PhonePool: On Energy-efficient Mobile NetworkCollaboration with Provider Aggregation

Joohyun Lee†, Kyunghan Lee‡, Yeongjin Kim† and Song Chong††{jhlee, yj.kim}@netsys.kaist.ac.kr, songchong@kaist.edu, ‡khlee@unist.ac.kr

Abstract— Energy consumption for cellular communication isincreasingly gaining importance in smartphone battery lifetimeas the bandwidth of wireless communication and the demand formobile traffic increase. For energy-efficient cellular communica-tion, we tackle two energy characteristics of cellular networks:(1) transmission energy highly varies upon channel condition,and (2) transmission of a packet accompanies unnecessary tailenergy waste. Under the objective of transmitting packets whenthe best channel is provided as well as a number of packets areaccumulated, we propose a new mobile collaboration framework“PhonePool” that aggregates smart devices across multiple cellularproviders. Compared to the standalone operation, even withouta buffering delay, PhonePool allows better channel and reducesmore tail energy in a statistical point of view. To maximize theenergy benefit while maintaining the fairness among the nodesin collaboration, we further develop a dynamic programmingframework providing the optimal algorithm of PhonePool and itsapproximated heuristic. Trace-driven simulations on our experi-mental HSPA/EVDO/LTE network traces show that PhonePool of5 devices achieves up to 42% of energy reduction.

I. INTRODUCTION

As smartphones become more powerful through advances inCPU, screen resolution and communication chipsets, the batterylifetime of them is getting more crucial. Conventionally display(and its backlight) and CPU have been the major sources ofbattery drain. But communication energy is increasingly gain-ing importance in smartphone battery time as the bandwidthof wireless communication and mobile traffic increase. Whenbrowsing webs in smartphones using LTE networks, batterylife can be as short as 5 to 6 hours even with a relatively largecapacity battery (e.g., 2500 mAh battery in Galaxy Note) [1]. Ameasurement study revealed that transmission energy accountsfor over 40% of total battery in daily uses [2].

To improve the energy-efficiency of cellular communication,in this paper we specifically focus on two energy character-istics of cellular networks: (1) transmission energy in 3G/4Gnetworks highly varies upon channel condition [3], [4], (2)transmission of a packet through 3G/4G networks accompaniesunnecessary ramp and tail energy waste [4]–[6] along with theactual transmission energy. According to a real measurement

This research was supported by the International Research & Devel-opment Program of the National Research Foundation of Korea (NRF)funded by the Ministry of Science, ICT and Future Planning of Korea(2013K1A3A7A03079321). This research was in part funded by UNIST (UlsanNational Institute of Science and Technology) and SK Telecom.

J. Lee, Y. Kim, and S. Chong are with the Department of ElectricalEngineering, KAIST, South Korea. K. Lee is with the School of Electricaland Computer Engineering, UNIST, South Korea.

study on vehicular traces, the communication energy per bitcan be as much as six times higher when the signal is weakcomparing to when it is strong [3]. Also, data transmissionover cellular networks consists of ramp energy due to thecharacteristics of electronic chipsets and tail energy mainly dueto the RRC (radio resource control) defined in communicationstandards. In both 3G and 4G networks, whenever transferringa small piece of data, expensive overheads in energy areinevitably paid. Specifically, tail energy is known to accountfor nearly 60% of total transmission energy consumption foreach packet transfer [5]. Thus, there is a room for significanttransmission energy reduction, which can be utilized if data canbe transferred when cellular signal strength is strong and if thesize of data for a single transfer can be larger.

An intuitive solution technique achieving energy-efficienttransmission might be “delaying” transfers to harness the bestchannel with a large-enough chunk of packets collected duringthe delay. To this end, there have been several solutions [3],[5]. These obviously save energy but the delay prohibits wideapplicability of the proposed solutions. We tackle this chal-lenge by proposing a new technique called “PhonePool” whichaggregates smartphones across multiple cellular providers fortheir cellular transmissions. PhonePool creates a group ofsmartphones which are located in proximity and optimallychooses at least one host who will be responsible for cellularcommunication. The hosts are chosen differently over timeconsidering both remaining energy and channel condition.Except the hosts, all other smartphones in the group workas guests and connect to cellular networks through WiFi orBluetooth connectivity to the hosts. Therefore, at a snapshotof time, PhonePool can be seen as a wireless tethering [7].The aggregation of smartphones over multiple cellular providersgives two immediate benefits without relying on the additionaldelay: (1) channel stability from provider diversity and (2) databundling from packet multiplexing.

Channel stability from provider diversity is given by the factthat cellular providers have different cell planning with het-erogeneous cellular standards (e.g., EDGE, CDMA, WCDMA,LTE, LTE-A).1 Thus, it is natural that smartphones at thesame location experience unequal channel conditions accordingto their cellular providers. For instance, it is common toobserve that AT&T users get high throughput where Verizonor T-Mobile users suffer from low data rates, and vice versa.Our provider-agnostic aggregation of smartphones alleviates

1For instance, in UK, 55% of base stations are not co-located [8].978-1-4799-4657-0/14/$31.00 c© 2014 IEEE

t1 t

2

Provider A Provider B

User b User a

t1 t

2 time

rate Host: user a Host: user b

t1 t

2 time

power

User a

User b

a + b

tail transmission

(c) Data rates of users (d) Energy reduction from cooperation

(a) No cooperation (b) Cooperation

t1 t

2

Provider A Provider B

Fig. 1. An example scenario of user cooperation in a moving vehicle.

channel dependency to a provider by having a high chance tochoose smartphones with good signal condition from the poolof smartphones with various cellular providers. The same effectcan be achieved in a single smartphone when it can subscribe tomultiple cellular providers and carry their corresponding SIMcards. However, this is highly unlikely to see in practice dueto (1) space concern in the small form factor of a smartphone,(2) energy concern with limited battery, and (3) complex ac-counting problem among providers. Data bundling from packetmultiplexing is rather intuitive. By grouping smartphones witha few hosts, the size of data to be handled by a host at atime becomes automatically larger as the host gets a bundle ofpackets multiplexed from the guest smartphones.

