]. Other work [13] [15] has focused on the offoading decisions, i.e., which tasks of an appication shoud be offoaded, to improve performance or save energy of the mobie devices. There have been some studies on computation offoading which aim to reduce the ceuar communication cost by soving the ong tai probem. Xiang et a. [16] proposed the technique of coaesced offoading, which coordinates the offoading requests of mutipe appications to amortize the tai energy. Tong and Gao [17] proposed appication-aware traffic scheduing in computation offoading to minimize energy and satisfy the appication deay constraint. Geng et a. [18] designed offoading agorithms to minimize the energy consumption considering the ong tai probem. However, a of them assume that mobie devices have good ceuar network connectivity. Some existing research has expoited peer-to-peer offoading in different networks. In [19] [21], authors proposed to offoad computation to neighboring nodes in disruption toerant networks, wireess sensor networks and sma-ce networks, respectivey. In [22], D2D communication was expoited to enabe offoading from mobie devices to other mobie devices in ceuar networks. Furthermore, Jo et a. [23] proposed a heterogeneous mobie computing architecture to expoit resources from D2D communication-based mobie devices. However, a of them offoad computation to neighboring mobies, instead of the faraway coud. Different from them, our work expoits one-hop D2D communication to everage a neighboring mobie device ony as a reay to offoad to the coud through ceuar network. Whie soving the connectivity probem by expoiting the D2D communication, we aso consider the ong tai probem in our proposed soution to better utiize the ceuar resources. To the best of our knowedge, none of the previous work attempted to sove the ong tai probem when expoiting the cooperative computation offoading. Our work is the first to sove both probems in mobie coud computing. C. Ceuar Traffic Offoading To dea with the traffic overoad probem in ceuar networks, some researchers proposed to offoad part of the ceuar traffic through other wireess networks. Some research efforts have been focusing on offoading 3G traffic through opportunistic mobie networks or D2D networks [24], [25]. Others utiized pubic WiFi for 3G traffic offoading [6], [7]. Besides offoading through WiFi or opportunistic mobie networks, existing work aso everaged mobie nodes with good signa. For exampe, UCAN [26] enabed 3G base station to forward data to mobie cients with better channe quaity, which then reay data to destination cients with poor channe quaity through peer-to-peer inks. Different from previous work which ony considered traffic offoading, our work focuses on computation offoading. III. BACKGROUND AND MOTIVATION In this section, we first introduce ceuar networks and their energy mode, and then give the motivation of our peer-assisted computation offoading. The Universa Mobie Teecommunications System (UMTS) is a popuar 3G standard deveoped by 3GPP. Whie GSM is based on TDMA, UMTS uses Wideband CDMA (WCDMA) radio access technoogy and provides a transfer rate of up to 384 Kbps for its first version Reease 99. After that, High Speed Downink Packet Access (HSDPA) has been introduced and provides a higher data rate up to 14 Mbps. In Reease 6, the upink is enhanced via High Speed Upink Packet Access (HSUPA) to support a peak data rate up to 7Mbps. Later, HSDPA and HSUPA have been merged into one, High Speed Packet Access (HSPA), and its evoution

3 GENG AND CAO: PACO IN WIRELESS NETWORKS 4567 Fig. 1. The power eve of the UMTS ceuar interface at different states. Fig. 2. Execution mode for offoaded tasks. HSPA+ has been introduced and standardized. HSPA+ offers a number of enhancements, supporting an increased data rate up to 84 Mbps [27]. The Long Term Evoution (LTE) is the atest extension of UMTS. LTE enhances both the radio access network and the core network. The targeted user throughput of LTE is 100Mbps for downink and 50 Mbps for upink, significanty higher than existing 3G networks [28]. A. Ceuar Networks and Power Mode The power mode of a typica data transmission in UMTS is shown in Fig. 1. Initiay, the radio interface stays in the IDLE state, consuming very ow power. When there is a data transmission request, it promotes to the DCH state. After the competion of data transmission, it stays in the DCH state for some time and then demotes to the FACH state before returning to the IDLE state. The extra time spent in the highpower DCH and FACH states is caed the tai time. HSPA+ and LTE have simiar power modes. Thus, we generaize the power consumption of the ceuar interface into three states: promotion, data transmission and tai. The power in the promotion and tai state are denoted as P pro,andp tai. We differentiate the power for upoads from downoads in data transmission, and denote them as P up and P down, respectivey. B. Task Execution Mode A task can be executed ocay on the mobie device or executed on the server through offoading. If task T i is executed on the mobie device, its energy consumption is denoted as Eoca i. If T i is offoaded to the remote server with the hep of a proxy, the energy consumption consists of two parts: the P2P part between the cient and the proxy, and the ceuar part between the proxy and the server. During offoading, the offoaded task may need some input data, denoted as s i up, which is sent from the cient to the proxy and then upoaded from the proxy to the server. The offoaded task may aso generate some output data, denoted as s i down, which is downoaded from the server to the proxy and then sent from the proxy to the cient. For the P2P part, the cient and proxy use the WiFi direct interface to transmit the offoaded task. WiFi direct has much higher speed and arger transmission range than its Buetooth counterpart. For WiFi direct, the promotion and tai energy are negigibe. Thus, the energy consumption to offoad task T i over P2P ink is cacuated as E i p2p = P p2p (s i up + si down )/r p2p, (1) where P p2p is the data transmission power, and r p2p is the transmission rate. The ceuar part consists of three steps: sending the upoad data, executing the task on the server, and receiving the downoad data. Sending and receiving data of task T i are denoted as two subtasks Tup i and T down i, and the energy consumption of them are cacuated as Eup i = P up s i up/r up and Edown i = P down s i down /r down, where the upoad and downoad data rate are denoted as r up and r down. There are two cases to cacuate the energy of offoading task T i over the ceuar network. In the first case (Fig. 2(a)), after sending the upoad data (Tup) i to the server, the proxy is ide waiting for the downoad data (Tdown i ) whie T i is executed on the server. Let Δt denote the interva between subtasks Tup i and T down i (i.e., T i s execution time on the server). Then, the energy consumption between these two subtasks (denoted as E(Tup i,ti down )) depends on Δt: 1)IfΔt is arger than the tai time t tai, the proxy wi consume some extra promotion energy and tai energy. 2) If Δt is smaer than t tai,thereis a partia tai and no promotion energy. In summary, { E(Tup i,ti down )= P pro t pro + P tai t tai, P tai max{δt, 0}, if Δt >t tai otherwise. (2) In the second case (Fig. 2(b)), after sending the upoad data (Tup i ) to the server, the proxy is busy offoading other tasks. Then there coud be mutipe subtasks between Tup i and Tdown i. Let S i denote the set of a offoaded tasks incuding T i,and S i = S i \{T i }. Each set can be considered as a sequence of subtasks ordered by their arriva times. We can use Eq. (2) to cacuate the energy between adjacent subtasks and then get the overa energy consumptions of set S i and set S i (denoted as E(S i ) and E(S i )). Then the energy consumption of T i in the ceuar part is cacuated as Ece i = E(S i) E(S i ). (3)

