April 2009, 16(2): 108–113 www.sciencedirect.com/science/journal/10058885 www.buptjournal.cn/xben

The Journal of China Universities of Posts and Telecommunications

Relaxed resource advance reservation policy in grid computing XIAO Peng ( ), HU Zhi-gang

School of Information Science and Engineering, Central South University, Changsha 410083, China

Abstract

The advance reservation technique has been widely applied in many grid systems to provide end-to-end quality of service (QoS). However, it will result in low resource utilization rate and high rejection rate when the reservation rate is high. To mitigate these negative effects brought about by advance reservation, a relaxed advance reservation policy is proposed, which allows acceptingnew reservation requests that overlap the existing reservations under certain conditions. Both the benefits and the risks of theproposed policy are presented theoretically. The experimental results show that the policy can achieve a higher resource utilization rate and lower rejection rate compared to the conventional reservation policy and backfilling technique. In addition, the policy shows better adaptation when the grid systems are in the presence of a high reservation rate.

Keywords grid computing, advance reservation, reservation violation, computing economy

1 Introduction

Advance reservation as an effective technique to support co-allocation and end-to-end QoS has been incorporated into many grid systems [1]. It allows applications to gain concurrent access to adequate resources, and guarantees the availability of resources at the required time [2].

However, advance reservation have many negative effects on resource sharing and task scheduling in the grid systems. For instance, studies in Refs. [3–9] show that the fixed- capability reservation results in a low resource utilization rate, and excessive reservation often leads to a high rejection rate. These negative effects inevitably influence the grid economy [10], where resource providers wish to increase the utilization rate of their resources to obtain maximal profits. Hence, how to mitigate the negative effects brought about by the advance reservation becomes an important issue to be addressed.

Conventionally, advance reservation is defined as a process of requesting resources for use at a specific time in the future [11]. The two key attributes of a reservation request are starting time and deadline. As the availability and performance of resources are unpredictable in large scale grid systems, precisely estimating these two parameters is difficult if not impossible. Consequently, applications tend to overestimate

Received date: 18-04-2008 Corresponding author: XIAO Peng, E-mail: xpeng4623@yahoo.com.cn DOI: 10.1016/S1005-8885(08)60213-7

these two parameters (especially the deadline) to ensure their successful execution [3]. This behavior results in a high rejection rate and a low resource utilization rate.

Motivated by these facts, the authors propose a relaxed advance reservation policy (RARP), which allows reservations to overlap each other under certain conditions. The objective of RARP is to increase the resource utilization rate and reduce the rejection rate when using advance reservation in grid environments.

The remainder of this article is organized as follows: Sect. 2 presents the related study. In Sect. 3, the relaxed advance reservation policy is introduced. In Sect. 4, theoretical analysis of the proposed policy is presented. In Sect. 5, simulations are conducted to verify the performance of the proposed policy. Finally, Sect. 6 concludes the article with a brief discussion of future study.

2 Related work

In Ref. [4], Smith and Foster investigate the impacts of advance reservation on the performance in terms of mean waiting time (MWT), mean offset time (MOT), and request rejection rate (RRR). Their experimental results show that all the three metrics increase when the system is in the presence of a high reservation rate. Their conclusions are repeatedly confirmed in Refs. [5–9].

Therefore, many techniques have been proposed to overcome the limitations of advance reservation. In Ref. [4],

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Foster et al. propose incorporating adaptive mechanism into advance reservation to provide a more flexible reservation policy. An extended globus architecture for reservation and allocation (GARA) [12] architecture is developed, in which the reservation mechanism is enhanced with an intelligent decision model and performance sensors. However, this adaptive reservation architecture is designed for high-end applications with high-bandwidth and dynamic flows, which means that it only adapts to bandwidth reservation for bulk-data transmission.

To increase the resource utilization rate, Backfilling [13] is widely used to improve the performance of reservation-based schedulers. In Ref. [5], a backfilling based gang scheduling mechanism is incorporated into the share-based coscheduling job (SCOJO) scheduler. The simulative results show that it can mitigate the negative effects of advance reservation for those applications with a high ratio of computation to communication. In Ref. [14], Sulistio et al. use several techniques, including rearranging subtask, interweaving task graphs, and backfilling, with reservation-based scheduling, to improve the resource utilization rate.

To solve the problem of high rejection rate, Kaushik [15] et al. propose a flexible reservation window scheme. By conducting extensive simulations, Kaushik concludes that when the size of the reservation window is equal to the average waiting time in the on-demand queue, the reservation rejection rate can be minimized close to zero. However, Kaushik does not address the issue of low resource utilization rate brought by advance reservation. In Ref. [16], Wu et al. study the bandwidth reservation for grid applications, and propose an adaptive mechanism for malleable bandwidth reservation, to reduce the rejection rate of advance reservation. Unfortunately, Wu’s study only adapts to the systems that support malleable reservation, and can only be used for bandwidth reservation.

