service-oriented heterogeneous resource sharing...

Service-Oriented Heterogeneous Resource Sharing forOptimizing Service Latency in Mobile Cloud

Takayuki NishioGraduate School of

Informatics, Kyoto UniversityYoshida-honmachi, Sakyo-ku,

Kyoto, [email protected]

Ryoichi ShinkumaGraduate School of



u.ac.jp

Tatsuro TakahashiGraduate School of



u.ac.jpNarayan B. Mandayam

Wireless Information NetworkLaboratory (WINLAB),

Rutgers University671 Route 1 South

North Brunswick, NJ, [email protected]

ABSTRACTFog computing is expected to be an enabler of mobile cloudcomputing, which extends the cloud computing paradigmto the edge of the network. In the mobile cloud, not onlycentral data centers but also pervasive mobile devices sharetheir heterogeneous resources (e. g. CPUs, bandwidth, con-tent) and support services. The mobile cloud based onsuch resource sharing is expected to be a powerful plat-form for mobile cloud applications and services. In thispaper, we propose an architecture and mathematical frame-work for heterogeneous resource sharing based on the keyidea of service-oriented utility functions. Since heteroge-neous resources are often measured/quantified in disparatescales/units (e.g. power, bandwidth, latency), we present aunified framework where all these quantities are equivalentlymapped to“ time” resources. We formulate optimizationproblems for maximizing (i) the sum of the utility functions,and (ii) the product of the utility functions, and solve themvia convex optimization approaches. Our numerical resultsshow that service-oriented heterogeneous resource sharingreduces service latencies effectively and achieves high energyefficiency, making it attractive for use in the mobile cloud.

Categories and Subject DescriptorsC.2.4 [Computer-Communications Networks]: Distri-buted Systems

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Keywordscloud computing, mobile cloud, fog computing, heteroge-neous resource sharing, service-oriented

1. INTRODUCTIONRecent advances of cloud computing platforms and mobile

devices have given rise to mobile cloud computing (MCC),which is a new paradigm for mobile applications and servicesthat promises to have a strong impact on our lifestyle. Ini-tially, MCC mainly focused on improving computing powerand storage capacity of mobile nodes by outsourcing tasksto more powerful cloud data center [1].

Mobile cloud architectures can be roughly classified intotwo types[2, 3]. The first type of architecture is the agent-client based architecture, where only a central data centerprovides resources (e.g. central processing unit (CPU) andstorage) for mobile devices and processes the tasks necessaryfor implementing a service. In this setting, mobile devicesjust use cloud resources and do not contribute any services[4]. The second type of architecture is a cooperation-basedarchitecture, where not only central data centers but alsomobile devices share their resources and support services.Such architectures can be widely varied as well as the mostpowerful due to the sheer numbers of devices available totake part in the cloud. The underlying concept behind sucharchitectures is also referred to as fog computing [5], whichextends the cloud computing paradigm to the edge of thenetwork.

The cooperation-based mobile cloud is the most inter-esting and visible research area of MCC at present. Therecent performance advances and diversification of mobiledevices bring a lot of ‘heterogeneous resources’ into localnetworks such as high-performance CPUs, high-speed LongTerm Evolution (LTE) connections, high volume storages,and multiple-sensor information. These correspond respec-tively to computational resources, communication resources,storage resources, and information resources. These hetero-geneous resources can be leveraged opportunistically mak-

19

ing cooperation-based cloud computing enabled by advancedmobile devices, a powerful platform for supporting a widevariety of applications.

Several technical issues still need to be solved to fully re-alize the cooperation-based mobile cloud. In this work, wefocus on the core problem of how to coordinate the sharingof heterogeneous resources between nodes. Conventional ap-proaches for achieving heterogeneous resource sharing usu-ally coordinate tasks (such as numerical calculations or evendownload of data) without consideration of the specific ser-vice that is being provided [2, 3]. In such task-oriented shar-ing, heterogeneous resources are often measured/quantifiedin disparate scales/units (e.g. power, bandwidth, latency),and tasks are allocated to optimize certain metrics based onthe the disparate scales/units. Consider the example of anavigation service composed of the tasks of calculating theoptimal route and downloading map images. Task-orientedsharing for such a service minimizes the processing (com-puting) time for each task. However, the navigation servicehas the peculiar feature that even if the route calculationis completed in just a few microseconds, users can not en-joy the service until they complete the downloading tasks.In this case, it makes no sense to optimize computationalresources; perhaps the optimization would waste the com-putational resources even. Instead, what would have beenbetter is the optimization of a service-oriented utility func-tion that better captures the benefits of such optimization.