4 4568 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY 2018 TABLE I MOBILE DEVICES AND NETWORK TYPES Fig. 4. Energy and deay with/without computation offoading. Fig. 3. Downink throughput of different carriers at different ocations. C. Motivation for Peer-Assisted Computation Offoading Existing study has shown that mobie devices within an area may have different service quaity, especiay when different service providers are used [9]. How wi the service quaity difference affect the efficiency of computation offoading? To answer this question, we have run some experiments. Our testbed consists of two types of smartphones, served by two ceuar carriers, as described in Tabe I. We picked 6 popuar ocations on our campus, and used these two phones to send data to our Linux server. We measured the data throughput of different carriers at each ocation, and the resuts are shown in Fig. 3. Then, we conduct computation offoading experiments at ocation 1, where Carrier 1 has extremey ow data throughput but Carrier 2 has much better service quaity. We have impemented an Optica Character Recognition (OCR) appication which automaticay recognizes the characters in images and outputs the text on Android smartphones. The detaied setup and impementation of our testbed wi be discussed in Section VII. We conduct experiments in three modes: no offoading and offoading with two different ceuar networks. We run the appication to recognize 10 images and repeat the test severa times to measure the average energy consumption and the deay. The resuts are shown in Fig. 4. As can be seen, offoading computation with poor service quaity (Carrier1-offoad) may consume more energy and increase the deay compared to executing the computation ocay. On the other hand, computation offoading under good service quaity (Carrier2-offoad) can significanty reduce the energy consumption and deay. Based on these resuts, mobie devices with poor service quaity shoud everage the node with better service quaity for computation offoading. IV. PACO SYSTEM ARCHITECTURE PACO considers the service quaity difference among mobie devices, and everages peers with better service quaity for computation offoading. In this section, we present a higheve overview of the PACO architecture. Fig. 5. Overview of the PACO architecture. The architecture of PACO is shown in Fig. 5. PACO shares simiar design with ConeCoud and ThinkAir by creating virtua machines (VMs) of a compete smartphone system in the coud. In this way, PACO enabes easy computation offoading between devices of diverging architectures, even different instruction set architectures (e.g., ARM-based smartphones and x86-based servers). On the mobie device side, PACO consists of three components. (1) Profiers for device, appication and network. The device profier measures the mobie device s energy consumption characteristics and buids its energy mode at the initiaization time. The appication profier tracks a number of parameters reated to program execution, such as the data size, the execution time and the resource requirements of individua tasks. The network profier continuousy monitors the network condition such as the data rate of the ceuar network. (2) Neighbor discovery, which identifies neighboring nodes that support PACO service and coects a ist of network quaity profies from them. (3) Offoad engine, which determines whether to offoad computation tasks and to which node (proxy) to offoad. If a mobie device is chosen as a PACO proxy, its offoad engine aso handes the communication with the coud server. It receives offoading requests from PACO cients, and sends the offoading requests to the server through the ceuar interface. After the server finishes the execution of an offoaded task, the proxy receives the resut and sends it back to the corresponding cient. The PACO server wi execute the offoaded tasks. It consists of two parts: offoad hander and profiers. The offoad hander manages the connection with the proxy. After the initia

5 GENG AND CAO: PACO IN WIRELESS NETWORKS 4569 requests through the ceuar ink for which the carrier charges a fee. This fee is determined by the user s service pan. For simpicity, we assume that this fee is known by the user and use DC i to represent the data cost of node i. The second part is reated to energy. We mode this part as node i s residua energy (RE i ), which is the fraction of the remaining battery energy and it is within the range of [0,1]. Therefore, we mode the cost of a node i as foows: Fig. 6. The work fow of the PACO cient and proxy. connection setup, the server waits to receive the offoading requests, executes the offoaded code, and sends the resuts back to the proxy. Aong with the resuts from executing the offoaded code, the server aso sends the profiing data coected by its profiers, which can hep future offoading decisions for the cient. To better understand how PACO works, Fig. 6 iustrates the work fow of the PACO cient and proxy. V. NEIGHBOR DISCOVERY AND PROXY SELECTION In PACO, the cient first uses neighbor discovery to find a ist of neighbors with better service quaity, and then decides which neighbor is chosen to be the proxy. In this section, we first expain this proxy discovery process and the incentives of being a proxy. Then we discuss the overhead and other reated issues in the process. A. Proxy Discovery and Incentives Each mobie device in PACO needs to detect nearby neighbors and identify which neighbors support PACO, i.e., are wiing to offoad tasks for others. We everage the DNS (Name Domain System) based service discovery (DNS-SD) to find neighbors. It aows mobie devices to discover neighboring nodes supporting a specific service using the WiFi direct interface directy, without the support of centra servers and access points. Android begins to support DNS-SD since Android 4.1 (Jey Bean). On each node, we register PACO as a service, with _http._tcp as the service type. And a oca port is assigned for this service. After registration, the node wi be abe to respond to the PACO requests from neighbors. When a cient joins PACO, it sends a PACO request using the WiFi direct interface. Each neighbor that supports PACO service wi respond to the request and provide its IP address and port number. Based on these information, two nodes can connect with each other