Advanced Wavelength Reservation Method Based on Deadline-Aware Scheduling for Lambda Grid Networks

2904 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 10, OCTOBER 2007

Advanced Wavelength Reservation MethodBased on Deadline-Aware Scheduling

for Lambda Grid NetworksHiroyuki Miyagi, Student Member, IEEE, Masahiro Hayashitani, Member, IEEE,

Daisuke Ishii, Student Member, IEEE, Yutaka Arakawa, Member, IEEE, and Naoaki Yamanaka, Fellow, IEEE

Abstract—A deadline-aware-scheduling scheme for the lambdagrid system is proposed to support a huge computer grid sys-tem based on an advanced photonic network technology. Theassignment of wavelengths to jobs in order to efficiently carryvarious services is critical in lambda grid networks. Such serviceshave different requirements such as the job-completion deadlines,and wavelength assignment must consider the job deadlines. Theconventional job scheduling approach assigns a lot of time slotsto a call within a short period in order to finish the job asquickly as possible. This raises the blocking probability of shortdeadline calls. Our proposal assigns wavelengths in the lambdagrid networks to meet quality-of-services guarantees. The pro-posed scheme assigns time slots to a call over time accordingto its deadline, which allows it to increase the system perfor-mance in handling short deadline calls, for example, loweringtheir blocking probability. Computer simulations show that theproposed scheme can reduce the blocking probability by a factorof 100 compared with the conventional scheme under the low loadcondition in which the ratio of long deadline calls is high. Theproposed scheduling scheme can realize more efficient lambdagrid networks.

Index Terms—Deadline scheduling, grid computing, lambdagrid, photonic network, wavelength assignment.

I. INTRODUCTION

W ITH THE growth of network technologies and high-performance computing, research on grid computing is

very popular [1]. Grid computing is the technique by which ahigh-performance virtual machine can be created by combiningPCs, data storage devices, various I/O devices, and so onvia networks; it provides the infrastructure that can realizehigh-processing capabilities. Using a high-performance virtualmachine made by grid computing makes it possible to executelarge-scale jobs. Such jobs include large-scale scientific andengineering calculations and the high-speed processing of largeamounts of data. To realize a grid-computing environment, the

Manuscript received November 7, 2006; revised June 26, 2007. This workwas supported in part by Japan Society for the Promotion of Science (JSPS)and in part by Keio University 21st century COE program on “Optical andElectronic Device for Access Network.”

H. Miyagi, D. Ishii, Y. Arakawa, and N. Yamanaka are with the YamanakaLaboratory, Department of Information and Computer Science, Keio Uni-versity, 3-14-1 Hiyoshi, Kohoku, Yokohama 223-8522, Japan (e-mail:[email protected]; [email protected]; [email protected]; [email protected]).

M. Hayashitani is with NEC Corporation, Tokyo 108-8001, Japan (e-mail:[email protected]).

Digital Object Identifier 10.1109/JLT.2007.904416

goals are to dynamically organize the many geographicallydispersed computing resources and then to run the processingcenters in parallel. Grid computing demands the transfer oflarge amounts of data such as resource information, input data,output data, and so on in a timely manner.

The lambda grid, which employs wavelength division mul-tiplexing (WDM) and optical paths, is an attractive candidate[2], [3]. The WDM offers large network capacity, so high-speed data transfer is possible. The optical paths guaranteenetwork availability for job-execution assurances, so data trans-fer is reliable. The grid environment requires that wavelengthinformation, such as bandwidth and the utilization of wave-lengths, be managed as resource information. A lambda gridsystem in which wavelengths are divided into time slots hasbeen proposed [4]–[6]. By managing wavelength information,we can know the network condition and can transfer dataaccordingly.

Advance reservation schemes were introduced to the gridsystems to guarantee resource availability at the time whenan application was executed [7]. Advanced multiple resourcereservation methods ensure that all resources are, simultane-ously, available when needed.