Fig. 1 illustrates the aforementioned benefits in the scenarioin which smartphones are moving together in a vehicle (e.g., atrain, metro, and bus). In a daily life, there are many chancesof forming a PhonePool with neighboring users. Accordingto a large-scale demographic study by American Time UseSurvey [9], [10], people are with their acquaintances for 8.5hours (excluding sleep time) on average in a day. Suppose thatAlice and Bob share a journey from t1 to t2 (i.e., they arewithin WLAN (e.g., WiFi) communication range). If Alice andBob subscribe to AT&T (provider A) and Verizon (provider B),respectively, they experience different channel conditions andthroughputs as shown in Fig. 1(c). Suppose that both Aliceand Bob generate download file requests around t1 and t2.Then, Alice and Bob serve their own traffic as in Fig. 1(a),and their cellular power consumption is as the top and middleof Fig. 1(d). When Alice and Bob cooperate with each other asin Fig. 1(b), their transfer energy can be reduced significantlyas their data is transferred in good channel conditions, and tailenergy can also be reduced as their packets are bundled asdepicted in the bottom of Fig. 1(d).

In order to fully maximize the benefits of PhonePool, weformulate an optimization framework using a discrete infinitehorizon dynamic programming with consideration of fairnessamong the participating nodes. We first obtain the optimal al-gorithm from the framework and suggest a practically efficientheuristic based on the optimal algorithm. Our framework and itsoptimal solution are general enough to accommodate a number

of mobile collaboration problems (e.g., collaborative GPS [11],cooperative sensing [10]) with minimal extension.

For demonstration of the efficacy of PhonePool in bothenergy saving and stability in achievable data rate, we collectedover 100 hours of cellular connectivity traces using five smart-phones. The smartphones subscribe to either of three majorcellular providers in Korea, SK Telecom, Korea Telecom, andLG Telecom, where we consider both 3G and LTE networksof SK Telecom and Korea Telecom. Our extensive empiricalstudy through trace-driven simulations reveals that PhonePoolcan save up to 42% of communication energy when five smart-phones group together. To our surprise, in order to obtain theenergy saving, our algorithm applied in PhonePool sometimesmixes LTE (the most speedy networks) and EVDO (the slowest,but most short-tailed networks) smartphones together as hostsof a group, which is indeed the best choice at the moment inthe view point of energy saving.

We focus on the download case throughout this paper sincemajority of mobile data is download traffic,2 but our results areeasily extendable for the upload traffic similarly.

The rest of our paper is organized as follows. In Section II,we summarize related work on smartphone energy saving. Ourmeasurement study is explained in Section III. We describe ourPhonePool architecture and main algorithms in Sections IV andV. Trace-driven numerical analysis is described in Section VI,and some discussions and future work are in Section VII.

II. RELATED WORK

Many recent studies have focused on saving the amountof cellular communication energy in mobile devices and haveproposed several algorithms which fall in to the following twocategories: (1) transfer energy reduction, and (2) ramp and tailenergy reduction. Schulman et al. [3] revealed that cellulartransfer energy per bit can be as much as 6 times higherwhen the signal is weak than when it is strong through realmeasurements with smartphones, and proposed an algorithmthat delays data transfers to a time window when strong signalis provided by foreseeing users’ movement patterns. Earlierthan [3], Nicholson et al. [12] proposed Breadcrumb, whichis a wireless LAN (i.e., WiFi) version of movement predictionand scheduling algorithm that aims to transmit data when beingassociated with a WiFi access point providing strong signal.

Ramp and tail energy in cellular networks are experimentallyidentified by several studies [3]–[7]. The tail energy is theresidual energy for a data transfer, in which a cellphone remainsin a high power state after completing a data transfer for about4 to 11 seconds in EVDO [3], EDGE [7], GSM [5], HSPA [4]and LTE [6]. Being in the high power state is inevitable sinceit is specified in the standard of RRC in 3G and 4G. Thereforean ultimate way of minimizing the tail energy is the cross-layer optimization which considers traffic condition in boththe cellphone and the cellular tower (i.e., uplink and downlinktogether), but this approach might be hard to be realized inpractice. The ramp energy is the energy spent to raise the power

2The amount of cellular download traffic is about 6 times more than that ofupload traffic [4].

state of the cellular chipset from its idle state. Since the rampenergy is relatively smaller than tail energy and it is rathercoming from the limitation of electronic devices, literatureshows little interest on it.

In order to mitigate tail energy waste, Balasubramanian et al.[5] proposed TailEnder that merges data transfers by delayingdata traffic. The larger chunk of data automatically suppressesthe tail energy consumption as the number of tails attachedto each small data transfer is substantially reduced. Qian etal. [13] proposed ARO (Application Resource Optimizer) whichreduces tail energy in popular smartphone applications, e.g.,Google Search and Pandora, by jointly analyzing the resourcessuch as radio resource channel state, application layer, andtransport layer. To be brief, ARO merges network requestsfrom multiple applications by delaying the requests to makea batch data transfer, which obviously reduces the numberof tails. Another series of studies [14], [15] utilizes a fastdormancy technique [16], which enables mobile device to forcethe 3G interface to sleep faster (i.e., go to an idle power state)than normal. They proposed adaptive tail reduction algorithmsthat predict traffic patterns and use fast dormancy to cut offunnecessary tail energy.

Several researchers have studied user cooperation to reduceenergy consumption from smartphone sensor chipsets [10],[11]. They addressed that energy-hogging sensors such as GPS(Global Positioning System) and dust sensor have the samereadings across nearby cellphones, as they monitor spatialcontexts that maintain their values in proximity. Thus, byturning on sensors only in one of the neighboring smartphonesand sharing sensing information among them, sensing energycan be reduced significantly. Considering the fact that peopleare with their acquaintances for 8.5 hours (excluding when theysleep) on average [9], [10] in a day, distributing a job overneighboring smartphones has its practical value.