via the WiFi direct interface and exchange the network quaity information. Since the proxy wi incur some cost in contributing its ceuar bandwidth to assist other cients, there is a need to provide some incentive to offset this cost. The cost incudes two parts. The first is the cost of transferring offoading C i = DC i. RE i As DC i increases, using the ceuar ink of node i becomes more expensive. As RE i decreases, the battery energy is more vauabe for node i, and thus its cost wi be higher. This cost mode can promote fairness between nodes. In the beginning, a node with higher throughput and sufficient battery ife is chosen to be the proxy. When serving cients, the proxy node contributes its own ceuar bandwidth to transmit cients offoading requests and its residua energy drops quicky, which wi increase its cost to serve as a proxy. As a resut, the node wi ess ikey to be chosen as a proxy ater. Based on this cost mode, we can then appy some credit-based incentive mechanism ike [9], [29]. Nodes are awarded credits for serving as proxies. These credits can be redeemed in the form of rea money, or be used to pay its proxy when the node becomes a PACO cient ater. In PACO, suppose a cient, say k, initiates a neighbor discovery. Nodes receiving this request wi estimate their cost of providing hep and send such information and their network quaity information to node k. After neighbor discovery, cient k coects a ist of network quaity profies and serving costs from neighbors. Then neighbors with higher data throughput than cient k are candidates for being proxy. A proxy candidates are isted in descending order of the data throughput. Assume cient k wants to offoad its computation tasks and is wiing to pay a cost of C. It wi check the proxy candidate ist, and seect the first neighbor i which satisfies C C i to be the proxy. B. Discussions 1) Neighbor Discovery Cost: The neighbor discovery process consumes extra energy. To quantify this extra energy cost, we measured the power consumption during the neighbor discovery process. Fig. 7 shows the power consumption of discovering three neighbors. The power eve of the initiaization process is much higher since the mobie device needs to start its WiFi direct interface for neighbor discovery. After initiaization, the power consumption becomes much ower. Frequenty performing neighbor discovery consumes too much energy, but many neighbors may not be detected with ow discovery frequency. To save energy, the neighbor discovery process in PACO wi ony be started when a node s proxy candidate ist is empty. 2) Proxy Update: The service quaity and the cost of mobie nodes may change with time due to mobiity, channe interferences and congestion at the proxy. In PACO, a node periodicay asks a nodes in its proxy candidate ist for information such as the current service quaity and the serving

6 4570 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY 2018 Fig. 7. The power consumption of the proxy discovery process. Fig. 8. Task burst and decision group. For simpicity, Tup i and Tdown i (sending upoad and receiving downoad data of T i ) are represented by box i and box i, respectivey. cost. A cient wi switch to a better proxy if the service quaity of the current proxy becomes worse than itsef. 3) Proxy Faiures and Recovery: The connection between a cient and its proxy wi be broken when the proxy moves out of range. The cient can detect such a faiure if it receives no response from the periodica proxy updates, or if the deay of an offoaded task is too ong. In such cases, the cient wi switch to another proxy in its proxy candidate ist. If the proxy candidate ist is empty, the cient shoud start another round of neighbor discovery to ook for a new proxy. VI. OFFLOADING DECISION For a PACO cient, its offoad engine decides whether a computation task shoud be offoaded. In this section, we present the offoading decision agorithms. A. Probem Statement Suppose a chosen proxy p is serving a group of cients (nodes) that run computationay intensive appications and generate N tasks in tota. After a task T i is generated, it is executed either ocay on the cient or on the remote server. The offoading decision probem is to find an offoading decision sequence 1,..., i,..., N which executes a tasks with the minimum amount of energy, where i indicates the offoading decision of task T i. When a task is offoaded via proxy p, the cient can save some energy by moving the computation to the server, but the proxy wi cost extra communication energy to offoad the computation to the server. Moreover, the communication between proxy p and the server suffers from the ong tai probem, which may impact the decisions of other tasks. Specificay, et us consider the foowing case. For a singe task T i at a cient, suppose offoading it costs more by considering the communication cost incuding the tai energy. If the proxy p has just offoaded some other tasks, the tai energy for offoading T i can be saved or reduced by those tasks. As a resut, it is possibe that offoading T i costs ess energy than executing it ocay. Therefore, it is a chaenge to cacuate the actua offoading cost for a singe task considering various decisions of other tasks. Athough Geng et a. [18] considers the effects of the ong tai probem, their work focused on singe mobie device which offoads tasks to the server sequentiay. Due to the use of proxy, mutipe cients offoad their tasks to the proxy which accumuates mutipe tasks, which makes existing soution unsuitabe. In the foowing, we first propose an offine offoading agorithm, which can minimize the energy consumption. However, it requires the compete knowedge of a tasks incuding the task arriva times. Thus, we reax these assumption and present an onine offoading agorithm. B. Offine Offoading Agorithm 1) Independent Decision Group: For the offine offoading probem, as each task in N can be either executed ocay or on the remote server, the soution space of this probem is O(2 N ). When N is arge, it is hard to find the optima soution. We find that the N tasks can be divided into severa sma groups with n tasks in each, where n is much smaer than N. The optima decision of each group is independent with each other. Therefore, the origina probem is divided into subprobems with a tractabe soution space O(2 n ). To identify such independent decision groups, we first introduce the concept of task burst. Suppose there is a set of tasks on a cient. For each offoaded task T i, we denote the arriva times of its two subtasks on proxy p as t i up and t i down. If two offoaded tasks from this cient have an interva smaer than the tai time t tai, the ceuar interface of proxy p wi stay in high power state during the whoe period between these two tasks. Then the offoading cost of one task depends on the offoading decision of the other. Therefore, a task burst is defined as a group of tasks (T 1,T 2,...,T j ),where t i up ti 1 down <t tai, 1 <i j. For exampe, in Fig. 8, the first task of cient 1 beongs to one task burst, whie the second and the third tasks beong to another task burst. For a group of cients that use the same proxy, as ong as any of their task bursts overap, the offoading decision of any task burst wi affect some other task burst. Therefore, these task bursts are formed into one decision group asshowninfig.8. Offoading decisions in different decision groups are irreevant since there is no overap in cacuating the tai energy. Thus, by combining the optima decisions of each decision group, we can obtain the goba optima offoading decision. 2) Probem Formuation: Suppose there are n tasks in a decision group, and our probem is to find an optima offoading decision sequence to minimize energy. This probem can be mapped to the shortest path probem as shown in Fig. 9. We introduce two dummy nodes: node V src as the source