3 Advance reservation model

The typical advance reservation model is described in Ref. [2], where resources are managed by a reservation manager (RM), which performs admission control and tracks all the reservations. All reservation requests are sent to the RM. Therefore, a reservation request can be characterized as

, ,i i it d c , where it is the reservation start time, id is the reservation deadline, ic is the resource demand of the reservation request.

On receiving a request, if a feasible time-slot is available, RM will respond to the request with a confirmative response. This suggests that a reservation contract has been successfully signed between the request and the RM; otherwise, it suggests

that the reservation request is rejected. Given a reservation contract, if the RM does not make the resource accessible for the request at time it , or fails to keep the resource accessible until time id , it indicates that a reservation violation occurs.

Given current time is 0t , a time slot table is shown in Fig. 1. The existing reservations are illustrated by rectangles with texture. Considering that a reservation request ir arrives, the RM finds that there is no available free slot that can strictly meet the requirements of ir . However, the RM notices that a free slot between 2r and 5r seems to be a good candidate, except that the starting time and the deadline of ir are slightly overlapping with the other existing reservations. As shown in Fig. 1, if the RM reserves this time slot to ir , then the start time of ir cannot be guaranteed because of 2r and

3r . Meanwhile, ir will interfere with the starting times of 5rand 6r .

Fig. 1 A time slot table in RARP

As mentioned earlier, reservation requests tend to overestimate the deadline to ensure their successful execution. If the actual deadlines of 2r and 3r are earlier than the starting time of ir , and the actual deadline of ir is earlier than the starting times of 5r and 6r , then, this time slot is actually feasible for ir .

The RARP takes such overestimation into account, and tries to accept some requests whose reservation requirements cannot be met in a conventional manner. Obviously, this strategy will take some risks of reservation violation. In the following sections, the authors’ studies mainly focus on analyzing the risks and benefits of this strategy and verifying its effectiveness through experiments.

4 RARP analysis

4.1 Problem definition

Given that the reservation request ir is denoted as , ,i i it d c , to meet the requirements of ir , the RM should

110 The Journal of China Universities of Posts and Telecommunications 2009

find a free slot that satisfies free iC c during the period [ , ]i it d , where freeC is the amount of free capacity at time it .It is obvious that there are two types of existing reservations that will block request ir . For convenient representation, the authors define them as two kinds of sets:

Definition 1 The starting time blocking set of ir consists of existing reservations whose deadlines overlap ir , denoted

as { | [1,2, , 1], }si j j i jS r j i t t d .

Definition 2 The deadline blocking set of ir consists of existing reservations whose starting time overlap ir , denoted

as { | [1,2, , 1], }di j j i jS r j i t d d .

Clearly, if s di iS S and free iC c , then request ir

can be guaranteed by the system. This is also the criterion of the conventional reservation mechanism. The RARP here follows a more relaxed policy, which tries to accept some reservation requests that do not obey the strict criterion of the conventional reservation mechanism. For example, as shown in Fig. 1, if the RM decides to accept ir , then the starting

time blocking set of ir is 2 3{ , }siS r r , and the deadline

blocking set is 5 6{ , }diS r r .

4.2 Policy analysis

Given there are 1i existing reservations before irarrives, to know the risk of accepting ir , the authors should figure out the probability of reservation violation if the RM accepts ir .

Let random event iE represent a condition where no

reservation violation occurs on ir , where random event siE

represents a condition where the reservations in siS do not

incur the violation of ir , and random event diE represents a

condition where ir does not incur any violation on all the

reservations in diS . The authors assume that all reservation

requests are independent, thus the probability of iE can be expressed as Pr{ } Pr{ }Pr{ }s d

i i iE E E (1) Let random variable TE ( [1,2, , ])j j i represent the

actual deadline of the reservation request jr . For each

reservation in siS , if its actual deadline is earlier than the

starting time of ir , this reservation will not actually block ir .

Furthermore, if there are a set of reservations in siS whose

actual deadlines are earlier than the starting time of ir , then there will be sufficient free resources for ir to guarantee its

starting time at time it . Therefore, the probability that siS

does not incur the violation of ir can be calculated as

1 freePr{ } Pr TE TE |n

si j i j i j i

j Jt t C c cE (2)

where the set 1 2{ , ,..., } sn iJ j j j S .