III. MEASUREMENT STUDY

A. Provider diversity

As providers have different cell planning with heterogeneouscellular technologies, co-located users with different subscrib-ing providers would experience different channel conditionsand data rates. To verify this, we measure 3G/4G data ratesof 5 cellular networks in various mobility conditions - high-speed train riding, highway driving, commute driving, andstatic. We developed an Android application which measuresdownload data rates by receiving a 100kB file through 3Gnetworks (1MB file through LTE networks) from our serverin every one minute interval, and recording the start and endtime of each transfer. We then simply divide the file size bythe transfer time and obtain download speed (i.e., goodput). Wecarry five smartphones in each mobility scenario where eachof the smartphones subscribes to one cellular network among5 different kinds of networks in Korea: SKT-HSPA/LTE, KT-HSPA/LTE, and LGT-EVDO,3 for more than 100 hours. Wedepict data rates of 5 networks in a highway driving trace

3We consider all five networks separately in this paper.

0 10 20 30 40 50 600

5

10

15

20

da

ta r

ate

(M

bp

s)

D−LTE E−LTE

0 10 20 30 40 50 600

0.5

1

1.5

2

time (min)

da

ta r

ate

(M

bp

s)

A−HSPA B−HSPA C−EVDO

Fig. 2. Data rates in 5 cellular networks over a highway mobility trace (A:SKT-HSPA, B: KT-HSPA, C: LGT-EVDO, D: SKT-LTE, E: KT-LTE). Averagedata rates of A, B, C, D and E are 0.78, 0.67, 0.41, 8.55 and 5.95Mbps, resp.

TABLE IPEARSON CORRELATION COEFFICIENTS OF DATA RATES FROM Highway.

A-HSPA B-HSPA C-EVDO D-LTE E-LTEA-HSPA - 0.01 -0.01 0.05 0.34B-HSPA 0.01 - 0.04 -0.09 -0.16C-EVDO -0.01 0.04 - -0.07 -0.07D-LTE 0.05 -0.09 -0.07 - 0.30E-LTE 0.34 -0.16 -0.07 0.30 -

in Fig. 2. For other mobility traces, we refer readers to ourtechnical report [17]. From our measurement, we find that thereis high variation in data rates in mobile traces, except in astatic trace. To verify that time-varying patterns of throughputare different among networks, we calculate Pearson correlationcoefficients between a pair of cellular networks’ data rates ina highway trace in Table I. As we find that almost all pairs ofnetworks show very low correlation in their data rates, potentialbenefit from provider aggregation is readily expected. We alsofind low correlation in other mobile traces, which are omitteddue to space limitation.

B. Wireless communication energy

We measure cellular transmission energy using MonsoonPower Monitor [18] by letting a smartphone download andupload a file from our server to a smartphone on a TCP socket.We only provide the measurements from download cases belowfor space concern as we consider download traffic in this paper.We note that upload transfer power is about 1.1-1.5 times thandownload transfer power, while upload data rate is about halfof download data rate. We refer readers to the experimentalsetting in [19], as we repeated the measurement methodologyexplained in the work. As shown in Fig. 3, a smartphone’scellular module is in either idle, transfer4, or tail5 mode, wherethe unit energy consumption (in Joule/sec) in each mode isdenoted by Eidle, Etran, and Etail. Each value is given in Table II.Starting from idle mode, the mode is changed from idle totransfer when it has data to transmit to or to receive from aBS (base station). After completing the transfer, the mode ischanged from transfer to tail, where the cellular module is ina tail mode at least for a tail duration, which is denoted byτ tail, before going into idle mode. We note that the networkC-EVDO has short tail duration compared to other networks.

4This mode is called DCH (Dedicated CHannel) mode in 3G and HSPA.5This mode is called FACH (Forward Access CHannel) mode in 3G and

HSPA, while it is called long DRX (Discontinous Reception) in LTE.

(a) Consumed power in states (HSPA). (b) State diagram.

Fig. 3. State transition in wireless modules.

TABLE II3G/4G ENERGY PROFILES.

Device Name Etran (J/s) Etail (J/s) Eidle (J/s) τ tail (sec)A-HSPA Galaxy Nexus 0.73 0.54 0.02 11.00B-HSPA Galaxy Nexus 0.77 0.56 0.02 10.80C-EVDO Galaxy S2 0.71 0.70 0.02 3.76D-LTE Galaxy Note2 1.35 0.67 0.02 9.74E-LTE Galaxy Note2 1.38 0.65 0.02 10.01

TABLE IIIP2P (WIFI AND BLUETOOTH) ENERGY PROFILES.

Etran (J/s) Etail (J/s) Eidle (J/s) τ tail (sec)WiFi Tether (Host) 0.67 0.60 0.14 1.00WiFi Tether (Guest) 0.75 0.42 0.01 1.00

Bluetooth Tether (Host) 0.17 - 0.04 -Bluetooth Tether (Guest) 0.53 - 0.01 -

We also measure power consumption in two wireless teth-ering interfaces, Bluetooth and WiFi, that most current smart-phones support by default, and summarize in Table III. We firsttether two devices, one host and one guest in either Bluetoothor WiFi. Again, we send a file from our server to a guestdevice, where a host device downloads the file from cellularnetworks and sends it to the guest device, and measure thepower difference from the case that Bluetooth or WiFi tetheringis not used (i.e., in Table II) in each mode. We find that WiFi hasquite short tail duration (i.e., 1 sec), while Bluetooth has almostno tail energy (the duration itself is too short compared to thecellular tail). Note that power consumption in each mode issimilar across devices. We find that Bluetooth tethering is low-power, but has low-data rates (about 1.5-3Mbps), whereas WiFitethering has high-data rates (over 20Mbps), but is high-power.Thus, we decide to use Bluetooth tethering in a cooperationamong 3G users (i.e., the networks A, B, and C), and use WiFitethering in a cooperation including at least one LTE user.

