Keywords: disk throughput, virtual machine, I/O scheduling, performance evaluation

Transcription

1 Simple and practical disk performance evaluation method in virtual machine environments Teruyuki Baba Atsuhiro Tanaka System Platforms Research Laboratories, NEC Corporation 1753, Shimonumabe, Nakahara-Ku, Kawasaki, Kanagawa , Japan Keywords: disk throughput, virtual machine, I/O scheduling, performance evaluation Abstract This paper proposes a disk access throughput evaluation method in virtual machine environments where multiple independent virtual machines share a common physical shared disk drive. drive simulation is one candidate to evaluate the total performance of disk throughput by modeling I/O management mechanisms inside virtual machine monitors. However, making such a model might be impossible when the source code of a target virtual machine monitor is not open. Therefore, a simple evaluation method is required. We propose a simple and practical method with an analytical model which has only two types of parameters: sequential access ratio and disk performance profile. These two parameters can be obtained without knowledge about operations inside a virtual machine monitor. The sequential access ratio is defined as the probability whether the next disk access is to the same file or not. It represents virtual machine monitor s I/O scheduling characteristics. The disk performance profile is the relationship between seek distance and throughput, and we assume, in this paper, it is measured in advance. We have developed a calculation method by combining the two parameters above. Then we have compared the estimation throughputs and the measured ones in Xen virtual machine environments with random read accesses. The experimental results show that errors of our method are no more than 1%. 1. INTRODUCTION Virtualization technology has been common in the field of IT system operation and management, providing benefits such as improved computer resource utilization, isolated systems, and easier management [1, 2]. Virtualization technologies can create multiple virtual machines (VMs) on a single physical machine. Each VM can run its own operating system (OS) as a guest OS. A software layer providing virtualization is called a virtual machine monitor (VMM). The VMM manages hardware resources and arbitrates the requests of the multiple guest OSs and applications. It divides physical resources (i.e. CPUs, disks, memories, network bandwidths) into multiple logical resources. The virtual machine is configured with the logical resources. Examples of VMMs are VMware [3], VirtualPC [4], and Xen [5, 6]. One of the most pressing problems faced by system administrators managing VMs is: how many VMs can be supported by a particular hardware configuration and virtualization platform? There is a trade-off between application performance and the number of VMs on a single physical machine. On the one hand, sufficient resources are required to avoid degradation in performance from the point of view of application performance. On the other hand, the number of VMs on a single physical machine should be increased from the point of view of cost reduction. Thus, system administrators need performance evaluation methods which enable them to predict the performance from the amount of logical resources. Performance evaluation methods of CPU power in virtual environments have been reported in references [7, 8, 9]. These methods can estimate response times and throughputs using queuing theory. performance, however, has not been sufficiently studied yet. One of the simplest management methods in virtual machine environments is based on disk size alone [7]. It decides each VM's disk size so that the summation of the disk size of all VMs does not exceed the size of the physical disk. Considering disk performance, disk access throughputs are an important factor that affects the performance of application software. The disk throughput is affected by position of data on the disk and frequency of disk access. The disk throughput is reduced with increases in the seek distance between data. The total disk throughput is reduced when multiple applications wish to access the disk simultaneously. In our experimental results, the disk throughput is decreased to about 5% when multiple VMs run on a single disk (see Section 2). A disk performance evaluation method for virtual machine environments is desired because multiple VMs which share a single disk drive could dramatically degrade disk throughput. drive simulations have been previously proposed [1, 11]. Since they are able to calculate accurate results, they are prospective candidates to evaluate the total performance of disk throughput by modeling I/O management mechanisms inside VMM. However, making such models might be impossible when the source code of a target VMM is not open. Moreover, they generally have another demerit in that simulation time is too SPECTS ISBN:

2 long. Analytical models [12, 13, 14] can reduce computing time for evaluating disk performance, although their results are more approximate. However, the existing analytical models need many parameters, such as rotation time, data transfer time, positioning time and maximum bandwidth. However, it is difficult to obtain these parameters. In this paper we propose a simple method of evaluating disk access throughputs in virtual machine environments. Our method addresses the problem with existing analytical methods, i.e., they need too many parameters. Our model uses only two types of parameters: sequential access ratio and disk performance profile. The sequential access ratio represents VMM's I/O scheduling characteristics, and is defined as the probability whether a disk access requires moving the disk head within a file or not. The sequential access ratio depends not on application software but on platforms like Linux and Xen. Once the ratio is measured with an application, it could be used for evaluating other application's I/O performance. The disk performance profile is the relationship between seek distance and throughput. This represents a device-specific performance characteristic. We derive disk access throughput by combining the sequential access ratio and disk profile. The two parameters can be obtained if the source code of the VMM is not open. The outline for the rest of the paper is as follows: Section 2 describes virtual machine environment and disk performance profile. Section 3 introduces our performance evaluation method. Section 4 evaluates the practicality of our method. Finally, Section 5 summarizes the main points of this paper. 2. TARGETS This section describes our targets, i.e., virtual machine environments and disk performance profile. The disk performance profile depends on the disk device. The performance profile measured in this section is used to estimate disk throughput by our method described in Section Virtual machine environment Our target virtual machine environment is shown in Fig. 1. Multiple VMs are created by a VMM on a single physical machine. The VMs share a single physical disk. Applications which run in VMs access the same disk simultaneously. We focus on a local disk in this paper. space is divided into multiple partitions. A VM image file which includes a guest OS and application data is made in each partition for security. The locations of the partitions can be decided when system administrators design a VM system. Each VM accesses its own partition. We propose a disk performance evaluation method using this disk access characteristic of VM in Section 3. Read throughput [MB/sec] Virtual machine Application Data Virtual machine monitor (VMM) Data 2.2. performance profile We measured the disk performance profile of our target disk device. The performance profile is the relationship between throughput and seek distance. The disk device described in this section is the same as that used for experimental evaluations described in Section 4. The specifications of the computer we measured are as follows: CPU is Pentium GHz, memory size is 3 GB and disk size is 16 GB (Western Digital, WD16JS). The disk is used as a local disk. The OS is Fedora Core 6 (Linux kernel ). We ran a random read program to access the disk device. In order to avoid the memory cache effect, we ran reads system calls at random positions on the disk. Reads system calls read fixed size data (4 kb). In this paper, a random read throughput (B random ) is defined by Sread B random =, T (Eq. 1) where T run is the running time of the random read program, and S read is the total amount of data which is read by the random read program in T run. We measured random read throughputs with varying seek distances. The experimental results are shown in Fig. 2. The horizontal axis of the graph is the average seek distance and the vertical axis is the random read run Virtual machine Application Partition Partition Fig. 1: Virtual machine environment access Average seek distance [GB] Fig. 2: performance profile of our target disk SPECTS ISBN:

3 throughput defined as Eq. 1. Generally, the seek distance is presented in cylinder units. However, in this paper, we present the seek distance in byte units because byte units are familiar to system managers. In our experiments, the size of a cylinder is 7.84 MB. As shown in Fig. 2, the throughput decreases to less than 5% when the seek distance is long. When multiple VMs access the disk simultaneously, there are two types of seek distances. One is short distance within one file in a VM. The other is long distance between VMs. Typical file size is less than 2 GB, which is the maximum size of the default Linux system. In this case, the average seek distance is 1 GB by uniform random access. When the average seek distance is 1 GB, the throughput is.45 MB. A is more than 1 GB typically. When the average seek distance is 1 GB, the throughput is.33 MB. In our method, we estimate disk throughput based on probabilities of two types of seek distances. 3. PERFORMANCE EVALUATION METHOD OF DISK ACCESS This section explains our disk access performance evaluation method in virtual machine environments. Our performance evaluation method does not simulate every seek distance but analytically calculates representative seek distances between representative locations of each file. To present these representative seek distances, we classify seek distances into two types, a seek distance within a file and a seek distance between files. Locations of s, in virtual machine environments, are limited by predetermined disk partitions, so that the two types of seek distances can be obtained as averages of partition size and distances between partitions. throughput is estimated based on probabilities of the two types of seek distances. To present the probabilities, which depend on the I/O scheduler, a sequential access ratio is defined. Total average seek distance is derived from the two types of seek distances and the sequential access ratio. In the rest of this section we describe these two definitions in detail. Section 3.4 describes the performance evaluation method of the disk access throughputs using the calculated total average seek distance and the disk performance profile Classification of seek distance First, let us define seek distances within / between files. Fig. 3 shows locations of files on a disk. For example, let us assume there are two files, file i and file j, on a disk. Let l ij denote an average seek distance between file i and file j, and l ii, an average seek distance within a file (file i). Assuming that the locations of disk accesses are distributed at uniform random, the average seek distance between file i and file j (l ij ) is the length between the mean points of file i and file j. The average seek distance within a file (l ii ) is the half length of the size of file i. In this paper, we take account of these uniform random accesses. In virtual machine environments, each VM accesses data in its own partition, because s are anchored in disk partitions. The locations of the partitions Sequential access ratio: α File i Seek distance within file: l i-i Transfer ratio to another file =(1-α)/(N-1) Seek distance between files: l i-j = l j-i Sequential access ratio: α File j N: Number of files Fig. 3: Definitions of seek distances within file and seek distances between files and sequential access ratio access throughput (B) B est (=Estimated throughput) performance profile: B = f(l) l ave (= Calculated total average seek distance) Average seek distance (l) Fig. 4: Estimation of disk access throughput using disk performance profile and average seek distance are decided when system administrators design a VM system. The two types of seek distances can be obtained easily Definition of sequential access ratio The definition of sequential access ratio is explained here. Fig. 3 shows an image of the definition of a sequential access ratio. There are two files, file i and file j, on a disk. These two files are accessed simultaneously. We define sequential access ratio (α) as the probability whether the next access is to the same file or not. For example, if the access sequence of file number is iiii i, the sequential access ratio is one (α = 1). The disk head moves within the same file (file i) after the head accesses data in file i. If ijij ij, the ratio is zero (α = ). When the current access is file i, the probability that the next access is one of the other files is (1-α)/(N-1), where the number of files is N (in Fig. 3 only two files (i and j) are presented). In this calculation, we assume that priorities of the disk accesses to all files are the same. The sequential access ratio is between zero and one. When the ratio is zero (α = ), after the disk head accesses data, the next access request always moves the disk head to another file. In this case, the seek distance is long; therefore, the disk access throughput is low. When the sequential access ratio is one (α = 1), the disk head moves within the same file. The seek distance is short; therefore, the disk access throughput is high. SPECTS ISBN:

4 In VM environments, the sequential access ratio presents a probability that the disk access request from the same VM is executed continuously by the I/O scheduler in a VMM Derivation of total average seek distance We derive a total average seek distance (l ave ) as Eq. 2, when the sequential access ratio and the two types of seek distances are defined as above. N 1 1 α l (Eq. 2) ave = α lii + lij N = i 1 i j N 1 In Eq. 2, N is the number of files which are accessed on the disk simultaneously, α is the sequential access ratio, l ii is the seek distance within a file (file i), and l ij is the seek distance between file i and file j. The first term is the expectation of seek distance within file i, and the second term is a summation of the expected seek distance from file i to file j (i j), where (1-α)/(1-N) represents the access probability to file j. The total average seek distance represents the average length of the disk head s trace when disk accesses are executed many times Estimation of disk throughput Finally, disk throughput is estimated from the performance profile of a disk device using the total average seek distance. The performance profile is the relation between seek distances (l) and throughputs (B) as B = f(l) in Fig. 4. The performance profile of the disk device is measured in advance. The method of measuring the disk performance profile was described in Section 2. The estimated throughput (B est ) is obtained from B est = f(l ave ) using l ave calculated in Eq EXPERIMENTAL RESULTS In this section, we evaluate our method by measuring disk access throughputs. The measured throughputs are compared with the estimated throughputs so as to demonstrate the practicality of our method when the number of VMs and the locations of s are varied. We measured the throughputs in Xen virtual machine environments and native Linux environments. (A normal Linux OS without virtualization is called native Linux in this paper.) We focused on random read accesses in our experiments, because the disk throughput of other access patterns is greater than those of random read access due to the memory cache effect Setups Experimental setups are shown in Fig. 5. Multiple random read processes access test files on a local disk simultaneously in Xen virtual machines and native Linux. The random read process is a test program that is described in Section 2. The fixed size of read data is 4 kb in our experiments. In Xen VM environments, a single random read process runs in a single VM (Fig. 5 (a)). In native Linux environment, multiple random read processes run in one native Linux OS (Fig. 5 (b)). The random read process VM (dom) Table 1: Specifications of physical machine and OSs CPU Memory OS (Kernel) Test file size =2 GB Partition size = size = 1 GB VM (domu) Random read Test file Native Linux 3 GB Xen Fedora Core 6 (Linux ) Scheduling by Xen scheduler Xen (version 3..4) Dom Pentium 4 3.8GHz 1 GB Test file Fedora Core 6 (Linux ) VM (domu) Random read (a) Xen virtual machine Random read Test file Native Linux Scheduling by Linux scheduler (b) Native Linux Test file Random read Dom U 16 GB (Western Digital, WD16JS) 256 MB Fedora Core 6 (Linux ) Partitioin 1 Partitioin 2 Partitioin 13 Partitioin 14 VM 1 image file VM 2 image file VM 13 image file VM 14 image file Test file Test file Test file Test file Fig. 6: Configuration of disk partitions Random read a test file Random read a test file Fig. 5: Experimental setups in Xen virtual machine environment and native Linux environment in the native Linux accesses the test file in the VM image file, which is mounted in the native Linux environment so that the same file is accessed in both environments. The same physical computer is used in both experimental environments to ensure that no machine condition will affect experimental results. Xen and native Linux are installed into the computer as a dual booting system. The specifications of the physical computer SPECTS ISBN:

5 Table 2: Selected virtual machines and total average seek distance in each experimental condition Total average Number Condition seek distance [GB] of ID Xen Native Linux processes α =. α = VM1 VM3 Selected Virtual machines VM1 VM VM1 VM VM1 VM VM1 VM VM1 VM VM1 VM2 VM3 VM VM2 VM4 VM6 VM VM1 VM3 VM6 VM VM1 VM5 VM9 VM VM1 VM2 VM13 VM VM1 VM2 VM3 VM4 VM5 VM6 VM7 VM VM1 VM2 VM5 VM6 VM7 VM8 VM9 VM VM2 VM3 VM6 VM7 VM8 VM9 VM12 VM VM1 VM3 VM5 VM7 VM8 VM1 VM13 VM VM1 VM2 VM3 VM4 VM11 VM12 VM13 VM14 are shown in Table 1. The machine has a Pentium GHz CPU, 16 GB HDD and 3 GB memory. The HDD is used as a local disk. This disk s performance profile, measured in Section 2 (Fig. 2), is as follows: B =.587 l [MB/sec] if 1 l 2 [GB] (Eq. 3) 1 B = [MB/sec] if l 2 [GB] (Eq.4).244 l In native Linux environment, Fedora Core 6 is operated as a native Linux OS. In Xen, a virtual machine is called a domain [5]. There are two kinds of domains, domain (dom ) and domain U (dom U). The domain is a special VM that is allowed to access the physical device directly. When another VM (domain U) operates I/O access, the domain U asks the domain to execute I/O access and returns the result of the I/O operation to the domain U. In this paper, we assume that applications run in domain Us. This is because the domain is used for administration and the domain Us are used for user applications, as is the usual case in Xen operations. The specifications of VM are as follows: The domain has a 1 GB memory and each of the domain Us has a 256 MB memory. The Fedora Core 6 is operated as the guest OS in the domain and the domain U. We divided the disk space into multiple partitions and a test file was created in each partition. Fig. 6 shows the configuration of disk partitions in our experiments. The size of each partition is 1 GB (135 cylinders). Fourteen partitions are made for VMs in the disk because Linux makes a maximum of 15 partitions, and one of them is an extended partition in which files are not recorded. A VM image file which includes a guest OS and a test file is deployed in each partition. The test file, which is accessed by the random read process, is created by using the following Linux dd command in each VM: $ dd if=/dev/urandom of=testfile bs=1m count=248 This command writes random numbers into the test file. The size of the test file is 2 GB (l ii = 1 GB in Eq. 2). When we measure the random read throughputs, the random read process reads fixed-size data (4 kb) 15, times. The total size of read data is 6 MB, which is about 3% of the test file (2 GB). Therefore, we can ignore the memory cache effect Conditions Table 2 shows the experimental conditions. We measured total random read throughputs at each condition in Xen virtual machine environments and native Linux environments. The total random read throughputs are the summation of all the random read processes throughputs, defined by Eq. 1. The numbers of active random read processes are 1, 2, 4 and 8. When multiple random read processes run, we have many combinations of the active VMs. We select the combinations shown in the fifth column of Table 2. In Xen virtual machine environments, the selected VMs are active and the other VMs are shut down. In native Linux environments, the selected VM image files are mounted and a test file in each selected VM is accessed by the random read process. The same files are accessed in Xen and native Linux environments. We select these conditions in order to have various total average seek distances. The total average seek distances in Xen VM and SPECTS ISBN:

6 Read throughput [M B/sec] Tim e [sec] Read throughput [M B /sec] Time [sec] (a) Xen virtual machine (l ave = 1 GB) (b) Native Linux (l ave = 1 GB) Fig. 7: Measured total disk access throughput (the number of processes (N) = 1) native Linux at each condition are shown in the third and fourth columns of Table 2. The total average seek distances are calculated using α =. and α =.99 in Xen VM and native Linux. These values are obtained by fitting Eq. 2 to the results of two processes conditions. The sequential access ratio (α) depends not on application software but on platforms such as Linux and Xen. The sequential access ratio measured in advance can be adapted to various application software. For example under condition 4-2, four VMs (VM2, VM4, VM6 and VM8) are active and a random read process runs in each VM in the Xen virtual machine environment. The seek distances between files are as follows: l 2,2 = 1 [GB], l 2,4 = 2 [GB], l 2,6 = 4 [GB], l 2,8 = 6 [GB], l 4,2 = 2 [GB], l 4,4 = 1 [GB], l 4,6 = 2 [GB], l 4,8 = 4 [GB], l 6,2 = 4 [GB], l 6,4 = 2 [GB], l 6,6 = 1 [GB], l 6,8 = 2 [GB], l 8,2 = 6 [GB], l 8,4 = 4 [GB], l 8,6 = 2 [GB], l 8,8 = 1 [GB] l ij represents the seek distance between the test files in the partition i and j. Here, it is assumed that the distance between files is equal to the distance between the partitions. l 2,4 represents that the seek distance between the test files in VM2 and VM4 is 2 GB. l kk represents the seek distance within file k. Since the size of the test file is 2 GB and the random read process accesses uniform random locations in our experiments, the average seek distances within a file l kk is 1 GB. Using these values in Eq. 2, the total average seek distances are calculated as 33.3 GB and 1.32 GB in Xen VM environment and native Linux Discussion Fig. 7 shows the measured disk access throughputs