Clearly, the authors hope to get an optimal set *J that can maximize Pr{ }siE . Hence, the problem of obtaining *J can be expressed as a programming problem as follows:

*free

*

max Pr{ }s.t.

si

j ij J

si

C c c

J S

E

The approach to finding *J is very similar to the 0-1 knapsack algorithm, and the details of the algorithm can be seen in Ref. [17].

To obtain Pr{ }diE , the authors first sort all the

, , ( )dk k k k k ir t d c r S in ascending order of kt and store them in a ordered set

1 2{ , ,..., }

mk k kr r r . Then, the lk that

satisfies the following inequation should be found: 1

1 1

max

l lk k

j i jj k j kc C c c (3)

where maxC is the total capacity of resources. As long as the actual deadline of ir is earlier than

lkt , the

authors can ensure that ir will not incur any violation on all

the reservation in diS . Therefore, the following can be

obtained:Pr{ } Pr{TE }

l

di i ktE (4)

Without loss of generality, the service time of requests is assumed to follow Exponential distribution with rate , then its cumulative distribution function can be expressed as

( ) 1 e tF t . Thus, Eqs. (2) and (4) can be rewritten as follows,

*

( )Pr{ } 1 e i jt tsi

j J

E (5)

( )Pr{ } 1 e k ilt tdiE (6)

Summarizing the earlier analysis, the authors list the steps to calculate the probability that no violation occurs on ir if accepting it as follows. It is clear that the risk of accepting iris 1 Pr{ }iE .

Algorithm to calculate Pr{ }iEBeginGet sets s

iS and diS

Use 0-1 knapsack algorithm to find *J

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Calculate Pr{ }siE by Eq. (5)

Sort dk ir S in ascending order of kt

Find lk that satisfies 1

1 1

max

l lk k

j i jj k j kc C c c

Calculate Pr{ }diE by Eq. (6)

Return Pr{ }Pr{ }s di iE E

End

4.3 Benefit analysis of RARP

After identifying Pr{ }iE , the authors can also calculate the expected benefits of accepting ir . Given p is the resource price under a condition that no reservation violation occurs, q is the penalty price that RM should pay if reservation violation occurs. If ir is accepted, the expected benefits ib can be estimated as

( ) Pr{ } (1 Pr{ })i i iE b p qE E (7) In Fig. 2, the authors describe the relationship between

Pr{ }iE and ( )iE b .

Fig. 2 Relationship between Pr{ }iE and ( )iE b

As shown in Fig. 2, if Pr{ }i vE , then the expected benefit ( )iE b is positive with a maximal value p, which means that accepting ir may be profitable. Hence, the RM may simply use v as its threshold to decide whether it accepts ir or not. However, Pr{ }i vE only means that accepting

ir is risky instead of nonprofitable. Therefore, the RM may use a more suitable * *(0 1)v v as its criterion, to decide whether it accepts ir or not. A high value of *v indicates that the RM is conservative when using RARP; a low *vmeans that it is willing to take more risks to improve the utilization rate of its resources; when * 1v , RARP is the same as in the conventional reservation policy. Hence, RARP is compatible with the conventional reservation policy and more general than the latter.

In Fig. 2, the case where the RM chooses a lower penalty

price 1q is illustrated. Correspondingly, v changes into 1v ,and 1v v . This means that lower penalty price will result in lower risks. This is consistent with common sense.

5 Performance evaluation

In this section, the performance of RARP with the conventional reservation policy and backfilling technique is compared.

5.1 Experimental settings

The authors use GridSim [18], a distributed resource management and scheduling simulator to conduct simulations. A multicluster grid model is constructed, which consists of ten high-performance clusters.

In the simulations, the authors choose Lublin-Feitelson Model [19] derived from real workload logs to generate experimental workload (reservation requests). The workload consists of 10 000 requests and is characterized by arrival time, resource demands, and estimation of execution time. Because there is no starting time of reservation in this workload, the authors add to each request with a reservation starting time. The starting time is set by adding the arrival time with a random value that is uniformly distributed in [100 s,1 000 s] . To reflect the overestimation of the reservation deadline, the running time of each request is multiplied with a random factor, overk (more details on overkare discussed in Sect. 5.3).

5.2 Comparison of utilization rate and rejection rate

First, the authors compare the performance of RARP with conventional advance reservation policy and backfilling technique.

The basic workload consists of 10 000 requests, and it is modified into four different workloads, each with an advance reservation rate of 10%, 15%, 20%, and 25%, respectively. In this experiment, the authors set * 0.8v , which means that the RM will accept a reservation request only when the probability of reservation violation for this request is less than 20%. The factor overk is set to be uniformly distributed in the interval [1.2,1.5], which means the reservation requests tend to overestimate their relative deadline with a mean value of 35%. The experimental results are shown in Figs. 3 and 4.