7 GENG AND CAO: PACO IN WIRELESS NETWORKS 4571 Fig. 9. Mapping the offoading decision probem to the shortest path probem. White nodes have i = M, whie grey nodes have i = S. node and node V des as the destination node. First we create a directed graph as a fu binary tree rooted from V src. Formay, we denote a node at depth i as V i i (or V i for simpicity), where i indicates the offoading decision of T i : { M T i is executed on the mobie device; i = S T i is executed on the remote server. Specificay, each node at depth h = i 1 has two chidren at depth h = i, where the eft chid VM i corresponds to task i being executed on oca mobie device and the right chid VS i corresponds to task i being offoaded to the remote server. We create a ink from each node at depth n to the destination node V des. In this graph, every path from V src to V des wi map to one specific offoading decision sequence, and vice verse. Fig. 9 shows an exampe of such a graph for four tasks. The highighted path corresponds to decision sequence M, M, M, S which means to execute tasks 1, 2, 3 on the mobie and to offoad task 4 to the server. The edge weight from a node V i 1 to its chid V i, denoted as Wi 1 i, is defined as the additiona energy consumed by T i. For edges that the endpoint has i = M, T i is executed on the cient. Then, the edge weight is the energy consumed to execute T i on the mobie device, which is Eoca i. For edges that the endpoint has i = S, T i is offoaded to the server. The computation of this weight is not straightforward, since the energy of an offoaded task is reated with previous offoaded tasks, which is determined by the offoading decision history of a previous tasks. To sove this probem, we have each node V i record the i vaues of a nodes aong the path from V src to V i. Based on this information, we can get sets S i and S i of task T i and cacuate the ceuar energy cost of offoading T i using Eq. (3). Since offoading T i incurs additiona P2P energy to transfer data between nodes, we aso need to add this energy cacuated by Eq. (1). In summary, we can compute the edge weight using Eq. (4) for a edges from V i 1 (V src ) to V i (1 i n). The edge weight from V n to V des is set to 0. W i i 1 = { Eoca i if i = M; Ece i + Ei p2p if i = S. Under this framework, we transform the offoading decision probem to finding the shortest path in terms of energy consumption from V src to V des in the graph. (4) 3) Offine Offoading Agorithm: We use the A search agorithm [30] to find the shortest path in the predefined directed graph corresponding to the optima offoading decision. In order to expand the fewest possibe nodes in searching for an optima path, a search agorithm must decide wisey which node to expand next. For exampe, Dijkstra s agorithm expands outwards from the source node and seects the node cosest to the source. The greedy best-first search works in a simiar way, except that it estimates the distance from any node to the destination. Instead of seecting the node cosest to the source, it seects the node cosest to the destination. It runs much quicker than Dijkstra s Agorithm because it uses the estimate to guide its way towards the goa very quicky. The A search agorithm combines the ideas of Dijkstra s agorithm and the greedy best-first search, and uses a specified rue to determine which one shoud be expanded next. For each node, A considers both its distance from the source node and its estimated distance to the destination. Specificay, in the A search agorithm, each node V i has a cost function ˆf(V i ) to estimate the cost of a shortest path constrained to go through it, which contains two parts, as defined in Eq. (5). ˆf(V i )=ĝ(v i )+ĥ(v i ), (5) where ĝ(v i ) is the distance from the source node to the current node, i.e., the sum of the edge weight on the path P from V src to V i,whichis ĝ(v i )= j j 1, (6) (V j 1,V j ) P W and ĥ(v i i ) is an estimate of the cost from V to the destination. For A agorithm to find the optima soution, ĥ(v i) shoud not be greater than the actua minimum cost from V i to the destination. To satisfy this property, we define ĥ(v i ) to be the minima energy to execute a the remaining tasks, as shown in Eq. (7). When the remaining task T j is executed on the oca mobie, the energy consumption is E j oca ;whenitis offoaded, we ignore the tai energy and ony account for the energy to transmit the data through the ceuar network and the P2P ink. Therefore, ĥ(v i ) wi aways be smaer than the actua minimum cost. ĥ(v i )= n j=i+1 min{e j oca,ej up + Ej down + Ej p2p } (7) The key idea of A is to expore a graph by expanding the most promising node chosen according to node s ˆf vaue. The detaied steps of the agorithm is shown in Agorithm 1. Specificay, it maintains an open set that keeps nodes that are about to be searched in the next round. The open set is initiaized as V src. In each round of the agorithm, A picks a node with minimum ˆf vaue from the open set and expands its neighbor nodes into the open set. Then this node is removed from the open set. Finay, when V des is picked from the open set, A can back track to V src and find out the optima soution.

8 4572 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY 2018 Agorithm 1 Finding the Optima Offoading Decision Using A Agorithm Data: Taskgraph 1 Initiaization: 2 Decision sequence S ; 3 OpenSet {V src } ; 4 ˆf(V src ) ĥ(v src) ; 5 Procedure FindOptimaDecision(V src, V des ) 6 whie OpenSet do 7 V i ; 8 if V i the node in OpenSet with min ˆf(V i ) vaue == V des then 9 return ConstructOptimaDecision (V i ; 10 end 11 OpenSet OpenSet \{V i} ; 12 for each chid V i+1 of V i do ) ĝ(v i i+1 )+Wi ; 13 ĝ(v i+1 i+1 14 ˆf(V 15 V i+1 ) Eq. (5) ;.parent V i ; 16 OpenSet OpenSet {V i+1 } ; 17 end 18 end 19 Procedure ConstructOptimaDecision(V i 20 whie V i V src do 21 if V i == V des then 22 V i V i.parent ; 23 continue ; 24 end 25 S[i] i ; 26 V i 27 end 28 return S ; V i.parent ; 4) Agorithm Anaysis: In this section, we discuss the optimaity of the offine agorithm to find the optima offoading decision and its compexity. We first introduce the notations used in the A agorithm. Let f(v ) be the actua cost of an optima path constrained to go through node V, from V src to V des.thenf(v) can be written as the sum of two parts: f(v )=g(v)+h(v), where g(v ) is the actua cost of an optima path from V src to V,andh(V) is the actua