The availability of grid computing has triggered interestfrom a diverse group of users looking for services such asthe efficient utilization of IT resources and the sharing of dataresources. One public computing grid service allows the usersto book processing unit hours with a credit card through a Web-based portal [8]. This trend only reinforces the understandingthat computing grid service users have different performancerequirements. The fees charged to users are high if the job isto be completed in the shortest time and low otherwise. Manyusers are prepared to accept some delay in job completion,provided that the job is completed within a deadline, in returnfor a lower service fee. Different users will have differentjob priorities and different deadlines, so job scheduling thatsatisfies all job deadlines is essential [9]. Since it is necessaryto transfer all input data to job-execution nodes before jobexecution can commence, it is important to efficiently assignwavelengths in lambda grid networks. The conventional job-scheduling approach assigns a lot of time slots to a new call inorder to finish a job as fast as possible, regardless of its deadline.Hence, the probability of a short deadline call being assignedtime slots is low, which raises the blocking probability ofsuch calls.

0733-8724/$25.00 © 2007 IEEE

MIYAGI et al.: ADVANCED WAVELENGTH RESERVATION METHOD BASED ON DEADLINE-AWARE SCHEDULING 2905

Fig. 1. Lambda grid system based on grid computing through opticalWDM paths.

Our solution is a deadline-scheduling scheme for wavelengthassignment in the lambda grid networks that can meet quality-of-service guarantees. The proposed scheme assigns time slotsto a call over an extended period according to its deadline.This makes more time slots available for short deadline calls.If no short deadline calls are received, the time slots reservedfor them are wasted, so we also propose a tentative reservationscheme that minimizes this waste. Computer simulations showthat the proposed scheme can reduce the blocking probabilityby a factor of 100, compared to the conventional scheme underthe low load condition.

II. SYSTEM MODEL

Fig. 1 shows the basic model of a lambda grid system. Eachnode has a scheduler, which is called “master,” to manage thecomputing resources. The masters exchange information on aregular basis. This information includes the load, the computa-tional capacity, the amount of free space of data storage, andthe devices available. When a user has a job to execute, theuser submits it to the local master. The local master dividesthe job into several subjobs. It then schedules the subjobsand distributes them to the remote sites via optical links. Jobdistribution follows the policy of job scheduling. For example,if the policy is to complete the job as rapidly as possible, thesubjobs may be distributed to one or remote sites that have highcapacity. Each remote site receives the subjobs, executes them,and returns the results to the local site. The local site combinesthe results into a single result and returns the result to the user.

The requests for data transmission (hereafter, “calls”) aregenerated with job execution since the input data needed for jobexecution are geographically dispersed. The user specifies thejob’s deadline when accessing the local master. The computingnode sends a call to the local master that includes data size, jobdeadline, and destination of the job-execution node. The masterdecides the deadline of data transmission based on the job’sdeadline.

Since calls will be randomly generated, the ideal approach isto set up fixed optical paths among the sites. We assume that theoptical paths have already been set up among the sites and thateach optical path is divided into time slots that range from 100to 1000 ms; the latter value is needed because data sizes willbe large in the grid environment [4]. When the channel linkcapacity is 1 Gb/s, one time slot can transfer from 100 Mb to1 Gb of data. The local master assigns time slots to calls, andthe computing node transfers the data using the assigned timeslots. Time-slot scheduling is completed within one time slot,and the master assigns time slots after the present time slot.

III. COMPLEXITY OF WAVELENGTH ASSIGNMENT

Advanced reservation methods were introduced to the gridsystems to guarantee resource availability at the time whenan application was executed [7]. Advanced multiple resourcereservation methods ensure that all resources are available whenneeded by the application. The reservation of data transmissiontime slots is often needed to guarantee that job completionoccurs within the deadline. For data transmission, calls thatspecify, among other details, data size, start time, and deadlineare issued to reserve time slots. With the conventional advancedreservation method, a new request may make it necessary toreschedule the reserved times. Farooq et al. [10] stated that idealresource reservation scheduling with a consideration of datasize, start time, and deadline is an NP-hard problem. That is,it is not possible to design an algorithm that can always give theoptimal reservation schedule. One solution is to make locallyoptimal decisions.