In this paper, we propose an architecture and mathemat-ical framework for heterogeneous resource sharing based onthe key idea of service-oriented utility functions. The pro-posed system model is shown in Figure 1. In our archi-tecture, a resource coordinator orchestrates tasks and re-sources service-by-service to maximize the utilities of nodesfor services. Since heterogeneous resources are often mea-sured/quantified in disparate scales/units (e.g. power, band-width, latency), we present a unified framework where allthese quantities are equivalently mapped to“ time”resour-ces. We formulate optimization problems for maximizing (i)the sum of the utility functions, and (ii) the product of theutility functions, and solve them via convex optimizationapproaches.

This paper is organized as follows. Section 2 introducesthe system model as well service-oriented utility functions.The proposed numerical model is discussed in Section 3.We discuss optimization of resource sharing in Section 4. InSection 5, scenarios for numerical analysis are discussed, andnumerical results are presented. We conclude the paper inSection 6.

2. SYSTEM ARCHITECTURE

2.1 AssumptionsWe assume that nodes use services through applications

installed in them. Nodes request resources service by service.A service is composed of multiple tasks such as computingand data downloading.

Figure 2 depicts an example of a task flow for a service.Nodes want to complete the tasks included in the serviceas soon as possible. To process tasks, nodes need to usetheir resources. The set of resources that node i has is givenas Ri = {Rm

i : m ∈ M}, where the label m indicates thespecific type of resource from the set of all available resourcesM . Further, the set of the sizes of tasks that node i has to

Resource coordinator

Service application

Physical link

Service request Nodes’ information - Location - Performance

Nodes’ information Task compositions for services

Task allocation

Figure 1: Service oriented mobile cloud with fogcomputing

process is given as Ti = {T li : l ∈ L}, where the label l

denotes the specific type of task from the set of all requiredtasks L. In other words, node i uses an appropriate amountof resources to accomplish the task l of size T l

i . It is possiblethat accomplishing two different tasks may require the sametype of resources in which case the specific type of resourcehas to be shared between these two.

Figure 2 (b) shows an example of services where node irequests additional resources and node j shares its resourceswith node i. A task of T l

i can be separated into smaller por-tions and, when node j shares resources with node i, node ioutsources some portions of the task to node j. The smallportion of the task outsourced to node j is denoted as ∆T l

ij

(∆T lij ≥ 0). Node i has to process the remaining (not out-

sourced) tasks ∆T lii. Note that the relationship between T l

i

and ∆T lij is T l

i =P

j∈N ∆T lij where N is the set of all nodes.

Outsourcing portions of a task reduces the processing timefor the task accordingly.

a) without resource sharing

Task 1 (T1i) � Service

start�Service request� Task 3 (T3

i) �

Task 2 (T2i) �

Task 1 (T1i) �

Service start�

Service request� Remaining Task 3 (ΔT3

ii) �

Outsourced task 3 (ΔT3ij) �

Task 2 (T2i) �

b) with resource sharing

Figure 2: Example of flow of tasks for service. Valuein bracket is the amount of the task.

2.2 System modelAn exemplary model of the architecture is shown in Fig-

ure 3 where neighboring mobile nodes are connected to othernodes and form a local network for resource sharing by us-ing short-range wireless connections such as WiFi in ad-hocmode and/or Bluetooth. Messages for resource sharing suchas resource requests, task instructions, and the results forthe tasks, are transmitted via the local network. Some of

20

Internet �

Data centers

Physical wireless link for resource sharing Physical (wireless) link for Internet access

Local resource coordinator

Local cloud

Figure 3: System model

the nodes have wireless Internet access using possibly 3G,LTE and WiFi connections.

Neighboring node in a local network form a group called alocal cloud. Nodes share their resources with other nodes inthe same local cloud. A local resource coordinator (LRC) iselected from the nodes in each local cloud. The coordinatormanages resource requests and allocates tasks to the nodesin the local cloud or data center in the Internet if neces-sary. The coordinator should be elected in accordance withthe connectivity to the local network, CPU performance andbattery life time. In this paper, we focus on resource coor-dination and have thus omitted the algorithms for the for-mation of a local cloud and selecting the LRC. Further, weassume that the short range connections necessary to sup-port formation of any networks for resource sharing are notbandwidth restrained. We also study resource allocationonly under the scenario of sharing of computation resour-ces, communication resources and information resources.