cost of an optima path from V to V des. Note that f(v src ) = h(v src ) is the cost of an unconstrained optima path from V src to V des. In fact, f(v )= f(v src ) for every node V on an optima path, and f(v ) > f(v src ) for every node V not on an optima path. Let ĝ(v ) be an estimate of g(v ), ĥ(v ) be an estimate of h(v ). Then we coud add them to form an estimate of f: ˆf(V )=ĝ(v)+ĥ(v). In the offine offoading agorithm, we have ĝ(v ) = g(v ) according to the definition of ĝ in Eq. (6), and ĥ(v ) h(v ) according to the definition of ĥ in Eq. (7). ) ) To formay prove the optimaity of the offine agorithm which uses A to search for the shortest path, we introduce the foowing emma and theorem based on [30]: Lemma 1: Suppose ĥ(v ) h(v ) for a V, and suppose A has not terminated. If a node is currenty in the open set of A, it is an open node. Then, for any optima path P from V src to V des, there exists an open node V on P with ˆf(V ) f(v src ). Proof: Since A has not terminated, there must be at east one open node on the optima path P according to the agorithm. Hence, there exists an open node V on P with ĝ(v )=g(v ) by definition of ĝ. Then by definition of ˆf, we have: ˆf(V )=ĝ(v )+ĥ(v ) = g(v )+ĥ(v ) g(v )+h(v )=f(v ). P is an optima path, so f(v )=f(v src ) for a V P, which competes the proof. Theorem 1: If ĥ(v ) h(v ) for a V,theA agorithm can find the minimum cost path from V src to V des. Proof: According to the Agorithm 1, the A agorithm must terminate at V des. We prove this theorem by assuming the contrary; that is, the offine agorithm terminates at V des without achieving minimum cost. Then at V des, ˆf(Vdes )= ĝ(v des ) >f(v src ). But by Lemma 1, there exists just before termination an open node V on an optima path with ˆf(V ) f(v src ) < ˆf(V des ).ThenV woud have been seected for expansion rather than V des, contradicting the assumption that the agorithm terminated. The time compexity of the A agorithm depends on specific situation of the graph. For a node V,ifĝ(V )+ĥ(v ) is bigger than the cost of the shortest path, then V and a its chidren wi not be searched by the A agorithm, and thus we can quicky find the shortest path. In the worst case, the offine offoading agorithm using A has to expand a nodes to find the optima path. Then the compexity of the agorithm is equa to that of the Dijkstra shortest path agorithm. In practica, the offine offoading agorithm achieves better performance by using heuristics to prune away many nodes. 5) Deay Constraint: Unti this stage, the ony objective of the offine offoading agorithm is to minimize the energy consumption. However, the task competion time shoud aso be considered for some appications with deay constraints. In this section, we sove the offoading decision probem considering both energy consumption and deay constraints. Under the same framework used in Section VI-B.2, the new offoading decision probem is to find the shortest path in terms of energy consumption from V src to V des in the graph (Fig. 9), subject to the constraint that the tota competion time of that path must be ess than or equa to the deay constraint, D deadine. In a forma description, we are ooking for min P P e(p ) s.t. d(p ) D deadine, (8) where P is the set of paths from V src to V des,ande(p ) and d(p ) are the tota energy and deay of the path P, respectivey.

9 GENG AND CAO: PACO IN WIRELESS NETWORKS 4573 In Section VI-B.2, the edge weight is defined as the energy consumption of executing a task, and e(p ) can be cacuated by summing up the weight of a edges on the path P. Simiary, when the edge weight is defined as the competion time of a task, d(p ) can aso be easiy cacuated. We omit the simpe mathematica cacuation of the edge weight using task competion time. D deadine is normay set by the user based on different appications. By defaut it is set to be the task competion time on the oca mobie device. This deay constrained east cost path probem has been proven to be NP-hard [31]. It can be approximatey soved by the LARAC agorithm [32] using Lagrange reaxation. Specificay, the Lagrangian function is defined as foows: L(λ) =min P P e λ(p ) λd deadine, where λ is the Lagrangian mutipier, and e λ (P )=e(p )+ λd(p ). Lemma 2: L(λ) is a ower bound to the probem defined in Eq. (8) for any λ 0. Proof: Let P denote an optima soution of Eq. (8). Then L(λ) =min e λ(p ) λd deadine P P e λ (P ) λd deadine = e(p )+λ (d(p ) D deadine ) e(p ) proves the emma. To obtain the best ower bound we need to maximize the function L(λ) and find the maximizing λ. We appy the LARAC agorithm described in Agorithm 2 to find the optima λ and the corresponding e λ -minima path for a given source and destination pair. In the agorithm, Shortest- Path(V src,v des,c) returns a shortest path from V src to V des in terms of cost c. The agorithm first finds the minima-energy path. If it satisfies the deay constraint D deadine, it wi be the optima path and the agorithm terminates. Otherwise, the agorithm stores the path as the best path that does not satisfy D deadine (denoted by P e ). Then it finds the shortest path on deay d. If the path satisfies the deay constraint (i.e., a feasibe soution), the agorithm stores this path as the current best appropriate path (denoted by P d ). Otherwise there is no soution, so the agorithm terminates. After that, the agorithm repeatedy updates P e and P d with other paths to obtain the optima λ. Athough this agorithm cannot guarantee to find the optima path, it is shown to have good performance and poynomia running time [32]. C. Onine Offoading Agorithm The offine offoading agorithm can minimize the energy consumption. However, it is a centraized agorithm which requires the compete knowedge of a tasks from a cients, and thus it can ony be used as a performance bound. In practice, we need an onine offoading agorithm, where each cient makes offoading decisions by itsef. Furthermore, it is Agorithm 2 Finding e λ -Minima Path for Deay Constrained Least Energy Path Probem Data: V src,v des,d deadine Resut: e λ -minima path : P λ 1 P e ShortestPath (V src, V des, e) ; 2 if d(p e ) D deadine then 3 return P e ; 4 end 5 P d ShortestPath (V src, V des, d) ; 6 if d(p d ) >D deadine then 7 return There is no soution ; 8 end 9 whie true do 10 λ e(pe) e(p d) d(p d ) d(p e) ; 11 P λ ShortestPath (V src, V des, e λ ); 12 if e λ (P λ )=e λ (P e ) then 13 return P d ; 14 ese if d(p λ ) D deadine then 15 P d P λ ; 16 ese 17 P e P λ ; 18 end 19 end impractica to accuratey predict future task arriva time of different users with different appications. Therefore, the onine offoading agorithm ony uses information of the current tasks. The basic idea of our onine agorithm is to offoad a task when the offoading can save energy whie satisfying the deay constraint. We first describe how to estimate the energy and deay of task offoading. Then, we present the offoading decision and congestion avoidance scheme. Last, we discuss the overhead of the onine offoading agorithm. 1) Deay Estimation: For task T i, if it is executed ocay, the execution time is denoted as Doca i. When offoaded to the remote server via the proxy node p, the process is shown in Fig. 10. Since most output data are sma and the ceuar downoad bandwidth is high, we ignore the queuing deay on the downoad ink simiar to existing work [16], [33]. Therefore, the deay of offoading task T i consists of four parts: the time to transmit data via the P2P interface, the queuing deay on ceuar upoad ink, the time to transmit data via the ceuar interface, and the execution time on the server. The P2P deay and the ceuar network deay depend on the upoad data size s i up, and the downoad data size si down. The queuing deay can be estimated by the queue size at the proxy p (denoted as Squeue p ). The task execution time on the server (denoted as d i server) can be obtained by task profiing. Putting them together, the deay to offoad T i via the proxy node p is: D i,p remote = si up + s i down r p2p + Sp queue + s i up + si down + d i r up r server. down (9) 2) Energy Consumption: For task T i, if it is executed ocay, the energy consumption is denoted as E i oca.when