IV. PHONEPOOL ARCHITECTURE

We depict our PhonePool architecture in Fig. 4. Each usercan download and upload data traffic through its subscribing3G or 4G provider via a cellular module when it works as ahost, and can connect to Internet via a P2P module (Bluetoothor WiFi) when it works as a guest. PhonePool has two keycomponents, group planner, and host selector.

The group planner collects context information (e.g., ex-pected trajectory, contact history, network condition, batterylevel, etc.) of a user and autonomously decides whether or notto form a group with neighboring users and how long it willcooperate in a group depending on users’ attributes. For moresimplification of PhonePool, we can easily deactivate groupplanners and let users manually choose whom to collaborate.Suppose that a user riding a train or a bus together can notifythat she is ready to collaborate by broadcasting the information.

Fig. 4. PhonePool architecture.

Then, others who are interested to collaborate choose her toform the group. This manual procedure can be repeated to forma large group at a location.

After a group is formed by the group planners of users,a host is chosen at each time slot, which serves all groupusers’ traffic (i.e., traffic of hosts and guests) and collectsdata rate and remaining tail information. The host selectorpredictively chooses a set of energy-efficient hosts (for thenext slot) according to channel variation, tail states, and queuelength. If a guest is promoted to a new host by the hostselector (which may happen when the data rate of the guestincreases while others decrease), the new host starts to servepending requests of the group and activates its host selector.Each user estimates its cellular data rate using a low-powerrate prediction algorithm that exploits signal strength, locationinformation,6 or past data rates. We refer readers to [20], [21]for rate prediction algorithms. In [20], the authors addressedthat accurate prediction of short-term cellular data rates ispossible by estimating channel on device and predicting radioresource scheduling at the BS. [21] proposed a rate predictionalgorithm which utilizes location information as a context.

In the rest of our paper, we only focus on the host selectorfor a group of N users since we believe that manual groupplanning works fine in most practical scenarios.

V. AVERAGE COST MINIMIZATION PROBLEM

In this section, we describe our system model and formulateour problem as an infinite horizon average cost minimizationproblem. Our formulation defined as a dynamic programmingwith cost and benefit functions under mobile collaborationscenarios can be easily generalized. On such a formulation,our interest lies in online algorithms which do not know futuretraffic arrival. We derive an optimal online algorithm under afew assumptions (e.g., Bernoulli arrival process and exponentialfile size distribution), in which we can view our problem asa finite-state Markov decision process. Our optimal algorithm

6Note that location information can be attained energy-efficiently in a groupusing collaborative sensing [10], [11].

requires traffic arrival rates and data rate distribution as wellas high computational complexity. Two heuristic algorithms,threshold-based and max-rate, are computationally simple andapplicable in practical settings.

A. System Model

(1) Network, Energy and Traffic model: We consider agroup of N neighboring users where each user subscribes toone cellular network. N users are within peer-to-peer (P2P)communication range for a sufficient amount of period (e.g.,a few hours), where this period is divided into time slotst ∈ {1, ..., T}. We index a user by i ∈ {1, ..., N} and a timeslot by t. The data rate of user i at time t is denoted by ri(t).As shown in Fig. 3, a user i’s cellular module is in either idle,transfer, or tail where the unit energy consumption per slot ineach mode is denoted by Eidle

i , Etrani , and Etail

i . The remainingtail duration of user i at time t is denoted by τi(t), where thisvalue is set to an integer value τ tail

i (unit is time slot) aftercompleting a cellular transfer, and decreased by 1 at each timeslot if user i does not transfer any data via cellular networks.When τi(t) becomes zero, the cellular module goes into idle.

For a P2P module (e.g., WiFi or Bluetooth), we assumethat each user has the same energy profile (as we verify inSection III), and energy consumption is depending on thetethering mode (host or guest). For example, if user i (host)delivers data traffic of user j (guest) at slot t, user i consumesEtran

P2P-host (addition to cellular transfer energy, Etrani ) and user

j consumes EtranP2P-guest, where Etran

P2P-host and EtranP2P-guest are unit

P2P transfer energy of host and guest nodes, respectively. Weassume that the P2P energy cost induced from control messages(e.g., queue, rate, and remaining tail information) is negligibleas they can be piggybacked to data packets and the size ofcontrol messages is sufficiently small compared to data traffic.

Each user generates file download requests according to astochastic arrival process, whose file size is randomly chosenfrom a given file size distribution. We denote qi(t) as the queuesize of pending requests of user i at time t.7

(2) State transition model: We denote a system state sas a tuple of rates, remaining tail durations, and queue,r(t) =

(r1(t), ..., rN (t)

), τ (t) =

(τ1(t), ..., τN (t)

), and

q(t) =(q1(t), ..., qN (t)

). We denote by st the system state

at slot t. The system state st+1 is dependent on the previousstate st and a control µt(st) (which will be explained shortly).We define µ : s 7→ µ(s) as a host selection policy which isdefined for each state s, where a control µ(s) selects a hostnode from {1, ..., N}, or does not select any host node (whichwe denote as µ(s) = 0) at state s.8 We denote by µt(st)a control in system state st and policy µ. If µ(s) = 0, nouser downloads data at state s. If µ(s) = 3, user 3 as a hostnode downloads data requests of N users at state s. We denoteU : s 7→ U(s) as the set of all feasible policies, where U(s) isa set of feasible controls in state s, i.e., for a feasible control

7We reuse qi(t) to also denote the number of pending requests in an optimalalgorithm.

