MPC-basedManagement of Computing and Wavelength Resourcesin Optical Grid Networks

GENKI MATSUI, KIMINAO KOGISO, TAKUJI TACHIBANA, KENJI SUGIMOTONara Institute of Science and TechnologyGraduate School of Information Science

8916-5 Takayama, Ikoma, Nara 630-0192JAPAN

{genki-m, kogiso, takuji-t, kenji}@is.naist.jp

Abstract: In this paper, we propose a dynamic management method with model predictive control (MPC) sothat the number of transmitted tasks can be decided based on dynamics of lightpath establish/release process.The proposed method utilize the number of lightpaths that has been established as the dynamics for deriving thenumber of tasks. This derivation is performed by solving the quadratic programming (QP). By using this method, itis expected that both the computing and network resources can be utilized effectively. We evaluate the performanceof the proposed method with Matlab and compare its performance with the performance of PID-based method. Innumerical examples, we investigate how computing and network resources can be utilized more effectively byusing our proposed method. In addition, we investigate the computation time of our proposed method and thePID-based method.

Key–Words:optical grid, resource management, model predictive control, quadratic programming, computingresources, wavelength resources

1 IntroductionIn Grid computing, a massive amount of data can beprocessed by using geographically dispersed comput-ing resources. Currently, the grid computing has beenutilized in scientific, engineering, and business appli-cations. Here, the recent large-scale scientific applica-tions require more expensive and powerful computingresources such as super computers, experimental fa-cilities, and massive storage systems. On the otherhand, in the existing grid computing, computer re-sources are connected via Internet and the high-speedand large-bandwidth connections cannot be provided.As a result, it is hard to process the recent scientificapplication by using the existing grid computing.

Recently, optical grid has been proposed and im-plemented in some projects [1], [2], [3]. In opticalgrid, end-to-end connections called lightpaths are es-tablished from a source node to a destination one (SeeFig. 1). A massive amount of data can be transmit-ted with the established lightpaths. Therefore, opticalgrid is expected to be utilized for processing the recentscientific applications.

Here, computing resources are shared by multiplegrid clients in optical grid networks, as is the case withthe conventional grid computing. In addition, wave-length resources (network resources) are also sharedby multiple clients. Therefore, in optical grid net-

works, both computing resource and network resourcehave to be managed dynamically so that grid clientscan share those resources effectively.

In order to manage the computing and networkresources effectively, [4] has proposed a dynamic re-source management based on proportional integralderivative (PID) control. In this method, the num-ber of tasks that are transmitted to resource site withPID control so as to utilize computing resource ef-fectively. Moreover, lightpaths are established or re-leased dynamically based on the output signal of PIDcontrol so that network resource can be utilized effec-tively. Here, in general, it takes some time to establishor release a lightpath. Therefore, frequent lightpathestablishment and release degrades the performanceof resource management. However, in the PID-basedmethod, dynamics of lightpath establishment and re-lease can not been considered. In this paper, we pro-pose a new dynamic management method with modelpredictive control (MPC) [5] so that the number oftransmitted tasks can be decided based on a dynamicsof lightpath establish/release process. The proposedmethod utilize the number of lightpaths that has beenestablished as the dynamics for deriving the numberof tasks. This derivation is performed by solving thequadratic programming (QP). By using this method,it is expected that both the computing and network re-

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Job

Gatekeeper

Job manager

Lightpath

establishment

Resource site

Resource managerClient

Results

Figure1: Computing Resource Management.

sources can be utilized effectively.We evaluate the performance of the proposed

method with Matlab and compare its performancewith the performance of PID-based method. In nu-merical examples, we investigate how computing andnetwork resources can be utilized more effectively byusing our proposed method.

The rest of the paper is organized as follows. Sec-tion 2 shows how computing and network resourcesare managed in optical grid and introduces some re-lated works. In Section 3, we explain our proposedmethod with QP-based MPC for dynamic resourcemanagement method. Numerical examples are shownin Section 4 and finally, conclusion are presented inSection 5.

2 Resource Management in OpticalGrid

2.1 Management Policy

Figure 1 shows how a grid job is executed and howcomputing resources are managed in optical grid net-works. Here, in this paper, we consider the executionof a grid job which consists of numerous indepen-dent tasks such as parameter search application [6].As shown in this figure, once a client generates a job,which consists of independent tasks, the generated jobis send to a computing site via lightpath and executed.