In our architecture, nodes can be resource users and re-source providers. Figure 4 illustrates an example of mes-saging between two nodes and a coordinator. Here, supposethat node i and node j are requesting resources, and node iis outsourcing its tasks for node j in accordance with somecoordination procedure. The messages are exchanged se-quentially as follows: (1) the nodes send request messagesto the coordinator; these messages include what and howmuch resources a node has, what and how much tasks thenode has to complete for a service, and MAC and IP ad-dresses of the node. (2) The coordinator allocates the tasksin order to maximize the utilities of nodes for the services,which is proposed in next section. The coordinator notifieseach node what and how many tasks the node should pro-cess; (3) node i sends an instruction message to node j inaccordance with the coordination result. The message in-cludes necessary information to process tasks of node i; (4)node j processes the tasks in accordance with the instruc-tions from node i; (5) node j sends the results of the tasksto node i; and (6) node i constructs the service based on theresults of tasks.

2.3 Service-oriented unified utility functionWe model the utility of nodes as a function of a service

latency. The reason why we focus on service latency is thatthe latency is a straightforward measure of the decrease in

Node j Node i

3) Task instruction

5) Result of task

time

4) Processing tasks

6) Constructing service

Local resource coordinator

1) Resource request

2) Result of coordination 2) Result of coordination

1) Resource request

Figure 4: Coordination flow

the quality of experience for the service [6]. We define ser-vice latency as the duration from when the first task of aservice being processed starts until all the tasks for that ser-vice are finished. We define the utility function of node i asUi(ti), which is a monotonically decreasing function such as−a · ti + b, where ti is the service latency of node i. Fig-ure 5 shows the service latency and the utility as a func-tion of outsourced tasks. As we can see in Figure 5, in-creasing the quantity of outsourced tasks increases the gainof the node for the resource sharing. Here, ti depends onRi, T

li , ∆T l

ij , ∆T lji (j ∈ N, and l ∈ L).

Serv

ice

late

ncy

ti’: w/o outsourcing tasks

Outsourced tasks

: Gain

Node i

Other nodes

Outsourcing tasks of ΔT

ti: w/ outsourcing tasks

ΔT

Figure 5: Gain of resource sharing

Using the unified utility function enables us to comparethe value of heterogeneous resources in the same dimensionof time. It could be a powerful metric for heterogeneous re-sources since we can treat any kind of resource as long asthe resource can reduce the service latency. For example,a high-performance CPU reduces the latency for processingcomputational jobs, and high-speed wireless access reducesthe latency for downloading data. A smart algorithm can re-duce the latency for processing a computational task. Con-tent can also be a resource, which can reduce the latency forobtaining the same content from the Internet. Sensor infor-mation can reduce latencies. For example, GPS informationcan be used to localize a node instead of other localizationtechniques that may be more computationally intensive andrequire completion of several communication tasks.

3. NUMERICAL MODEL FOR SERVICE-ORIENTED RESOURCE SHARING

In this section, we discuss the proposed architecture interms of service latency and energy consumption, which areimportant factors for mobile users.

21

3.1 Service latencyFigure 6 shows the different scenarios possible for how

tasks may need to be accomplished in providing a service.For a service (a), we can easily calculate the latency as thesum of the latencies for all tasks. For a service (b), we alsocan calculate the latency as the pointwise maximum of thelatencies for all tasks. However, a service generally consistsof multiple sequential tasks as shown in Fig 6 (c). Here, wedefine a sequence as a set of tasks which have to be processedin order. As shown in Figure 6 (d), we can define the service(c), identified as s, as Qs = {Qu

s : u ∈ Us}, where the labelu indicates the specific identification of the sequence fromthe set of all sequences included in the service Us. Since thelatency of each sequence can be calculated as the sum of thelatency for processing the tasks included in the sequence,the service latency of node i ti is written as

ti = maxu∈Us

(X

l∈Qus

tmli ), (1)

where tmli is the latency required for node i to complete task

l when using the resources appropriate for the task Rmli .

b) Parallel case

Task A � Service start�

Service request� Task B �

a) Sequential case

Task A � Service start�

Service request� Task B �

Sequence 1 �Service

start�Service request� Sequence 2 �

Sequence 3 �

d) Parallelized sequences

Task A �Service

start�Service request� Task C �

Outsourced task C’ �

Task B �

c) Mixed case

Task D �

Figure 6: Task sequences for service

The tmli should be defined appropriately for the resources

ml. For computational and communication resources, wedefine the latency as T l

i /Rmli . This definition of latency is

accurate, since, for example, the processing time of compu-tational operations T l

i when using a CPU that performs Rmli

operation per second, and the downloading time of a datasize of T l

i with throughput of Rmli bps could be calculated

using the definition.Next, we discuss information resources. We regard these

resources as alternative resources to communication and com-putational resources. For example, when a map image isrequired for a service, if a node caches the image, the nodecan use it without downloading the image from the Inter-net. Suppose that in a navigation service, if a node cachesa route calculation result, the node can leverage that resultinstead of calculating the route. If node i has alternative in-formation for a task T l

i , the node can finish the task withoutprocessing the task using resources R

mli . Let us define

δlij =

(

0 (Ili ⊆ Rinfo

j );