8This can be generalized to multi hosts if we define a control as any subsetof all users, {1, ..., N}.

at state s, µ(s) ∈ U(s). We assume that for a state s suchthat q(t) > 0, 0 6∈ U(s), i.e., at least one user downloads dataas a host node when the queue is not empty (we assume thatthe queue is work conserving). Data requests are assumed tobe served in a FIFO (First-In-First-Out) manner. We denoteby ps,s′(u) the transition probabilities that the discrete-timesystem moves from state s to s′ using a control u. Each timethe system is in state s and a control u is applied, a weightedcost g(s, u) =

∑Ni=1 wigi(s, u) is incurred depending on the

modes of users, where gi(s, u) is an instantaneous energy costof user i and ~w = (w1, ..., wN ) is non-negative weights ofusers. For example, if user i is in a transfer mode and user j isin a tail mode in state s and a control u, gi(s, u) = Etran

i andgj(s, u) = Etail

j , when P2P energy cost is zero. P2P energyconsumption of users is also added in gi(s, u) depending onthe modes of P2P modules. Note that g(s, u) is the sum energycost of users when wi = 1,∀i.

B. Problem Definition

For flexible operations between maximal energy saving andfair energy saving, we design an objective to minimize the p-norm (p ≥ 1) of the average cost vector (Jµ1 (s1), ..., J

µN (s1))

over all policies µ ∈ U and given initial state s1:

minµ∈U

(N∑i=1

(Jµi (s1)

)p)1/p

, (1)

where Jµi (s1) = limT→∞1T E[∑T

t=1 gi(st, µt(st)

)]. Note

that when p = 1, p-norm minimization becomes sum min-imization that maximizes energy reduction. When p → ∞,it achieves min-max fairness. It is well-known that p-normminimization satisfies fair rational preference relation [22]. Wealso define a weighted sum minimization:

minµ∈U

N∑i=1

wiJµi (s1). (2)

In general, finding an optimal solution achieving Eq. (1) ismathematically challenging because the p-norm itself breaksthe linearity of cost accumulation. On the other hand, theweighted sum minimization in Eq. (2) can be easily solved us-ing dynamic programming by using the weighted sum of instan-taneous costs g(s, u) at each stage. We suggest to solve Eq. (1)through Eq. (2) by proving that p-norm energy minimization forp > 1 can be solved by weighted sum minimization for ~w suchthat wi =

(Jµ

?

i (s1))p−1

, where µ? is an optimal solution ofEq. (1).9 In the rest of our paper, we consider the weighted summinimization problem for ~w that achieves p-norm minimizationfor an arbitrary p.

C. Optimal Algorithm

We take the following assumptions to make our discrete-timesystem as a finite-state Markov decision process where an op-timal cost and policy can be derived by dynamic programmingas in [23].

9Due to space limitation, detailed derivation is given in our technicalreport [17].

A1. Bernoulli traffic arrival and finite buffer. Traffic arrivesas a Bernoulli process, i.e., qi(t + 1) = qi(t) + 1 withprobability λi < 1, where qi(t) is the number of pendingrequests of user i at time t.10 Each queue has a sufficientlylarge buffer size B, i.e., qi(t) ≤ B.

A2. Exponential file size distribution. We assume that file sizeof user i is exponentially distributed with mean 1/νi.

A3. Discrete data rates. Users have a finite set of possible datarates, and the data rate of each user in the next time slotis only dependent on the current data rate of the user.

A4. Underloaded network. Et[ri(t)] >∑jλj

νjfor all i.

Theorem 5.1: The followings hold for the average cost perstage problem in Eq. (2) under assumptions A1-A4.

(i) The optimal average cost J? is the same for allinitial states and together with some vector h? =(h?(1), · · · , h?(m)

)satisfies Bellman’s equation

J? + h?(s) = minu∈U(s)

[g(s, u) +

m∑s′=1

ps,s′(u)h?(s′)

], (3)

for all states s = 1, · · · ,m, where the number of all statesis m. If a policy µ attains the minimum in the aboveequation for all s, the stationary policy µ is optimal. Inaddition, out of all vectors h? satisfying this equation,there is a unique vector for which h?(1) = 0.

(ii) If a scalar J and a vector h satisfy Bellman’s equation,then J is the optimal cost per stage for each initial state.

Proof: For a state s0 such that q(t) = 0, there is a positiveprobability that s0 is visited at least once within the first l stagesfor any initial states and all feasible policies, for some integerl > 0. The rest of the proof follows the Proposition 4.1 ofChapter 7 in [23], which is omitted here for brevity.

The relative value iteration algorithm [23], which yields anoptimal policy is as follows:

hk+1(s)=(1−γ)hk(s)+minu∈U(s)

[g(s, u)+γ

m∑s′=1

ps,s′(u)hk(s′)

]

−minu∈U(s)

[g(s0, u)+γ

m∑s′=1

ps0,s′(u)hk(s′)

]for all s = 1, ...,m, where s0 is some fixed state with h0(s0) =0, and 0 < γ < 1.

Theorem 5.2 (Optimality of the value iteration algorithm):As k goes to infinity, hk(s) converges to h?(s)/γ andminu∈U(s)

[g(s, u) + γ

∑ms′=1 ps,s′(u)h

k(s)]

converges to J?

where µ? which obtains minimum in every state is optimal.The proof of Theorem 5.2 can be derived by showing that any

feasible policy u is a unichain11 policy. We refer readers to [23]for the proof of convergence under the unichain assumption. Apolicy iteration algorithm can also be derived as in [23].

Our online algorithm yields an optimal policy under assump-tions A1-A4, but it is computationally too complex to be used

10This can be regarded as a discrete-time version of Poisson process if atime slot is sufficiently small.

11A unichain is a finite-state Markov chain that contains a single recurrentclass plus, perhaps, some transient states.

in practice. The complexity of an iteration is O(m2), wherem is the number of states, which exponentially increases withN (m =

∏Ni=1 n

ratei τ tail

i (B + 1), where nratei is the number of

discrete rates of user i). Also, the assumptions are hard tohold in practice (e.g., exponential file size, Bernoulli trafficarrival, and discrete data rates). Thus, we devise two low-complexity heuristic algorithms: (1) threshold-based algorithmand (2) max-rate algorithm, as follows.