Here, computing resources are shared by multi-ple clients, and hence the number of available com-puting resources changes over time [7]. Neverthe-less, each job should be stably executed without in-terruption by sharing computing resources effectively.It is also preferable to complete the job execution asquickly as possible. To this end, the resource manageris required to store a constant number of tasks in itsown buffer at all times [8].

Then, in optical grid networks, the tasks are trans-mitted from the job manager to the resource managerwith lightpaths. Here, the number of installed wave-

lengths is limited. In addition, in optical grid, wave-length resources (network resources) are shared bymultiple clients. Therefore, lightpaths should be es-tablished and released dynamically depending on thenumber of transmitted tasks so that wavelengths arenot wasted.

2.2 Related Work

In terms of the computing resource management inconventional grid, [8] has proposed a dynamic man-agement method so that a resource manager can storea constant number of tasks in its own buffer. In thismethod, feedback information about the number oftasks in the buffer is returned from the resource man-ager to the job manager. Then, based on the feedbackinformation, the job manager adjusts the number oftransmitted tasks dynamically with proportional inte-gral (PI) control. By simulation using a Matlab andSimgrid that is a discrete time simulator for the Grid,it has shown that grid jobs are executed more stablethan a conventional method, and the job execution cancomplete more quickly.

On the other hand, in terms of the wavelength re-source management, many dynamic lightpath estab-lishment methods have been proposed in the litera-ture. These methods often utilize generalized multi-protocol label switching (GMPLS) [9]. With theseGMPLS-based methods, lightpaths can be establishedand released dynamically on demand, and wavelengthresources can be shared by many users effectively.These methods can manage computing resources orwavelength resources effectively in optical grid net-works. Meanwhile, in optical grid networks, it is ex-pected that both computing and network resources areshared by multiple clients effectively. Nevertheless,the existing methods can not manage both computingand wavelength resources at the same time.

Moreover, in this paper, we utilize MPC in orderto manage computer and network resources. Here,MPC determines the current control action by solv-ing online and it is utilized in order to control severaltypes of applications [10], [11]. On the other hand,the optimal control problem in MPC has been morecomplex and larger recently. Therefore, QP is widelyused to derive such a optimal control problem due toits short computation time.

In [10] this paper has utilized MPC for trafficcoordination in railway systems, and has shown thatproposed control with MPC would be able to recoverfrom delays in an optimal way while breaking con-nections and letting some trains run faster than theplanned speed profile.

In [11], this paper has proposed a neural networkMPC of TCP flows and show the superior, transient,

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Job

Job managerResource manager

Lightpath

Buffer

1 step delay

Figure2: Configuration of optical grid.

steady state behavior and the general stability of MPCover the PI controller as it is applied to optimize thelength of a TCP queuing window in a bottleneckedAQM link.

In this paper, we utilize QP with MPC for deriv-ing the number of transmitted tasks quickly.

3 Proposed Dynamic Resource Man-agement

As described in the previous section, in optical gridnetworks, both computer resources and wavelengthresources have to be dynamically managed at the sametime. To this end, we propose a dynamic resourcemanagement method where MPC is utilized.

Figure 2 shows a configuration of the optical grid,where a job manager transmits tasks to a resourcemanager with lightpaths. The proposed method is im-plemented in a job manager, and the job manager con-sists of a controller, a task transmission controller, anda lightpath controller. Once a client generates a job, ajob manager is generated. The job manager selectsa computing site where the job is executed and thenit manages the job as shown in the following subsec-tions.

3.1 Buffer in Resource Manager

At first, the job manager receives feedback informa-tion from the resource manager in terms of the num-ber of tasks in its buffer (the initial value is zero). Letxb(t) ∈ ℜ denote the number of tasks which are storedin the resource manager’s buffer at timet. Here,xb isgiven by

xb(t+ 1) = xb(t)− Tw(t) + T u(t− 1), (1)

wherew ∈ ℜ (w ≥ 0) is the number of tasks that areprocessed on the computing site andu ∈ ℜ (u ≥ 0) isthe number of tasks that are transmitted from the job

Lightpath

controller

Delay

Job manager

transmission constraint

No delay

Controller

Task

Buffer (Plant)

Figure3: Block diagram.

manager to the buffer. Note thatt ∈ Z+ denotes step(Z+ is the set of positive integers) and thatT > 0 issampling period. Then,xb ≥ 0 is finite and can beobserved,u(−1) = 0．

In this paper, we assume that the resource man-ager returns the information aboutxb(t) to the jobmanager (see Step 1 in the previous subsection). Justafter the job manager receives the feedback informa-tion, the job manager transmits the tasks so thatxb(t)is kept close to a reference valuer. Here, we assumethat the transmission delay of tasks from the job man-ager to the resource manager is constant, equal to 1step. This is because lightpaths are used only for thetransmission of tasks. On the other hand, we assumethat the transmission delay of feedback information iszero due to the simplicity.