1 (Ili 6⊂ Rinfo

j ),(2)

where Ili is an alternative information resource for task l and

Rinfoj denotes the set of all information resources for node

j. Using Eq. (2), we define the latency for a task as

tmli (T l

i ) = δlii

T li

Rmli

. (3)

3.2 Procedure for sharing resourcesAs shown in Figure 4, in order to share resources, nodes

have to exchange messages and process tasks for other nodes.For example, suppose that node i outsources a set of tasks∆T l

ij to node j. The instruction message from node i in-structs node j how to process each task in the set and nodej processes the tasks using its resources R

mlj . When it fin-

ishes processing the tasks, node j sends the results of thetasks back to node i. We define the latency for an out-sourced task tl

ij as the duration from when the first messageis sent until the result is received.

The latency tlij is written as

tlij = t

mlj (∆T l

ij) + tt(Dlins(∆T l

ij)) + tt(Dlr(∆T l

ij)) + ∆tmlj ,(4)

where tt(D) indicates the time needed to transmit a messagevia short-range communications, the length of which is D;Dl

ins(∆T lij) is the data size required for instructing the node

how to process the task ∆T lij ; Dr(∆T l

ij) is the data size of

results for task ∆T lij ; ∆tml

j is an additional latency that

depends on when node j starts to process task T lij . In this

paper, we simply define them as

Dlins(T

lij) = wl

ins, Dlr(T

lij) = wl

rTlij , and tt(D) = D/θ,

(5)where wl

ins and wlr are weight parameters and θ is the through-

put of a short-range wireless link.Outsourced tasks and the other remaining tasks can be

processed in parallel. Then, the latency for task l becomes

tmli = δli

i · MAX(tmli (∆T l

ii), tli1, t

li2, ..., t

liN ), (6)

3.3 Trade-off between gain and energy con-sumption

As we mentioned in Section 1, we intuitively know thatsharing resources with nodes close to you should be moreefficient and effective than sharing with distant nodes.

There is a trade-off between the gain from cooperatingwith distant nodes and the energy consumption. Increasingthe number of cooperating nodes might enable the nodes toobtain a greater gain, since the nodes would share a largeramount of remote resources. To increase the number of co-operating nodes, the nodes must improve their communica-tion range. Suppose that there are three nodes i, j and k.The distances between each pair of nodes are dij , djk, anddik, respectively. Here, dik and djk are larger than dij . Inorder for node i to share resources with node j, node i hasto transmit messages to node j. In that case, the commu-nication range of node i has to be longer than dij . If nodei and j cooperate with node k, their communication rangeshave to be longer than dik and djk respectively. Nodes i andj can obtain greater gain by sharing resource with node k,while they require a larger energy for transmission to obtainmore communication range.

Energy is consumed when nodes send/receive data. Thevalues Etx(D, d) and Erx(D) represents the consumed en-ergy in sending and receiving a message, where D is thedata size of sent or received data, and dr is the requiredcommunication range to share resources with a node, whichis almost the same as the geographical distance between asender and a receiver. Etx(D, d) and Erx(D) monotonicallyincrease as D and d increase. In particular, they increaseexponentially as d increases while maintaining the signal tonoise ratio (SNR) [7]. Energy is also consumed when nodes

22

process tasks. Eml(T l) is the consumed energy for process-ing the task T l while using resource ml. It also mono-tonically increase as the amount of tasks increases. Here,we simply define Eml(T l) = eml · T l, Erx(D) = erx · D,Etx(D, d) = etx · (d)2 · D, where eml indicates the energyconsumed in a second for fully usage of the resource ml;erx indicates the energy consumed to receive a data size of1 Byte; etx indicates the energy consumed to send a datasize of 1 Byte to a node distance of 1 m. Then, the energyconsumed by node i when sharing resources with node j is

Eij =X

l∈Lji

{erxwlins + eml∆T l

ji + etx(dij)2wl

r∆T lji}

+X

l∈Lij

{etx(dij)2wl

ins + erxwlr∆T l

ij}, (7)

where Lij is the set of labels for tasks outsourced to node jby node i. In addition, node i has to complete the remainingtasks. Then, the total energy consumption of node i becomes

Ei = eml

X

l∈L

(∆T lii) +

X

j∈N,j 6=i

Eij . (8)

4. RESOURCE SHARING OPTIMIZATIONWe consider a case where a coordinator ideally knows all

information such as Rmi and T l

i . The coordinator instructsevery node to allocate their tasks to other nodes in order toi) maximize the sum of the gains of all nodes or ii) maximizethe product of gains of all node. First we discuss the generalcase. Then, we explicitly formulate an optimization problemfor a specific case where two nodes shares resources.