D. Threshold-based AlgorithmOur threshold-based algorithm selects a host node that min-

imizes communication energy in transferring pending requestsunder practical assumptions such that data rates of users remainthe same until the completion of pending requests, and no trafficarrives until the end of tail period. Note that the time durationtypically spans up to a few tens of seconds. We define C tran

i (t)and C tail

i (t) as the expected transfer and tail energy cost of useri at slot t, respectively:

C trani (t) =

q(t)

ri(t)Etrani +

q(t)− qi(t)ri(t)

(EtranP2P-host + Etran

P2P-guest),

C taili (t) =

(τ taili − τi(t)

)Etaili ,

where q(t) =∑i qi(t). The term q(t)

ri(t)Etrani in C tran

i (t) repre-sents the cellular transfer energy in serving the group queue,q(t), and the second term represents the P2P transfer energy inserving the group queue, except i’s queues.12 The tail energycost term is the product of unit tail energy and increased tailduration, τ tail

i − τi(t). The total expected weighted cost of useri at slot t is defined as Ci(t) = wi

(C trani (t) + C tail

i (t)). This

cost term can be regarded as a rough representation of h(·)function in dynamic programming in Section V-C, where h(·)is the relative cost from the state s0 with an empty queue andcurrent tail durations such that h(s0) = 0, and wi = 1,∀i.

We denote by v(t) the host node at slot t. Initially, the firsthost node v(1) is selected randomly. When all users are idle(i.e., τi(t) = 0,∀i), a node with the smallest cost is selected asa host. Otherwise, a host is changed only if there is a node thathas smaller cost than the current host node, v(t) (i.e., Ci(t) <Cv(t)(t), where Cv(t)(t) is a threshold). The threshold-basedselection algorithm is as follows.

Threshold-based host selection algorithm1: At each slot t such that q(t) > 0,2: if τi(t) = 0,∀i,3: v(t+ 1) = argmini Ci(t).4: else if mini

[Ci(t)− Cv(t)(t)

]< 0,

5: v(t+ 1) = argmini[Ci(t)− Cv(t)(t)

].

6: else v(t+ 1) = v(t).

E. Max-rate AlgorithmIn the max-rate algorithm, a user with the highest data rate is

simply selected as a host node, i.e., v(t+ 1) = argmax ri(t).To avoid frequent host changes, when a node is promoted as anew host node, it remains as the host node for at least δ slots.

12Note that we pragmatically assume that P2P data rates are faster thancellular data rate of a host node, hence there will be no buffering in P2Pcommunication.

TABLE IVAVERAGE INTER-BLOCK TIME AND FILE SIZE OF 5 PARTICIPANTS’ TRAFFIC.

Inter-block time (sec) File size (kB) Intensity (kB/min)1 67.8 [0.9, 155.0]] 7.5 [0.3, 11.1] 6.72 32.1 [0.9, 59.8] 8.7 [0.2, 9.4] 16.23 31.5 [0.7, 76.5] 66.0 [0.1, 16.2] 125.84 25.7 [0.7, 81.3] 65.8 [0.2, 132.3] 153.55 19.2 [0.6, 53.5] 725.4 [0.3, 358.0] 2268.0

] Mean [10th percentile, 90th percentile].

VI. TRACE-DRIVEN NUMERICAL ANALYSIS

A. Setup

We develop a PhonePool simulator and run trace-drivensimulations over real traces of data rates. Our simulator hasthree input parameters, (1) traffic arrival, (2) data rates, and(3) energy profiles. For data rates and energy profiles, we useour measurement in Section III. As an input traffic, we use (a)synthetic and (b) real traffic traces. The role of synthetic trafficis to verify energy gain of PhonePool in diverse traffic patterns,e.g., inter-arrival time and file size distributions.

(1) Cellular traffic: We measure traffic patterns of 5 par-ticipants’ Android phones using an Android version of tcp-dump [24] during the daytime (defined as 15:30 ∼ 23:30) ona weekday. We extract download packets from the trace andmerge a series of consecutive download packets which havesmall inter-packet time (less than 500ms as used in [14]) into ablock. We summarize traffic patterns of participants in Table IV.

We find that inter-block time of each user fits well withan exponential distribution,13 and file size fits well with aWeibull distribution14 with k < 1. This implies that file sizes ofreal mobile traffic follow a heavy-tailed distribution as shownin [25]. For our fitting graphs, we refer readers to [17].

We also generate synthetic traffic to verify the performanceof PhonePool in diverse traffic patterns. We generate nine trafficpatterns with three inter-block time distributions (30 sec, 3 min,and 10 min) and three traffic intensities (10kB/min, 100kB/min,and 500kB/min), assuming that users in a group have the sameparameters of inter-traffic time and file size distribution. Theaverage file size is chosen so that the average file size overinter-block time is equal to traffic intensity. We assume thatfile size follows a Weibull distribution with k = 0.4.

(2) Data rates of users: We use a highway trace throughoutthis section, which is summarized in Fig. 2. The duration ofthe chosen trace is 2-hour long and it contains data rates of5 cellular networks. We obtain similar results in other traces,which are omitted due to space limitation.

(3) Energy model: We use the unit energy consumption of 5cellular networks in each mode as in Table II, and P2P transferenergy of host and guest devices as in Table III. We assumethat in a group with at least one LTE user, all group users useWiFi as a P2P module, and in a group without a LTE user, usersuse Bluetooth as a P2P module, since data rates of Bluetoothtethering (1.5-3Mbps) is sufficient to support 3G data rates. We

13The PDF of the exponential distribution with the parameter β is1βexp[−( x

β)].

14The PDF of the Weibull distribution with the parameters α and k iskα( xα)k−1 exp[−( x

α)k]. When k < 1, the distribution is heavy-tailed.