Naiksatam and Figueira [11] proposed squeeze in stretchout (SISO), which is a heuristic algorithm for advanced reser-vations. Their objective was time-slot utilization close to theoptimal value. The idea is interesting; however, some incomingrequests are blocked if any of them overlap the existing reserva-tions. This is because SISO does not support flexibility in termsof the start time. The next section proposes a simple heuristicalgorithm that offers sophisticated reservation performance.The proposed method uses start-time elasticity to handle thejob deadlines well.

IV. PROPOSED SCHEME

A. Procedure

The conventional job scheduling approach selects the sitethat can complete job execution in the shortest time, includingdata-transfer time [9]. Therefore, it tends to assign as manytime slots as it can to a new call using many wavelengths [4].Hereafter, we call this approach the Greedy scheme (GS).The GS reserves as many time slots as needed for each callon the order of available vacant time slots. Fig. 2 shows theGS procedure when the data size of a call is four and thedeadline is t8. The shortest (longest) wavelength is λ0 (λ3).The numbers (A1, A2, . . .) in Fig. 2 show the order of the time-slot assignment in the GS. If the master can reserve vacanttime slots equaling the data size within the deadline, the masterassigns the time slots to the call. The computing node transfers


Fig. 2. Time-slot reservation in GS for call A, whose data size is four anddeadline time is t8.

Fig. 3. Searching order of vacant time slots in the deadline-first reservation ofthe proposed scheme.

Fig. 4. Searching order of vacant time slots in the Greedy tentativereservation.

data using these time slots. If the assignment fails, the call isblocked. Since the GS assigns time slots without consideringthe deadline, the short deadline calls tend to be blocked. Inresponse, we propose a scheme that reserves time slots for acall according to its deadline.

The proposed scheme is a combination of two ideas: Oneis the deadline-first reservation, and the other is the Greedytentative reservation. We use the deadline-first reservation tomake long-term reservations, and we use the Greedy tentativereservation to improve the utilization of time slots. We explainthese proposals in the following.

Fig. 3 shows the search order for vacant time slots in thedeadline-first reservation scheme. The master locates the vacanttime slots from the deadline time to the present time, startingwith the shortest wavelength. When the master discovers asmany vacant time slots as the data size, the master reservesthem. By searching time slots in this way, the probability thatthe master can assign time slots to short deadline calls is greatlyincreased. However, this also means that some frequenciesare not utilized. The deadline-first reservation emphasizes theuse of the shorter wavelengths, so the utilization efficiency of

Fig. 5. Example of time-slot reservation in the proposed scheme under call A(6, t8).

Fig. 6. Example of time-slot reservation in the proposed scheme undercalls A (4, t8) and B (4, t4).

longer wavelengths tends to be low. Our solution is to combinethe deadline-first and Greedy tentative reservations to improvethe utilization of current time slots at longer wavelengths.

The master reserves as many time slots as needed for thelatest new call using the deadline-first reservation. After suc-cessfully reserving the slots, it tentatively reserves additional


Fig. 7. Pseudocode of the proposed scheme.

slots using the Greedy tentative reservation on the order shownin Fig. 4, up to the number needed to complete the call. Ifno other call is received, the first call uses the slots assigned(deadline- and Greedy-based) starting from the shortest fre-quency and the earliest time (see Fig. 5). As tentative slotsare used, the equivalent number of reserved slots is released,starting from the most future time. If a new call is received inthe middle of this procedure, the master applies the deadline-first reservation in the same way, as shown in Fig. 6. Here,call A (4, t8) is accepted using wavelengths λ0 and λ1, and itis tentatively given reserved time slots by using the Greedy ten-tative reservation. Thus, the deadline-first reservation for call B(4, t4) is attempted on frequencies λ1, λ2, and λ3. As there areonly three vacant time slots, call B has an insufficient numberof slots. Thus, the master releases the tentatively reserved slots

for call A and reserves them for call B. In this case, the masterdoes not tentatively reserve additional slots using the Greedytentative reservation. At times t2 and t3, the master drops threetentative slots for call A. As shown in Fig. 6, calls A and B arecompleted after time slot t4.