4.1 Objective

4.1.1 Maximizing sum of gains in utilityThe simplest objective is to maximize the sum of the gains

of all nodes. It is written as

objective: max∆Tij (i, j∈N)

X

i∈N

(Ui(ti) − Ui(t′i)), (9)

where ∆Tij = {∆T lij : l ∈ L} and t′i is a service latency when

node i does not share resources. If we can define the utilityfunction as Ui(ti) = −a · ti + b (ti > 0), the problem tomaximize the sum of the gains in utility of all nodes is equalto the problem of maximizing the sum of reduced servicelatencies. Then, the objective can be written as,


X

i∈N

(t′i − ti). (10)

As described in [9], a nonnegative, nonzero weighted sumof convex (concave) functions is convex (concave). Then, ifti is convex or concave for ∆Tij , the objective is concave orconvex for ∆Tij , respectively.

4.1.2 Maximizing Product of gains in utilityAn objective of the optimization problem should be


Y

i∈N

(t′i − ti). (11)

This objective is based on the idea of the Nash bargainingsolution, which is a solution that brings Pareto efficiency andproportional fairness. However, the objective is not neces-sarily convex, which makes the optimization problem hardto solve.

4.2 ConstraintsNext, we discuss constraints. In this paper, we consider

constraints for task amounts and incentives on service la-tency and energy consumption. The constraints are writtenas:

subject to:

T li =

X

j∈N

∆T lij (for any i and l), (12)

∆T lij ≥ 0 (for any i,j and l), (13)

Ethi > Ei − E′

i (for any i), (14)

t′i > ti (for any i), (15)

where Ethi is threshold for energy consumption and E′

i isenergy consumption of node i without resource sharing.

Eqs. (12) and (13) mean that the size of tasks should bepositive, and nodes cannot outsource more tasks than thenodes have. Eq. (14) and Eq. (15) mean that node i ismotivated to join the resource sharing only if its additionalenergy consumption is kept smaller than its threshold Eth

i

and if the resource sharing reduces its service latency. Whywe consider the constraints is that we can expect that nodesdo not share their resources without ensuring an incentivefor the sharing. Resource sharing can reduce not only servicelatency but also energy consumption [8]. These reductionscan be incentives for resource sharing, but we expect thatthese two do not go together since there are trade-offs, asdiscussed in Section 3.3.

From Eq. (8), Ei andP

j∈N ∆T lij are the sum of an affine

function. Then constraints except for ti are evidently convexor concave for ∆T l

ij . If we use objective (i) and ti is convex orconcave, the optimization problem becomes a convex opti-mization problem, which can make optimization easier thanthe general case since any local solution must be a globalsolution.

4.3 Case study: Resource sharing in two-nodecase

We discuss a simple case where a node shares computa-tional, communication and information resources with an-other node to minimize the latency for a service composedof a computational task and a communication task.

We consider a scenario where two nodes 1 and 2 share theircomputational and communication resources, the amountsof which are indicated by R1

i and R2i respectively (i = 1 or 2).

A common service requested by nodes 1 and 2 consists of acomputational task and a communication task, the amountsof which are T 1

i and T 2i , respectively (i = 1 or 2.) The

latency of each task is assumed to be T li /Rl

i as described inSection 3.1.

Here, we assume that these two tasks can be processed inparallel. In this case, as discussed in Section 3.1, the servicelatency of node i when they do not share resources becomes

ti = MAX(δ1ii

T 1i

R1i

, δ2ii

T 2i

R2i

). (16)

From Eqs. (5) and (6), when node i and j share theirresource, the latency for a task l of node i is

tli = δli

i MAX(T l

i − ∆T lij + ∆T l

ji

Rl,

tt(Dins(Tlij)) + δli

j

T lij

Rli

+ tt(Dr(Tlij))). (17)

23

In this scenario, from (17), either ∆T lij or ∆T l

ji should be

0 at the optimal equilibrium. We define ∆lij as

∆lij =

∆T lij (∆T l

ji = 0);−∆T l

ji (∆T lij = 0).

(18)

Then

∆T lij − ∆T l

ji = ∆lij . (19)

From Eq. (19), Eq. (17) can be described as

tli(∆

lij) =

8

>

>

>

<

>

>

>

:

δlii MAX{T l

i −∆lij

Rli

,

wins∆lij

θ+ δli

j∆l

ij

Rli

+wr∆l

ij

θ}. (∆l

ij > 0);

δlii

T li −∆l

ij

Rl . (∆lij ≤ 0).