A C avg. A C avg. A C avg. A C avg.0

0.05

0.1

0.15

0.2

No cooopration Max−rate Threshold (p=1) Optimal (p=1)Avera

ge e

nerg

y c

ost (J

oule

/sec)

100%90%

80% 79%

3G tail 3G tran 3G idle P2P guest P2P host

Fig. 5. Energy consumption in a group of two users with subscribing providers,A-HSPA and C-EVDO, in no cooperation, max-rate, threshold and optimal(p = 1). The traffic interval and file size are assumed to be exponentiallydistributed with mean of 1 min and 100kB. The numbers (-%) are the relativecost in max-rate, threshold, optimal compared to no cooperation.

assume that P2P idle energy is negligible by using an energy-efficient sleep mechanism in tethering such as [26].

Using the above traces, we run simulation and compare ourthreshold-based algorithm with no cooperation, in which eachuser serves its own traffic, and max-rate, in which a user withthe highest data rate is selected as a host node at each slot,with δ = 10 sec. For synthetic traffic traces, we generate 100traffic traces and obtain the average of energy consumption.

B. Comparison of Algorithms: Two user caseIn this subsection, we compare the threshold-based algorithm

with the optimal algorithm. We consider a scenario of a two-user group with different subscribing providers, A-HSPA andC-EVDO. Fig. 5 depicts the energy consumption in no coop-eration, max-rate, threshold and optimal (p = 1) for synthetictraffic traces of 1-minute interval and 100kB/min intensity. Weuse exponentially distributed file sizes for the assumption A2 inour optimal policy in Section V-C. We find that in the max-ratealgorithm, the user with A-HSPA is likely to be selected as ahost node since the average data rate of A-HSPA (0.78Mbps)is faster than that of C-EVDO (0.41Mbps). In the thresholdand optimal algorithms, the user with C-EVDO is selected asa host node more often since the tail energy is smaller in C-EVDO (about 4s) than A-HSPA (about 11s). We find that ourthreshold-based algorithm obtains almost similar energy savingas the optimal algorithm since our assumption (i.e., data ratesremain the same until the completion of pending requests) holdsin most cases in traces we collect.

In the rest of our paper, we only show the results of thethreshold-based algorithm as the complexity of the optimal al-gorithm significantly increases while its performance is similarto that of the threshold algorithm.

C. Energy Saving(1) Impact of traffic types: We first run simulation in synthetictraffic to show energy reduction of user cooperation in diversetraffic patterns in Fig. 6. In all three policies, energy costincreases as inter-block time reduces (i.e., tail cost increases)and file size increases (i.e., transfer cost increases). We find thatour threshold policy is better than max-rate and no cooperationin all traffic patterns, where the max-rate policy is even worsethan no cooperation policy in some traffic patterns (e.g., 3 mininterval and 10kB/min intensity). The threshold policy achievesabout 40-50% of energy reduction, when the average inter-traffic time is sufficiently short (i.e., 30 seconds), or traffic

(0.5,10) (3,10) (10,10) (0.5, 100) (3,100) (10,100) (0.5,500) (3,500) (10,500)0

0.2

0.4

0.6

0.8

1

1.2

(Traffic interval (min), intensity (kB/min))

Avera

ge e

nerg

y c

ost (J

oule

/sec)

53%

75%

69%

101%

87%101%

60%

71%

71%

87%

73%80%

58%62%

60%66%

56%58%

No cooperation

Max−rate

Threshold

Fig. 6. Total energy consumption in synthetic traffic patterns in a group of 5users (no cooperation, max-rate and threshold). The numbers (-%) represent therelative cost in max-rate and threshold (p = 1) compared to no cooperation.

A B C D Eavg. A B C D Eavg. A B C D Eavg. A B C D Eavg. A B C D Eavg.0

0.1

0.2

0.3

No cooopration Max−rate Threshold (p=1) Threshold (p=2) Threshold (p=3)

Avera

ge e

nerg

y c

ost (J

oule

/sec)

100%

70%58% 62% 64%

Fair:0.45Fair:0.67 Fair:0.93 Fair:0.98

3/4G tail 3/4G tran 3/4G idle P2P guest P2P host

3/4G tail

Fig. 7. Energy consumption of each user under different operations in realtraffic patterns (no cooperation, max-rate, threshold (p = 1, 2 and 3)). Thenumbers (-%) represent the relative cost in max-rate and threshold comparedto no cooperation. The numbers Fair indicate the Jain’s fairness index [27].

intensity is sufficiently large (i.e., 0.5MB/min). We emphasizethat in a short inter-traffic time case, tail energy reduction bypacket bundling is prominent, where in large traffic intensity,transfer energy reduction by provider diversity is magnified.

We run simulation over real traffic traces that we measuredas in Table IV. We divide each traffic trace of a participant into2-hour traces, and in each time zone, a participant is assumed tosubscribe to one cellular network among 5 networks, such thatthere is no overlap. Thus, there are 5!× 4 = 480 distinct casesin total and we run simulation over all traffic traces and obtainthe average of energy consumption in each user and mode (e.g.,3G/4G tail, transfer, idle, P2P guest and host) as in Fig. 7. Evenif there is large P2P transfer energy consumption (12% of totalenergy consumption in threshold), a group of 5 users yields42% of energy reduction on average in the threshold (p = 1)policy compared to no cooperation policy, where the tail energyis reduced by 38% and the transfer energy is reduced by 78%.The average energy reduction in max-rate is 30%, where thetail energy is reduced by 8% and the transfer energy is reducedby 84%. This gain is mainly induced from (1) transfer energyreduction from high speed networks (i.e., D-LTE and E-LTE),(2) tail energy reduction by packet bundling, and (3) tail energyreduction from short-tailed networks (i.e., C-EVDO).

The threshold policy with p = 1 gives substantial amount ofenergy saving but it lacks fairness. To show that the fairnesscan be improved with p-norm, we run the threshold policy withp = 2 and p = 3 by using the weight update rule summarizedin our technical report [17]. Note that the weight vector ~w thatachieves p-norm minimization is unknown since µ? for p-normminimization is not given in advance. We evaluate the fairnessusing Jain’s fairness index [27] ranging from 1/N (least fair)to 1 (most fair). As p increases, expectably the energy saving

2 users 3 users 4 users 5 users0

10

20

30

40

50

Energ

y r

eduction (

%)

Size of a group

Fig. 8. Energy reduction in different group sizes using the threshold (p = 1).