10 4574 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY 2018 Fig. 10. The process of offoading task T i. For simpicity, Tup i and T down i (sending upoad and receiving downoad data of T i ) are represented by box i and box i, respectivey. Fig. 12. offoaded. Ceuar energy consumption at proxy p before and after T i up is Fig. 11. Offoading subtasks at proxy p and Tup i s tai window. For simpicity, Tup i and T down i (sending upoad and receiving downoad data of T i)are represented by box i and box i, respectivey. this task is offoaded to the server via the proxy node p, the energy consumption incudes the energy consumed by the P2P interface, and the data transmission energy consumed at node p. The P2P energy (Ep2p i ) can be computed using Eq. 1. We show how to estimate the data transmission energy as foows. First, we show the tasks at proxy node p assuming T i has been offoaded via p in Fig. 11. Assume task T i is generated at time t i. We can estimate the time when p can start to send the upoad data Tup i (denoted as t i up) by adding the P2P deay and queuing deay to t i. Before time t i up, proxy p has the information of a the past offoaded tasks from a cients it serves. After time t i up, proxy p is expecting the downoad data of some aready offoaded tasks. The data transmission energy of T i consists of the energy of its subtasks Tup i and T down i. Since the energy cacuations of the two subtasks are the same, we use Tup i as an exampe. We introduce the concept of tai window for estimating the ceuar energy of offoading Tup i as foows. After Tup i is transmitted on the ceuar upink, the ceuar interface enters the ong tai state. The tai energy reated to Tup i can be affected in two cases (shown in Fig. 11). In the first case, when there is a subtask within time period (t i up t tai,t i up ), offoading T up i can cut the ong tai generated by that subtask. In the second case, when there is a subtask within time period (t i up,t i up + s i up /r up + t tai ), the ong tai generated by sending Tup i can aso be cut. Therefore, to cacuate the actua tai energy to send Tup i, we ony need to consider the subtasks in the period (t i up t tai,t i up + s i up/r up + t tai ), which is defined to be the tai window of T i up. We denote the previous and the next tasks of T i up in its tai window as T pre and T next, respectivey. Before T i up is offoaded (above in Fig. 12), the ceuar energy consumed by proxy p between T pre and T next (denoted as E(T pre,t next )) can be cacuated based on interva Δt using Eq. (2). After Tup i is offoaded, we use E(T pre,tup i ) to denote the tai energy between subtasks T pre and Tup; i E(Tup,T i next ) denotes the tai energy between subtasks Tup i and T next. Each of them can be cacuated based on interva Δt 1 and interva Δt 2 using Eq. (2). Then, we can get the ceuar energy consumption of proxy p to offoad Tup i as the energy difference between before and after Tup i is offoaded, which is E i,up ce = P up s i up /r up + E(T pre,t i up ) + E(T i up,t next ) E(T pre,t next ). (10) Simiary, we can get the ceuar energy consumption of proxy p to offoad Tdown i as Ei,down ce. In summary, the energy consumption to offoad T i via the proxy node p is: E i,p remote = Ei p2p + Ei,up ce + Ei,down ce. (11) 3) Offoading Decision and Congestion Avoidance: In a PACO group, proxy p serves severa cients and handes their offoaded tasks. For task T i generated by cient k, to decide whether it shoud be offoaded, cient k sends a query to proxy p for the task information within T i s tai windows and the current queuing deay. Based on the query resuts, the cient computes the energy and deay when offoading T i via proxy p. The cient wi offoad T i when offoading can save energy (i.e., E i,p remote <Eoca i ), and satisfy the deay constraint (i.e., D i,p remote Ddeadine i ) at the same time. The deay constraint Ddeadine i is normay set by the user based on different appications. By defaut it is set to be the competion time of task T i on the oca mobie device (Doca i ). A compete description of the onine agorithm is shown in Agorithm 3. For a PACO proxy, serving too many offoaded tasks wi increase the ength of queue and thus increase the queuing deay for ater tasks. Assume a cient k makes offoading decision for task T i given a chosen proxy p. If the deay to offoad T i via p is too ong, e.g., onger than executing ocay, cient k wi stop using proxy p and switch to a better proxy in its proxy candidate ist. If no better proxy is found, the cient wi start another round of neighbor discovery to ook for a new proxy as described in Section V-B. 4) Overhead Anaysis: The signaing overhead of the onine offoading agorithm is very sma and can be negected. Each cient ony needs to send queries about its own tasks and then make decisions ocay. Since the query is very sma and the

11 GENG AND CAO: PACO IN WIRELESS NETWORKS 4575 Agorithm 3 The Onine Offoading Agorithm on Cient k Data: Task set on cient k, proxy p 1 Initiaization: 2 Decision sequence S ; 3 Procedure MakeDecision(T i ) Eq. (9) ; 5 Ep2p i Eq. (1) ; 6 T pre, T next get the tai windows of Tup i and Tdown i ; 7 E i,up ce,ei,down ce Eq. (10) ; 4 D i,p remote 8 E i,p remote 9 if E i,p Eq. (11) ; remote <E i oca 10 offoad T i to proxy p ; 11 S[i] S ; 12 ese 13 execute T i on cient k ; 14 S[i] M ; 15 end and Di,p remote D i deadine then transmission rate of the P2P ink is high, the transmission deay of the query is negigibe. The responses are aso sma, which ony contains the start time and the execution time of severa tasks. For a proxy, athough it needs to maintain information of offoaded tasks and answer cient queries, its processing overhead is sma since the queries and the responses are very sma. The computation overhead of the onine offoading agorithm is aso very sma. When a cient generates a task, it sends query and receives response about the current task information at the proxy. Based on the response, the cient can estimate the deay and energy to offoad the task using Eq. (9) and Eq. (11). Then the cient can quicky decide