This function is convex, since, as proved in [9], if f1 andf2 are convex functions then their pointwise maximum f,defined by f(x) = max{f1(x), f2(x)}, is also convex.

Next, we discuss the energy consumption. From Eq. (8),the energy consumption of node i when sharing resources is

Eli =

8

>

>

<

>

>

:

δlii {el · (T l

i − ∆lij) + etx · (dij)

2 · wins∆lij

+erx · wr∆lij} (∆l

ij > 0);δli

i el · (T li − ∆l

ij) − erx · wins∆lij

−etx · (dij)2 · wr∆

lij (∆l

ij ≤ 0).

The function is continuous and obviously convex for δ(Ili , R

infoi )

= 0 or 1.Using the above functions, we can write the optimization

problem as:

objective: max∆1

ij ,∆2ij

Gi + Gj (20)

subject to:

Gi = MAX(δ1ii

T1i

R1i

,δ2ii

T2i

R2i

)−MAX(t1i (∆1ij),t2i (∆2

ij)),

Gj = MAX(δ1jj

T1j

R1j

,δ2jj

T2j

R2j

)−MAX(t1j (−∆1ij),t2j (−∆2

ij)),

Gi, Gj ≥ 0,

T li ≥ ∆l

ij ≥ −T lj (l = 1 and 2),

Ethi > E1

i − e1T1i + E2

i − e2T2i .

MAX(t1i (∆1ij), t

2i (∆

2ij)) is convex.1 Then, Gi and Gj are

evidently concave functions. As described in [9], a nonneg-ative, nonzero weighted sum of convex (concave) functionsis convex (concave). Then, Gi + Gj is concave. As men-tioned above, other constraints are also convex. Therefore,the optimization problem is a convex optimization problem.

While we have discussed the 2-node case with 2 tasks thusfar which lends itself to formulation as convex optimization,the extension to the general case of N-nodes with L-tasksmay not necessarily yield such convex optimization formu-lations. We instead outline a heuristic approach below thatwill be an aspect of further study. Specifically, a heuristicfor the N-node optimization problem can be to use subsetsof the 2-node optimization problems, where these subsets

1We define t1i (∆1ij , ∆

2ij) = t1i (∆

1ij)+0·∆2

ij and t2i (∆1ij , ∆

2ij) =

t2i (∆2ij) + 0 · ∆1

ij . These functions are convex since they arethe sum of convex functions and zero. Then their pointwisemaximum of MAX(t1i (∆

1ij , ∆

2ij), t

2i (∆

1ij , ∆

2ij)) also has to be

convex. Since MAX(t1i (∆1ij , ∆

2ij), t

2i (∆

1ij , ∆

2ij)) is equal to

MAX(t1i (∆1ij), t

2i (∆

2ij)), MAX(t1i (∆

1ij), t

2i (∆

2ij)) is also con-

vex.

may be chosen according to various criteria as described be-low: minimizing the average geographical distance betweennodes, maximizing the average reduced service latency, ormaximizing the product of reduced service latencies.

5. NUMERICAL EXAMPLES

5.1 Scenario setupTo illustrate our approach, we consider a scenario where

nodes share their communication and computational resour-ces. The nodes want to use a navigation service. For theservice, node i has to download load information and mapimages, and calculate the optimal route. We assume herethat the load information is already stored in the nodes.Then a latency for downloading the load information is 0.The total data size of the map images is T 1

i and the num-ber of operations for calculating the route is T 2

i . Node idownloads data at a throughput of R1

i and calculates com-putational tasks at the speed of R2

i . We assume that nodescan process the image downloading and route calculationsimultaneously. In this case, an optimization problem forthe resource sharing becomes the same as that of (20) when

δlii = δlj

j = 1 for any l.Here, we assume that the local resource coordinator men-

tioned in Section 2.2 ideally solves the optimization problemdiscussed in Section 4 and determines the optimal allocationof tasks; however, the constraints for energy consumptionsare not considered in order to observe the adverse effects ofgeographical distance. We solve this non linear optimizationproblem by using the generalized reduced gradient technique[10].

We describe the parameters used in the study in the cap-tions of specific figures. These parameters are chosen con-sidering the performance of actual CPUs and wireless accessusing 3G, LTE, and Wi-Fi. [11, 12, 13]

5.2 Comparative EvaluationWe compare our service-oriented approach with a numer-

ical upper bound and a task-oriented approach.