TABLE VCOMPLETION TIME AND EFFECTIVE DATA RATES OF 5 USERS.

Small-sized files (≤ 100kB) (92.4%†) Large-sized files (> 100kB) (7.6%†)No coop. Max-rate Threshold No coop. Max-rate Threshold

A 25.4 (0.61)‡ 0.18 (5.94) 0.52 (2.22) 77.8 (0.59) 3.06 (10.18) 4.60 (8.71)B 46.4 (0.41) 0.18 (5.94) 0.50 (2.28) 148.3 (0.32) 3.06 (10.18) 4.22 (9.14)C 101.6 (0.28) 0.18 (5.94) 0.67 (2.05) 281.0 (0.18) 3.06 (10.18) 5.20 (8.38)D 0.07 (5.85) 0.18 (5.94) 0.49 (2.33) 3.38 (9.34) 3.06 (10.18) 3.98 (9.24)E 0.57 (4.22) 0.18 (5.94) 0.61 (2.22) 8.09 (6.73) 3.06 (10.18) 3.96 (9.30))† Portion of small and large files in number.‡ Completion time in second (effective data rates in Mbps).

is more fairly distributed among users with a small penalty (4-6%) in the overall saving. Also, all users have positive energysaving for p ≥ 2.

(2) Impact of group size: We vary the size of a group from 2to 5 users and obtain the energy reduction of threshold (p = 1)compared to no cooperation in Fig. 8. For each group, weassume that users have non-overlapping subscribing networksamong 5 networks. As the energy reduction varies dependingon the subscribing networks in a group and traffic traces, wedepict the 70% confidence interval of energy reduction in eachgroup size. We find that the average energy reduction increasesalmost linearly until 5 users, which incentivizes users to forma larger group.

D. Network Stability: Data Rates of PhonePoolAs PhonePool exploits provider diversity, most users in

cooperation would experience higher data rates. We summarizethe average of completion time15 and effective data rates ofeach user in Table V, where we define an effective data rate ofa file as its file size divided by completion time. We classifyfiles into two categories: small-sized and large-sized files. Inno cooperation, A, B, and C have much higher completiontime and lower data rates than D and E as they use lower-level technology (i.e., 3G). If users cooperate (max-rate andthreshold), the data rates increase for most of users, whichin turn reduces completion time significantly (especially forslow networks, A, B, and C). The max-rate policy achievesthe smallest completion time and the highest data rates since itexploits provider diversity in data rates maximally. Surprisingly,D-LTE, the most speedy network, also obtains higher ratesin max-rate. We find that threshold policy shows completelydifferent data rates according to the size of file, since thehost decision in threshold depends on file size (or queuelength, precisely). For large-sized files, threshold approximatesthe performance of max-rate. The effective data rates of thethreshold policy in small-sized files are quite slow, but usersmay not be bothered since the completion time is very small(less than 1 sec).

15The amount of time required to complete a file from the arrival time.

VII. CONCLUDING REMARK

In this paper, we proposed an energy-efficient mobile col-laboration architecture, PhonePool, which exploits (1) providerdiversity, and (2) packet bundling by user cooperation.Through measurement studies, we revealed that multiple cel-lular providers have uncorrelated data rates and heterogeneoustail energy. We devised a heuristic algorithm that chooses anenergy-efficient host node, which mimics the optimal algorithmbased on dynamic programming. Our trace-driven simulationsover measurement data on channel condition and traffic genera-tion in mobile traces demonstrated that our heuristic algorithmachieves up to 42% of energy saving as well as significantincreases in effective data rates, where energy saving gets morefairly distributed for all users as p increases, only with a smallpenalty (4-6%) in the overall reduction.16 Our proposed dy-namic programming formulation can be easily generalized andhence widely applicable to collaborative mobile services (e.g.,collaborative GPS [11], cooperative sensing [10]). We also notethat benefits of utilizing provider diversity include significantimprovement on the cellular connectivity coverage of mobiledevices, especially in rural areas or developing countries, evenif in our measurement, this effect is not shown as Koreanproviders have full coverage in traces that we collected.

We remark that more energy saving can be attained byapplying more functionalities in PhonePool, which we leaveas future work. First, as P2P data rates are much faster thancellular data rates as of now and will become faster, schedulingP2P transfers such that the transfer time is minimized canreduce P2P energy significantly. Also, PhonePool can detectoverlapping requests (e.g., popular contents) by using contentcaching techniques [28], [29], which in turn reduces unnec-essary cellular communication energy when group users havesimilarities in their traffic. Note that the gain from contentcaching increases as the size of the group gets larger.

The main focus of our study is purely performance oriented.So, we ignored a few technical and policy issues that will beincorporated in our future work. First, we have not consideredsignaling overhead to update information (queue sizes, rates,and tail durations). We note that they can be piggybacked todata packets17 and information can be updated in a larger timeinterval.18 Also, we give little attention to group formation,since it may be better to leave the choice of joining to thegroup to minimize privacy concern.

We also do not examine issues of billing and privacy. As auser’s data can be served by other users’ subscribing providers,billing should be accounted to the user who originally generatesthe request. Also, some users would be reluctant to cooperatewith strangers, which in turn reduces chances of energy saving(Still, there are abundant opportunities with acquaintances [9]).Despite these issues, we believe that the impact of our work issignificant as we devised a novel collaboration framework and

16Note that our measurement data can be biased by the mobile traces as wellas the participants.

17The size of control information is negligible compared to data packets.18For example, tail duration can be calculated from previous host selection,

and queue sizes are needed to be updated only when new data traffic arrives.

showed large potential saving in cellular communication energyas well as potential benefit in connection stability from usercooperation. Given the high energy saving and network stabilityfrom user cooperation, we foresee that the providers may offertechnical solutions with a new mutual pricing scheme.

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