whether to offoad the task considering both energy and deay constraints. This decision process ony needs some simpe mathematica computations. VII. PERFORMANCE EVALUATIONS In this section, we first use experiments to evauate the benefits of peer-assisted computation offoading, and then use simuations to evauate the performance of our system under various scenarios. A. Experimenta Setup We have impemented PACO on four smartphones (3 GS3 and 1 GS4 As isted in Tabe I). we have measured the power eve of the wireess interface at different states using a Monsoon Power Monitor [34], as shown in Tabe II. For the server, we create a cone VM by running the Android x86 virtua machine [35] on Orace s VirtuaBox. The cone executes on a dua-core desktop with a 2.3GHZ CPU and 6GB RAM running Linux. A phones have pre-instaed three computationay intensive appications: a face detection appication, an optica character recognition (OCR) appication and a speech-to-text TABLE II STATE MACHINE PARAMETERS OF DIFFERENT NETWORKS appication. The face detection appication identifies a the faces in a picture and returns simpe metrics for each detected face, such as the mid-point between the eyes, the distance in between, and the pose of detected faces. We have impemented the OCR appication based on the Tesseract ibrary [36]. The OCR appication provides automatic conversion of photographed images of printed text into machine-readabe text. The speech-to-text appication takes an audio fie and transates the speech into text using the Sphinx tookit [37]. To evauate the performance of PACO, we run each appication on a different GS3 phone. Then we turn on PACO on a the phones and put them within WiFi direct communication range. Each cient discovers three neighbors that support PACO service. As LTE has arger throughput than HSPA+, the GS4 phone is seected as the proxy among a candidates. We compared PACO with the foowing approaches: A-Mobie: a tasks are executed on the oca mobie devices. Sef-Offoad: a tasks are offoaded to the remote server using the mobie devices own ceuar networks. Proxy-A-Offoad: a tasks are offoaded to the remote server via the proxy s ceuar network. Proxy-ThinkAir-Offoad: the offoading decision is made using the approach in ThinkAir [3]. It compares the energy consumption of running the computation ocay and that of offoading to the coud, and ony offoads the computation when energy can be saved via the proxy s ceuar network. However, ThinkAir does not consider the ong tai probem. The metrics used for comparisons are energy consumption and deay. If a task is offoaded, the deay consists of communication deay (WiFi direct or Ceuar deay) and computation deay. We use a Monsoon power monitor to measure the energy consumption. For A-Mobie and Sef-Offoad, we ony consider the energy consumption of GS3 phones (cients). For Proxy-Offoad and PACO, we aso consider the energy consumed by the proxy node. B. Experimenta Resuts In this section, we run some experiments to show the efficiency of PACO. The PACO prototype has one proxy node that serves three cients with different appications. In tota, the cients generate 40 tasks, and the parameters of the tasks are shown in Tabe III. We compare the performance of PACO with others and Fig. 13 shows the experimenta resuts. As can be seen,

12 4576 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY 2018 TABLE III DATA SIZES AND EXECUTION TIMES OF DIFFERENT APPLICATIONS Fig. 14. Energy consumption of different components in PACO. Fig. 13. Energy and deay of different offoading approaches in rea experiments. our offoading scheme ( PACO ) consumes ess energy than other approaches. Sef-Offoad consumes more energy than the A-Mobie approach, which suggests that computation offoading is not hepfu or even degrades performance when the cient has poor service quaity, Proxy-A-Offoad ony consumes 10% ess energy than A-Mobie, which indicates that the energy saved by offoading the computation to the remote server is comparabe to the extra energy wasted by transmitting more data to the remote server. Athough the tota energy consumption is ess than A-Mobie, the energy consumption of the proxy is much higher compared to that of other cients. PACO consumes 36% ess energy than A- Mobie. Compared to Proxy-A-Offoad, PACO makes better offoading decisions to save more energy and utiize the proxy more propery. For Proxy-ThinkAir-Offoad, since it does not consider the ong tai probem, it may offoad a task even though the actua energy consumption incuding the tai energy is more than oca execution, and hence consumes more energy than PACO. Fig. 13(b) compares the average deay of a task. For A-Mobie, the communication deay is 0 since its computation is not offoaded. For Sef-Offoad, athough it manages to offoad the task for faster execution on the server (i.e., ess computation deay), it takes much onger time to transmit the offoading requests over the poor ceuar connections. For Proxy-ThinkAir-Offoad, since it does not consider the ong tai probem, it may offoad more tasks than PACO by underestimating the offoad cost. Therefore, the communication deay consisted of ceuar deay and WiFi direct deay is much onger than PACO. However, Proxy-ThinkAir- Offoad has ess computation deay by offoading more tasks. Overa, PACO has a smaer deay than Proxy-ThinkAir- Offoad. Besides saving energy, PACO aso reduces the deay. Generay, PACO decides to offoad a task when energy can be saved. Since energy is cosey reated to Fig. 15. Energy and deay of different offoading approaches in simuation. the communication deay and the computation deay, saving energy normay resuts in reduced deay. Aso, it normay takes a cient onger than the tai time to generate a new task, so there is aways a promotion deay for the ceuar interface to offoad a new task. PACO aggregates the offoaded tasks from mutipy cients to the proxy, and then such promotion deay can be avoided. On average, PACO can reduce the deay by about 43% compared to A-Mobie. Fig. 14 shows the energy consumption of different components in PACO, which incudes the ceuar interface, WiFi direct interface, neighbor discovery and other system cost such as network profiing and offoading decision making. In genera, data transmission consumes most of the energy, among which the ceuar interface (ceuar trans + ceuar tai) consumes much more energy than the WiFi direct interface. The tai energy is very high because there are sti ide time intervas between data transmissions on the proxy, thus introducing some tai energy. Other components ony consume imited amount of energy. For exampe, neighbor discovery consumes ess than 5% of the tota energy, and system consumes ess than 3% of the tota energy. C. Simuation Resuts We have coected the task traces from the rea experiments, and then use them to evauate the performance of the offoading agorithms. Such simuations wi give us more fexibiity to study the effectiveness and scaabiity of our agorithms. In the simuations, we compare A-Mobie, Sef- Offoad, Proxy-A-Offoad, Proxy-ThinkAir-Offoad and two variants (Offine and Onine) of our PACO offoading scheme.