3.2 Determination of number of transmittedtasks with QP-based MPC Controller

Next, the controller determines the number of tasksthat will be transmitted to the resource manageru(t)so thatxb is kept close to reference valuer. In our pro-posed method, the number of transmitted tasks are de-termined by using QP-based MPC. Here, Fig. 3 showsa block diagram of our proposed method. In Fig. 3,our proposed QP-based MPC is used in the controllerof the job manager.

Now, we define the bandwidth of a lightpath asβ,the number of established lightpaths that are availableat time t asn(t). In this case, the maximum num-ber c(t) of tasks that can be transmitted is given byc(t) = n(t)β. As a result, the job manager can trans-mit at mostc(t) tasks. Therefore, the number of trans-mitted tasks are constrained byc(t). Note thatc(t) isa dynamic constraint condition of this system, and itchanges depending on the establishment and releaseof lightpaths.

From the above, a control problem foru(t) can be

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Figure 4: Dynamic lightpath establishment and re-lease algorithm.

formulated as the following QP optimization problem:

min{ut+k}k∈N

J(ut, x(t)) = min{ut+k}k∈N

∑k∈N

∥∥yt+k|t − r∥∥Qk,2

,

s.t. xt+k+1|t = Axt+k|t +B1ut+k +B2wt+k|t,

yt+k|t = Cxt+k|t,

0 ≤ ut+j ≤ c(t), ∀k ∈ N ,

A =

[1 10 0

], B1 =

[0T

], B2 =

[−T0

], C = [1 0].

where N is prediction horizon, andN ={0, 1, · · · , N − 1}.

By solving the above QP problem, the optimal se-quence{u∗t+k}k∈N is derived. Finally, the optimalnumber of transmitted tasksu(t) = u∗t is determined.

3.3 Lightpath Controller

Then, the lightpath controller performs our proposeddynamic lightpath establishment and release pro-cesses. Figure 4 shows how a lightpath is establishedor released by the lightpath controller. As shown inthis figure, the lightpath controller compares the num-beru(t) of tasks in the buffer with the maximum num-berc(t) of tasks that can be transmitted.

Onceu(t) = c(t) is satisfied at timet, the light-path controller starts to establish a new lightpath.

Table 1: Maximum and average value ofw.Time t[s] 0∼10 10∼20 20∼30 30∼40 40∼50 50∼60γ [Gbit/s] 0.30 0.40 1.0 0.7 0.85 0.6

E[w] [Gbit/s] 0.15 0.20 0.50 0.35 0.425 0.30

Table 2: Maximum and average value ofw with A.Time t[s] 0∼10 10∼20 20∼30 30∼40 40∼50 50∼60γ [Gbit/s] A 2A 3A 4A 5A 6A

E[w] [Gbit/s] 0.5A A 1.5A 2A 2.5A 3A

Here,Ts ∈ Z+ denotes the lightpath establishmenttime andks(t) denotes a counter. Ifks(t) becomesequal toTs, the lightpath establishment process iscompleted and a new lightpath is established. Here,we assume thatTs is a constant.

On the other hand, in terms of the lightpath re-lease,Tr ∈ Z+ denotes the threshold for lightpathrelease. Moreover,ds(t) = 1 means that a lightpathhas been established at timet. If u(t) ≤ c(t) − β issatisfied andds(t) = 0, counterkr(t) increase by one.Whenkr(t) becomes equal toTr, an established light-path is released. However ifkr(t) < Tr and lightpathestablishment process starts,ds(t) becomes one andkr(t) becomes zero. This denotes that the lightpathestablishment has a higher priority over the lightpathrelease process. WhenTr is set to be small (large), alightpath is (not) released frequently.

Therefore bandwidthc(t) is determined accord-ing to the following process

c(t+ Ts) = c(t) + β, if u(t) = c(t), (2)

c(t+ Tr) = c(t)− β, (3)

if u(t+ i) < c(t+ i)− β,

∀i ∈ {0, · · · , Tr − 1}.