As seen in Fig. 3, for the conventional reservation policy, with an increase in the reservation rate from 10% to 25%, the resource utilization rate drops dramatically from 56% to about 25%. It is because many requests have been blocked by the existing reservations. When applying the backfilling technique,

112 The Journal of China Universities of Posts and Telecommunications 2009

the utilization rates have been increased significantly by about 14%, when compared to the conventional reservation policy where the reservation rates are about 10% and 15%. At such a low level of reservation rate, the performance of RARP is not as good as it is in backfilling, but still better than in the conventional reservation policy. As the reservation rate increases to 20% and 25%, the RARP’s resource utilization rate becomes higher than in both conventional mechanism and backfilling.

Fig. 3 Resource utilization rate

Fig. 4 Reservation rejection rate

An interesting finding is that RARP’s utilization rate increases about 3% when the reservation rate increases from 15% to 20%. The reason is that there are more free slots that can be allocated by using RARP when the reservation requests increase. However, such an increase cannot be sustained when the reservation rate increases to 25%.

Reservation rejection rate is shown in Fig. 4. Similar to the resource utilization rate, when using the conventional reservation policy, the rejection rate increases sharply from about 7% to 34% as the reservation rate increases from 10% to 25%. Also, the authors notice that backfilling cannot lower down the rejection rate. On the contrary, it leads to a slightly higher rejection rate when compared to the conventional

policy. This is because the workload used in the simulations is very long (10 000 requests), and the RM only deals with a small part of the reservation requests each time. Thus, some nonreservation requests are backfilled into a lot of free slots, which probably may be allocated to other reservation requests later, if using RARP. That is why the backfilling technique leads to a higher rejection rate. When RARP is used, the rejection rate is only about 50% of the conventional reservation policy in all cases.

Based on the above experimental results, the authors draw the following conclusions:

1) Backfilling is effective to improve resource utilization rate when the reservation rate is below 15%.

2) When the system faces high reservation rate (>15%), RARP is more effective than backfilling.

3) RARP can reduce rejection rate as long as the grid applications overestimate their deadlines.

5.3 Effects of *v and overk on RARP

As is mentioned earlier, the authors multiply the deadline of each reservation with a factor over over( 1)k k to reflect the overestimation of the deadline. In this experiment, they have conducted extensive simulations with different levels of overk .More specifically, they have set overk uniformly distributed at different intervals, such as, [1.0,1.2], [1.2,1.5], and [1.5,1.8], respectively. They denote them as 1 2 3, , k k k for the sake of simplifying the representation. When overk is set at level 1k ,it means that the requests in the workload tend to overestimate their deadlines with a mean value of 10%. Hence, 2k means 35% overestimation, and 3k means 65% overestimation.

Parameter *v is the threshold, by which RM decides whether a free time slot can be allocated to an overlapped reservation or not. Thus, *v is a strategic parameter of the RM. A higher value of *v indicates that the RM is conservative.

The results of simulations are shown in Fig. 5. It is clear that more overestimation of the deadline leads to lower reservation violation rate. This is because many overlapped reservations do not actually overlap with the run time, which makes RARP more effective.

In the simulations, the authors increase *v from 0.6 to 0.95, gradually. The results show that for 1k and 2k the violation rate drops rapidly when *v is increased from 0.6 to 0.8, and then the decline becomes stable. In all the tested cases, the authors find that the reservation violation rate can be limited below 10% when * 0.8v . If they set * 0.9v , the violation can be controlled below 5%.

Issue 2 XIAO Peng, et al. / Relaxed resource advance reservation policy in grid computing 113

Fig. 5 Effects of *v and overk on RARP (advance reservation rate = 15%)

The reservation violation is the price the authors have to pay when using RARP. The experimental results indicate that the violation rate can be limited to a relatively low level by adjusting parameter *v . Currently, many systems have a support reservation renegotiation mechanism, such as EASY [13], COSY [5], etc. Combining RARP and reservation renegotiation, the RM can take the advantages of RARP while avoiding the risk of reservation violation.

6 Conclusions

In this article, the authors have studied the negative effects brought about by advance reservation in grid environments. To mitigate these effects, they propose a novel RARP based on the fact that applications tend to overestimate their reservation time to ensure their successful execution. The experimental results show that RARP can bring about a higher resource utilization rate and lower rejection rate with a slight increase in reservation violations. Furthermore, it also shows better adaptation in the presence of a higher reservation rate. Although the reservation violation rate is the price the authors have to pay, they can still limit it by setting a higher value of

*v . Because parameter *v has a significant influence on the performance of RARP, the authors plan to provide an adaptive mechanism for RM to dynamically set an optimal *v based on resource’s runtime load in the future.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (60673165).

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(Editor: ZHANG Ying)