Fig. 7 shows the pseudocode of the proposed scheme.Data_size and deadline are specific call data size and dead-line, respectively. Map table[number_of_wavelength][time] isused to manage the states of time slots. There are threetime-slot states: vacant, reserved, and tentatively reserved.Index[data_size] manages the time of each reserved time slot.From lines 4 to 12 of Algorithm 1, the master locates the vacanttime slots that meet the deadline. If the master can discoverthe requested number of vacant time slots, the master reservesthem and calls function GreedyTentativeReservation(). If the


TABLE IGENERATING CALLS

master discovers only an insufficient number of time slots,the master searches the other calls’ tentatively reserved timeslots. Algorithm 2 shows the procedure of Greedy tentativereservation. After the decision of reservation is made by thedeadline-first scheme, the master reserves the tentative slotsusing the Greedy tentative reservation.

B. Complexity of Proposal

In the proposed scheme, the data size and the deadline arespecified to reserve time slots in advance. Let us considerthat wnum is the number of wavelength, datamax is the max-imum number of time slots, and deadlinemax is the specifiedmaximum call deadline. For the deadline-first reservation, ittakes O(wnum × deadlinemax) to locate the vacant time slots.Furthermore, for the Greedy tentative reservation, it also takesO(wnum × datamax × deadlinemax) to find the preference oftime slots. The proposed scheme can calculate in finite time.

V. PERFORMANCE EVALUATION

This section uses computer simulations to compare theblocking probability of the proposed scheme with that of theGS. In addition, we compare the state of calls generated at eachtime slot for the GS and the proposed scheme. We focus ona specific site and assume that the optical paths have alreadybeen set up. Each optical path has four wavelengths. Calls aregenerated according to the ON/OFF model. Calls are generatedonly in the ON state. The ON/OFF periods follow a geometricdistribution. Calls are equally split between long deadline callsand short deadline calls. The long deadline calls are classifiedas either type 1 or 2; their ratios are 0.45 and 0.05, respectively.The data size and the deadline of each call are uniformly set inthe range shown in Table I. As the first step of our research,a performance evaluation was conducted under a geometrictraffic distribution. However, considering real traffic, the heavy-tailed traffic model is very realistic. The effectiveness of theproposed method may be almost the same for both models.Confirming this is an important task.

Fig. 8 shows the blocking probability of the GS and theproposed scheme. In Fig. 8, deadline-first means the proposedscheme without the Greedy tentative reservation. We defineload ρ as the generation probability of calls in one time slot. Theproposed scheme reduces the blocking probability compared tothe GS. This is because the GS raises the blocking probabilityof short deadline calls. Moreover, the proposed scheme reducesthe blocking probability compared to the deadline-first. This isbecause, in addition to the long-term reservation according tothe deadline, using Greedy tentative reservation can improvethe utilization of time slots.

Fig. 8. Blocking probabilities of GS and the proposed scheme versus the load.

Fig. 9. State of calls generated at each time slot for GS, and the proposedscheme under traffic load ρ is 0.2. Traffic overloading occurs when callscannot be assigned with the number of time slots requested within the deadlinespecified, and the value is the sum of data sizes of blocked calls.

Fig. 9 shows the state of calls generated at each time slotfor the GS and the proposed scheme; traffic overloading occurswhen calls cannot be assigned with the number of time slotsrequested within the deadline specified, and the value is thesum of data sizes of blocked calls. The results show that the GSallows the frequent occurrence of overloading. This is becausethe GS does not consider the deadline, and the probability thatthe GS cannot accept short deadline calls is high. Deadline-first handles heavy traffic demands better than the GS since itreserves time slots considering the call’s deadline. However,it fails to fully utilize the time-slot resources around timeslots 26–28, as shown in Fig. 9. This is because it does notuse the time slots efficiently. The proposed scheme preventstraffic overloading and offers the maximum capacity since theGreedy tentative reservation improves the utilization of time-slot resources. Therefore, the proposed scheme with tentativereservation can process a larger number of short deadline callsthan the GS.

Fig. 10 shows the blocking probability of the GS and theproposed scheme versus parameter α, which is the generation


Fig. 10. Blocking probability versus ratio of long deadline calls α. α isdefined as α = traffic load of long deadline calls/ρ, and the load ρ is 0.3and 0.5.

TABLE IIGENERATING CALLS

ratio of long deadline calls to all calls. α is defined as

α =traffic load of long deadline calls

ρ.