5.2.1 Numerical upper boundThe numerical upper bound is obtained when the sum of

reduced service latencies is maximized without consideringincentives for nodes. In particular, in this scenario, we solvethe following optimization problem for 2 nodes i and j as:

objective: max∆1

ij ,∆2ij

Gi + Gj (21)

subject to:

Gi = MAX(T1

iR1

i

,T2

iR2

i

)−MAX(t1i (∆1ij),t2i (∆2

ij)),

Gj = MAX(T1

j

R1j

,T2

j

R2j

)−MAX(t1j (−∆2ij),t2j (−∆2

ij)),

T li ≥ ∆l

ij ≥ −T lj (l = 1 and 2).

5.2.2 Task-orientedIn the scenario of a task-oriented method, the coordina-

tor first allocates communication tasks for minimizing theaverage latency for downloading map images and then al-locates computational tasks for minimizing the average la-tency for calculating the optimal route. Then, the task-oriented method first solves the optimization problem of Eq.

24

0

0.2

0.4

0.6

0.8

1

5 10 15 20

Fair

ness

inde

x�

Amount of communication resource of node i (Mbps)�

Service-oriented Upper bound Task-oriented

-1

0

1

2

3

4

5

5 10 15 20 Aver

age

redu

ced

serv

ice

late

ncy

(sec

)�



Figure 7: Average reduced service latency and fair-ness index as a function of communication resourceof node i. Nodes i and j share computational andcommunication resources. Parameters are as fol-lows: dij is 1 m; T 1 = 5 MByte; R1

i is variable; R1j is

10 Mbps; T 2 is 50 G floating-point operation; R2i is

12 G floating-point operation per second (FLOPS);R2

j is 27 G FLOPS.

(22) with l = 1 and determines ∆1ij . After that, it solves the

optimization problem of Eq. (22) with l = 2 and determines∆2

ij .

objective: max∆l

ij

Gli + Gl

j , (22)

subject to: Gli = T l

i /Rli − tl

i(∆lij),

Glj = T l

j/Rlj − tl

j(−∆lij),

T li ≥ ∆l

ij ≥ −T lj .

5.3 Numerical results

5.3.1 Basic performanceWe observe the average reduced service latency and a fair-

ness index. The fairness index is defined as

F (G) =(P

i∈N Gi)2

|N |P

i∈N G2i

, (23)

where G = {Gi : i ∈ N}. The fairness index becomes lowerthan 1/N only when ∆ti (i ∈ N) includes a negative value,which means the resource sharing works to the detriment ofsome nodes.

Figure 7 plots the average reduced service latency and fair-ness index as a function of the communication resource ofnode i in the two node case. As we can see in Figure 7, whennode i does not have enough communication resources, nodesdo not share any resources in the service-oriented method.This is because, as we can see from the result of the fairnessindex, when node i has few communication resources, node jincreases its service latency by providing both its computa-tional and communication resources to node i. When node ihas communication resources grater than 10 Mbps, the av-erage reduced service latency with resource sharing usingthe service-oriented method is almost the same as the upperbound and is larger than that of the task-oriented method.

Next, we consider a 3-node example,2 where nodes i, j,and k share their communication and computational resour-ces. Figure 8 plots the average reduced service latency and

2We easily extend two node case to three node case byconsidering following simple assumption: when node i re-ceives two tasks ∆l

ji and ∆lki, the latency of these tasks are

tlji = tl

ki = (∆lji + ∆l

ki)/Rmli .

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Fair

ness

inde

x�



0

1

2

3

4

5

5 10 15 20

Aver

age

redu

ced

serv

ice

late

ncy

(sec

) �



Figure 8: Average reduced service latency and fair-ness index as a function of communication resourceof node i. Three nodes share computational andcommunication resources. Parameters are as fol-lows: dij, djk and dik are 1 m; T 1 = 5 MByte; R1

i

is variable; R1j and R1

k are 10 Mbps; T 2 is 50 G

floating-point operation; R2i is 12 G FLOPS; R2

j is

27 G FLOPS; R2k is 4 G FLOPS;

0

0.5

1

0 5 10 15 20

Ene

rgy

effic

ienc

y �

Service-oriented

Upper bound

Task-oriented

Without sharing resources

Distance between node i and j (m)

Figure 9: Energy efficiency as a function of distancebetween nodes i and j. Two nodes share computa-tional and communication resources.

fairness index as a function of the communication resource ofnode i. In this case, the average reduced service latency withthe service-oriented method is almost the same as that ofthe upper bound and is larger than that of the task-orientedmethod. The fairness index of the service-oriented methodis always larger than that of other methods. This result sug-gests that, as discussed in Section 3.3, if the number of nodesincreases, the service-oriented method would reduce servicelatency more than the other methods without reducing thefairness index.