13 GENG AND CAO: PACO IN WIRELESS NETWORKS 4577 Fig. 16. Energy saving rate as a function of computation oads. 1) Performance Comparison: The energy consumption and deay of different approaches are shown in Fig. 15. Overa, our PACO offoading scheme can save 39% of energy and reduce the deay by 45% compared to that without computation offoading. By comparing Fig. 15 and Fig. 13, we can see that the simuation resuts are consistent with the experimenta resuts. The energy consumptions of a approaches are a itte higher than the simuation resuts since mobie devices consume some extra energy in ide state. Fig. 15 aso shows that the onine offoading agorithm can achieve simiar energy and deay saving rate as the offine soution, athough not as good as the offine agorithm. 2) Impact of Computation Load: The computation workoad affects the computation time at the mobie device and the server, and hence it affects the overa deay and energy consumption of offoading agorithms. For a task with arger computation oad, the advantage of offoading to a fast server over executing ocay wi be more obvious. In this section, we change the computation oad by mutipying an ampification factor (i.e.[0.5,2.0]) to the origina vaue, and evauate its effects on performance. Fig. 16 shows the energy saving rates of different approaches compared to A-Mobie. When the computation oad increases, offoading the task wi reduce more computation time, resuting in higher energy saving rates. However, the advantage of our agorithms over Proxy-ThinkAir- Offoad drops as the task workoad increases. The reason is that the energy saved for computation graduay dominates the overa energy saving as the task workoad increases, and then our agorithm s efforts on energy saving of data transmission incuding the tai energy become ess obvious. When the task workoad decreases (i.e., the ampification factor decreases from 1.0 to 0.5), Proxy-A-Offoad even consumes more energy than AMobie. This is due to the fact that tasks at this time are too simpe to be offoaded, and the energy saved in computation is not as much as the energy spent on data transmission. For Sef-Offoad, its energy saving rate is aways negative, which means it consumes more energy than A-Mobie in a cases. The energy saving rate decreases and becomes ower than 200 when the ampification factor decreases from 1.0 to 0.5, where 200% means that it consumes 200% more energy than A-Mobie. This vaidates that a mobie device with poor service quaity cannot benefit from computation offoading in most cases. Fig. 17. Variation of the energy saving rate of different approaches with varying group size. 3) Impact of Group Size: We define the group size as the number of cients served by a proxy. Intuitivey, as the size of the group increases, more offoaded tasks can be aggregated at the proxy and more ikey to save the tai energy. In this section, we change the group size and evauate its impact on the performance. Fig. 17 shows the energy saving rates of different approaches compared to A-Mobie. For Sef-Offoad, each cient in the group uses its own ceuar connection to offoad tasks to the remote server. Thus, the group size has no direct effect on its performance. The resut shows that Sef-Offoad aways consumes much more energy than the one without offoading, where 180% means that it consumes 180% more energy than A-Mobie. For Proxy- ThinkAir-Offoad, it offoads more tasks than our PACO offoading scheme since it ignores the ong tai probem and underestimates the offoading cost. Thus, the energy saving rate of PACO is aways higher than Proxy-ThinkAir-Offoad. As expected, the energy saving rates of other approaches increase as the size of the group is increased. However, there is an upper-bound of this performance improvement. Consider an extreme scenario where a offoaded tasks are sent together as one bunde, then adding more cients (their tasks) has no advantage in further amortizing the tai energy. For Proxy-A-Offoad, the negative energy saving rate when the group size is sma means that it consumes more energy than the one without offoading. On the other hand, our PACO offoading scheme can achieve better performance even when the group size is sma. With more cients joining the group, the performance of PACO becomes even better. VIII. CONCLUSIONS In this paper we proposed PACO, a system that enabes computation offoading in wireess networks, which is especiay hepfu for mobie devices suffering from poor service quaity. PACO can identify neighbors with better service quaity and choose a proper proxy. With PACO, cients send offoading requests to the proxy via WiFi direct interfaces, and the proxy offoads the computation to the remote server. This paper addressed research chaenges such as how to discover the proxy for a cient, and how to make offoading decisions to minimize the energy consumption. To vaidate our design,

14 4578 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 7, JULY 2018 we have impemented PACO on Android. Experimenta and simuation resuts show that PACO can significanty reduce the energy and deay for mobie devices when running computationay intensive appications. REFERENCES [1] K. Kumar, J. Liu, Y.-H. Lu, and B. Bhargava, A survey of computation offoading for mobie systems, Mobie Netw. App., vo. 18, no. 1, pp , [2] E. Cuervo et a., MAUI: Making smartphones ast onger with code offoad, in Proc. ACM MobiSys, Jun. 2010, pp [3] S. Kosta, A. Aucinas, P. Hui, R. Mortier, and X. Zhang, Thinkair: Dynamic resource aocation and parae execution in the coud for mobie code offoading, in Proc. IEEE INFOCOM, Mar. 2012, pp [4] B.-G. Chun, S. Ihm, P. Maniatis, M. Naik, and A. Patti, Conecoud: Eastic execution between mobie device and coud, in Proc. ACM EuroSys, Apr. 2011, pp [5] A. Chakraborty, V. Navda, V. N. Padmanabhan, and R. 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Accessed: Feb. 17, [Onine] Avaiabe: Yei Geng (S 15) received the B.S. degree in computer science and technoogy from the Huazhong University of Science and Technoogy in 2008 and the M.S. degree in computer architecture from the Chinese Academy of Sciences in She is currenty pursuing the Ph.D. degree with the Department of Computer Science and Engineering, Pennsyvania State University. Her research interests incude energy management for smartphones, mobie coud, and mobie networks. Guohong Cao (S 98 M 03 SM 06 F 11) received the Ph.D. degree in computer science from The Ohio State University in Since 1999, he has been with the Department of Computer Science and Engineering, Pennsyvania State University, where he is currenty a Distinguished Professor. His research interests incude wireess networks, mobie systems, wireess security and privacy, and Internet of Things. He has pubished over 200 papers which have been cited over times, with an h-index of 70. He was a recipient of severa best paper awards, the IEEE INFOCOM Test of Time Award, and the NSF CAREER Award. He has served on the Editoria Board of the IEEE TRANSACTIONS ON MOBILE COMPUTING, the IEEE TRANSACTIONS ON WIRELESS COMMU- NICATIONS, and the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and has served on the organizing and technica program committees of many conferences, incuding the TPC Chair/Co-Chair of the IEEE SRDS, MASS, and INFOCOM.