We examined the ρ values of 0.3 and 0.5. The data size andthe deadline of both the short and long deadline calls are shownin Table II. The blocking probability of the GS is almost con-stant, regardless of α. This is because the blocking probabilitydoes not depend on the deadline since the GS reserves time slotswithout considering the deadline. Under the condition that therate of long deadline calls is 1.0 and load ρ is 0.3, however, theGS has lower blocking probability. This is because there are noshort deadline calls in this condition. When there are only longdeadline calls, the blocking probability improves. Note that theblocking probability of the proposed scheme is always betterthan that of the GS. This superiority strengthens as α increases.This is because deadlines become more critical as α increases,and the proposed scheme reserves time slots considering thedeadlines. Therefore, the proposed scheme is better than the GSunder the situation in which both the short and long deadlinecalls exist. The proposed scheme is particularly effective underlarge α.

As described in Section III, the optimal solution can beidentified only under homogeneous data size and deadline con-dition. Fig. 11 shows the blocking probabilities of the optimalsolution and the proposed scheme. Data size and deadlinesof all calls are set to 4 and 20, respectively. Load ρ is 0.3.As shown in Fig. 11, their blocking probabilities are almostthe same.

Fig. 11. Blocking probability of the optimal solution and the proposal. Allcalls have the same data size and deadlines.

VI. CONCLUSION

A wavelength assignment scheme that combines thedeadline-first reservation and the Greedy tentative reservationhas been proposed. The scheme can reduce the blocking prob-ability achieved by the conventional method by a factor of100. The deadline-first reservation selects time slots by fillingthe time slots on the shortest frequency up to the request’sdeadline. This approach tends to waste the resources of thelonger wavelengths. The Greedy tentative reservation improvesthe utilization of time slots, regardless of the wavelength.Computer simulations showed that the proposed scheme canreduce the blocking probability by a factor of 100 comparedwith the conventional scheme under the low load condition.

REFERENCES

[1] I. Foster and C. Kesselman, The Grid: Blueprint for a New ComputingInfrastructure. San Mateo, CA: Morgan Kaufmann, Nov. 1998.

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[3] S. Figueira, S. Naiksatam, H. Cohen, D. Cutrell, P. Daspit, D. Gutierrez,D. B. Hoang, T. Lavian, J. Mambretti, S. Merrill, and F. Travostino,“DWDM-RAM: Enabling grid services with dynamic optical networks,”in Proc. IEEE CCGrid, Chicago, IL, Apr. 2004, pp. 707–714.

[4] H. Lee, M. Veeraraghavan, H. Li, and E. K. P. Chong, “Lambda schedul-ing algorithm for file transfers on high-speed optical circuits,” in Proc.IEEE CCGrid, Chicago, IL, Apr. 2004, pp. 617–624.

[5] A. Banerjee, W. Feng, B. Mukherjee, and D. Ghosal, “Routing andscheduling large file transfers over lambda grids,” in Proc. PFLDnet,Lyon, France, Feb. 2005.

[6] N. R. Kaushik and S. M. Figueira, “A dynamically adaptive hybrid al-gorithm for scheduling lightpaths in lambda-grids,” in Proc. IEEE/ACMCCGRID/GAN, Cardiff, U.K., May 2005, pp. 418–425.

[7] I. Foster, C. Kesselman, C. Lee, R. Lindell, K. Nahrstedt, and A. Roy,“A distributed resource management architecture that supports advancereservations and co-allocation,” in Proc. IEEE IWQoS, London, U.K.,May/Jun. 1999, pp. 27–36.

[8] Network World. [Online]. Available: http://www.networkworld.com/news/2006/031506-sun-grid.html

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[10] U. Farooq, S. Majumdar, and E. W. Parsons, “Dynamic scheduling oflightpaths in lambda grids,” in Proc. IEEE Broadband Netw., Oct. 2005,vol. 2, pp. 1463–1472.

[11] S. Naiksatam and S. Figueira, “Elastic reservations for efficient band-width utilization in LambdaGrids,” in Future Gener. Comput. Syst.—Int.J. Grid Computing: Theory, Methods Applications, vol. 23, Jan. 2007,pp. 1–22.