In this algorithm, lightpaths are established and re-leased dynamically by comparing output signalu(t)of controller with the maximum numberc(t) of trans-mitted tasks. Therefore, it is expected that computingresources and network resources are effectively man-aged simultaneously.

4 Numerical Examples

In this section, we evaluate the performance of theproposed method by using Matlab. In the following,unit timeT is set to 0.01 s, and simulation time is 60 s.The buffer size in the resource manager is 3.0 Gbits,and the reference valuer of the number of tasks in thebuffer is 1.5 Gbits. The initial value of the number

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0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

3

Time [sec]

rand

xb(t

)

xbr

(a) r andxb.

0 10 20 30 40 50 600

20

40

60

80

100

120

Time [sec]

u(t

)and

c(t

)

u(t)c(t)

(b) c andu.

Figure5: Time response.

xb(0) of tasks in the buffer is set to 0.4 Gbits, and theinitial valuec(0) of constraint is set to 10 Gbps.

Moreover, bandwidthβ of a wavelength is setto 10 Gbps, and the maximum number of availablewavelengths is 12. The initial valuen(0) of the num-ber of established lightpath is set to one. The lightpathestablishment timeTs is set to 50 ms and control pa-rameterTr for lightpath release is set to 50 ms. Interms of the computing resources, the numberw(t)of tasks that are processed on a computing site is dis-tributed uniformly on [0,γ(t)] Gbits. γ(t) changesover timet according to Table 1.

Here, the controller does not have the completeinformation aboutw(t). Therefore we assume that thecontroller has the information about the time averageE[w] of w(t). As a result,w(t) in equation (1) is re-placed byE[w].

4.1 Time response ofxb and c

Figures. 5(a) and (b) show time responses ofxb(t)andc(t), respectively, when QP-based MPC methodis used. From Fig. 5(a), we can find that our pro-posed method tries to makexb close tor. In Fig.5(b), the value of constraintc is dynamically increasedand decreased by processing of lightpath establish-ment and release. In addition, we can find that thenumber of transmitted tasks is determined to satisfythe value of constraintc. From these figures, we canfind that our proposed method determine appropriatenumber of tasks that transmitted and establish and re-lease lightpath depending on the numberw(t) of tasksthat are processed.

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.05

0.1

0.15

0.2

0.25

0.3

A [Gbits]

Ave

rage

dev

iation

ofx

b

PIDQP

(a)Average deviation ofxb.

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

1

2

3

4

5

6

7

8

A [Gb its]

Aver

age

num

ber

of

lightp

ath

s

PID

QP

(b) Average number of lightpaths.

Figure 6: Performance comparison againstγ.

4.2 Performance comparison againstγ

In this subsection, we compare the performance of theproposed method with that of PID method. Here,γchanges over timet according to Table 2. AsA be-comes large, the number of tasks that can be processedincreases.

Fig. 6(a) and (b) show the average of the devi-ation of xb againstr and the average number of thelightpath, respectively. From Fig. 6(a), we can findthe average of the deviation of the proposed methodis smaller than that of PID method regardless ofA.In addition, in Fig. 6(b), the average number of light-paths is smaller than that of PID method regardless ofA. Therefore, our proposed method with QP-basedMPC is more effective than the PID method.

4.3 Performance comparison againstTr

Then, we also compare the performance of the pro-posed method with that of PID method. Here, thresh-old of the lightpath releaseTr changes from 0.01 s to0.1 s.

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Fig.7(a) and (b) show the average of the deviationof xb againstr and the average number of lightpaths,respectively. From Fig. 7(a), it is clear that the aver-age of the deviation of the proposed method is smallerthan that of PID method regardless ofTr. In addi-tion, in Fig. 7(b), the average number of lightpaths issmaller than that of PID method. Therefore, it is clearthat our proposed method is more effective than PIDmethod.

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tr [s]

Ave

rage

dev

iation

ofx

b

PIDQP

(a)Average deviation ofxb.

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

7

Tr [s]

Aver

age

num

ber

of

lightp

aths

PID

QP

(b) Average number of lightpaths.

Figure 7: Performance comparison againstTr.

5 Conclusion

In this paper, we proposed the dynamic resource man-agement method with QP-based MPC which is imple-mented in a job manager. In the proposed method,QP-based MPC is utilized in order to manage bothcomputing resources and network resources. We eval-uated the performance of our proposed method withsimulation. From the numerical examples, we foundthat the proposed method can manage computing re-source effectively by using a smaller number of light-paths than the conventional PID method.

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