5.3.2 Energy consumptionNext, we discuss the effect of geographical distance. We

define the energy efficiency as

(P

i∈N t′i) · (P

i∈N E′i)

(P

i∈N ti) · (P

i∈N Ei), (24)

where Ei is the energy consumed for a service of node i whilesharing resources. ∆t′i and E′

i are the service latency andthe energy consumption for a service of node i without shar-ing resources, respectively. If the energy efficiency becomeslower than 1, nodes should not share their resources. Fig-ure 9 plots the energy efficiency as a function of distancebetween nodes i and j. We can see that the service-orientedmethod is more energy-efficient than the task-oriented one.However, when the distance becomes large, energy efficiencyof the service-oriented method drops lower than 1. Thismeans that, as we mentioned in Section 3.2, we should limitthe sharing of resources while considering geographical dis-tances.

25

6. CONCLUSIONIn this paper, we proposed an architecture and mathemat-

ical framework for heterogeneous resource sharing based onthe key idea of service-oriented utility functions. Since het-erogeneous resources are often measured/quantified in dis-parate scales/units (e.g. power, bandwidth, latency), wepresented a unified framework where all these quantitieswere equivalently mapped to ”time” resources. We formu-lated optimization problems for optimizing various metricsbased on such service-oriented utility functions and solvedthem via convex optimization approaches. Our numerical re-sults show that the service-oriented heterogeneous resourcesharing reduces service latencies effectively and achieves highenergy efficiency, making it attractive for use in the mobilecloud. While the numerical scenarios studied in the paperhave considered only the cases of 2 or 3 nodes, the approachoutlined here is extensible to larger sets of nodes. The prob-lems of scalability and distributing these algorithms as thenumber of nodes increase are of interest as topics of futurestudy.

AcknowledgementsThis work is supported in part by the National Instituteof Information and Communications Technology (NICT),Japan, under the new generation network R&D programfor innovative network virtualization platform and its appli-cation.

7. REFERENCES[1] “Mobile Cloud Computing Forum,”

http://www.mobilecloudcomputingforum.com/.

[2] Guan, L., Ke, X., Song, M., and Song, J., 2011, Asurvey of research on mobile cloud computing, Proc.of the 10th IEEE/ACIS International Conference onComputer and Information Science, pp. 387-392.

[3] Dinh, H.T., Lee, C., Niyato, D., and Wang, P., 2011,A survey of mobile cloud computing: architecture,applications, and approaches, WirelessCommunications and Mobile Computing.

[4] Bifulco, R. , Brunner, M., Canonico, R., Hasselmeyer,P., and Mir, F., 2012, Scalability of a mobile cloudmanagement system, Proc. of the first edition of theMCC workshop on Mobile cloud computing, p. 17.

[5] Bonomi, F., Milito, R., Zhu, J., and Addepalli, S.,2012, Fog computing and its role in the Internet ofthings, Proc. of the first edition of the MCC workshopon Mobile cloud computing, pp. 13-16.

[6] Reichl, P., Egger, S., Schatz, R., and D’Alconzo, A.,2010, The logarithmic nature of QoE and the role ofthe weber-fechner law in QoE assessment, Proc. ofIEEE International Conference on Communications,pp.1-5.

[7] Friis, H.T., 1946, A note on a simple transmissionformula, Proc. of the Institute of Radio Engineers.

[8] Kumar, K., 2010, Cloud Computing for Mobile Users:Can Offloading Computation Save Energy?,Computer, vol. 43, no. 4, pp. 51-56.

[9] Boyd, S., and Vandenberghe, L., 2004, ConvexOptimization,” Cambridge, U.K.: Cambridge Univ.Press, 2004.

[10] Lasdon, L.S., Waren, A.D., Jain, A., and Ratner, M.,1978, Design and Testing of a Generalized ReducedGradient Code for Nonlinear Programming, ACMTransactions on Mathematical Software, vol. 4, no. 1,pp. 34-50.

[11] Henning, J.L., 2000, SPEC CPU2000: measuring CPUperformance in the New Millennium, Computer, vol.33, no. 7, pp. 28-35.

[12] Mahesri, A. and Vardhan, V., 2005, PowerConsumption Breakdown on a Modern Laptop, Proc.of the 4th International Workshop on Power-AwareComputer Systems, vol. 3471, pp. 165-180.

[13] Balasubramanian, N., Balasubramanian, A., andVenkataramani, A., 2009, Energy consumption inmobile phones, Proc. of the 9th ACM SIGCOMMconference on Internet measurement conference, pp.280-293.

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