Hiroyuki Miyagi (S’07) received the B.E. degreefrom Keio University, Yokohama, Japan, in 2006. Heis currently working toward the M.S. degree with theYamanaka Laboratory, Department of Informationand Computer Science, Keio University.

Since 2005, he has been researching the lambdagrid system.

Mr. Miyagi is a student member of the Institute ofElectronics, Information, and Communication Engi-neers of Japan.

Masahiro Hayashitani (S’05–M’07) was born inKanazawa, Japan, in 1981. He received the B.E. andM.E. degrees in information and computer sciencefrom Keio University, Tokyo, Japan, in 2005 and2007, respectively.

He is engaged in research on photonic networks.He is currently with NEC Corporation, Tokyo, wherehe is engaged in research on photonic networks.

Mr. Hayashitani is a member of the Institute ofElectronics, Information, and Communication Engi-neers of Japan.

Daisuke Ishii (S’03) was born in Tokyo, Japan, in1980. He received the B.E. and M.E. degrees in infor-mation and computer science from Keio University,Yokohama, Japan, in 2003 and 2005, respectively. Heis currently working toward the Ph.D. degree withYamanaka Laboratory, Department of Informationand Computer Science, Keio University.

In 2003, he has researched traffic engineering inoptical burst switching. Currently, he is researchingthe distributed autonomous protocol in an opticalnetwork, particularly in generalized multiprotocol-

label-switching networks.Mr. Ishii is a student member of the Optical Society of America of the USA

and the Institute of Electronics, Information, and Communication Engineers ofJapan.

Yutaka Arakawa (S’01–M’06) received the B.E.,M.E., and Ph.D. degrees from Keio University,Yokohama, Japan, in 2001, 2003, and 2006,respectively.

Since 2001, he has been researching optical net-work architecture and traffic engineering, particu-larly in optical burst switching. From 2004 to 2006,he was the Research Assistant with the Keio Univer-sity COE Program “Optical and Electronic Deviceon Access Network” of the Ministry of Education,Culture, Sports, Science, and Technology, Japan.

He is currently an Assistant with the Yamanaka Laboratory, Department ofInformation and Computer Science, Keio University.

Dr. Arakawa is a member of the Institute of Electronics, Information, andCommunication Engineers of Japan and the Information Processing Society ofJapan.

Naoaki Yamanaka (M’85–SM’96–F’00) receivedthe B.E., M.E., and Ph.D. degrees in engineeringfrom Keio University, Yokohama, Japan, in 1981,1983, and 1991, respectively.

In 1983, he was with Nippon Telegraph andTelephone Corporation’s (NTT’s) CommunicationSwitching Laboratories, Tokyo, Japan, where he wasengaged in research and development of the high-speed switching system and technologies for Broad-band ISDN services. Since 1994, he has been activein the development of ATM-based backbone net-

works and systems, including Tb/s electrical/optical backbone switching asNTT’s Distinguished Technical Member. He is currently researching futureoptical IP networks and optical multiprotocol-label-switching router systems.He is currently a Professor with the Yamanaka Laboratory, Department ofInformation and Computer Science, Keio University, and a Representative ofthe Photonic Internet Laboratory. He has published over 126 peer-reviewedjournal and transaction articles, has written 107 international conference papers,and has been awarded 182 patents, including 21 international patents.

Dr. Yamanaka is a Technical Editor of IEEE Communication Magazine, aBroadband Network Area Editor of IEEE Communication Surveys, and wasan Editor of the IEICE Transactions as well as the Vice Director of the AsiaPacific Board of the IEEE Communications Society. He received the Best ofConference Awards from the 40th, 44th, and 48th IEEE Electronic Compo-nents and Technology Conference in 1990, 1994, and 1998, respectively, theTELECOM System Technology Prize from the Telecommunications Advance-ment Foundation in 1994, the IEEE CPMT Transactions Part B: Best Transac-tions Paper Award in 1996, and the IEICE Transaction Paper Award in 1999.

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Advanced Wavelength Reservation Method Based on Deadline-Aware Scheduling for Lambda Grid Networks