in the case where a single random read process accesses one given test file in partition 12. Figs. 7 (a) and (b) present the results in a Xen VM environment and in a native Linux environment. Since there is a single active test file, we consider only the seek distance within a file. In both environments, the seek distance within a file is 1 GB and the average seek distance calculated from Eq. 2 is 1 GB, because the test file size is set to 2 GB. The horizontal axis in Fig. 7 is the amount of time elapsed after starting the random read and the vertical axis is the random read throughput of each process. The throughput is initially low, because it takes considerable time to search the test file in the file system. When the same test file is accessed many times, the search in the file system becomes more effective and the throughput increases. We measured the random read throughput in the range where the throughput is stable. The random read throughputs are.456 MB/sec and.459 MB/sec in the Xen virtual machine and in the native Linux. These results lead to the conclusion that a Xen virtual machine has almost no overhead in disk accesses. In addition, we measured the effect of VM s memory size on disk throughput. When the memory size of domain U is set to 512 MB, the measured throughput is the same value as that measured in the case where the domain U s memory size is 256 MB (Fig. 7 (a)). When the memory size of domain is 512 MB, we measured the same throughput that as that obtained in the case where the domain s memory size is 1 GB (Fig. 7 (a)). This ensured that the memory sizes of domain U and domain did not affect disk performance in our experiments. Fig. 8 shows measured disk access throughputs in the case where two random read processes run. Figs. 8 (a-1) and (a-2) present the results in a Xen VM environment and (b-1) and (b-2) present those in a native Linux environment. Fig. 8 (a-1) and (b-1) present the random read throughputs measured under the condition 2-1 given in Table. 2. Figs. 8 (a-2) and (b-2) present the results under the condition 2-6. Under the condition 2-1 (Fig. 8 (a-1) and (b-1)), VM1 and VM3 are active. In this case, the seek distance between VM1 and VM3 (l 1,3, l 3,1 ) is 2 GB and that within file (l 1,1, l 3,3 ) is 1 GB. The average seek distances are calculated from Eq. 2 as 2. GB and 1.19 GB in a Xen virtual machine environment and in a native Linux environment. In the Xen virtual machine s result (a-1), the throughputs of both process 1 and process 2 are.132 MB/sec. The total random read throughput is 64 MB/sec. In the native Linux s result (b-1), throughputs of process 1 and process 2 are.192 MB/sec and.197 MB/sec. The total random SPECTS ISBN:

7 Read throughput [M B/sec] P rocess1 P rocess Time [sec] Read throughput [M B/sec] P rocess1 P rocess Tim e [sec] (a-1) Xen virtual machine under condition 2-1 (VM1, VM3) (b-1) Native Linux under condition 2-1 (VM1, VM3) (l ave = 2. GB) (l ave =1.19 GB) Read throughput [M B/sec] Process1 Process Time [sec] Read throughput [M B /sec] Process1 Process Time [sec] (a-2) Xen virtual machine under condition 2-6 (VM1, VM13) (b-2) Native Linux under condition 2-6 (VM1, VM13) (l ave = 12 GB) (l ave =2.19 GB) Fig. 8: Measured total disk access throughput using different VM images (the number of processes (N) = 2) throughput is.389 MB/sec. The estimated total throughputs are calculated from the average seek distances, which from Eq. 3 and Eq. 4 are 94 MB/sec and.442 MB/sec. Under the condition 2-6 (Fig. 8 (a-2) and (b-2)), VM1 and VM13 are active. In this case, l 1,13 = l 13,1 = 12 GB and l 1,1 = l 13,13 = 1 GB. The average seek distances are calculated as 12 GB and 2.19 GB in the Xen virtual machine environment and in the native Linux environment. The measured total random read throughputs are.151 MB/sec and.383 MB/sec. The estimated total throughputs are.171 MB/sec and.383 MB/sec. In the Xen virtual machine environment, the total random read throughput decreased to 5% of that in the case where a single random read process accesses, when the total average seek distance is long. In native Linux, however, there is very little decrease in total throughput from the result of a single random access case. When we focus on flucuation of throughput, the throughput of each process in Xen is almost the same, but those in native Linux varied widely. This is because native Linux, which has a large sequential access ratio, tends to access one file sequentially. These results show that there is a trade-off between total disk throughput and fairness of disk access. Xen may have a policy that Xen hypervisor provides throughput to each VM as fairly as possible. On the other hand, native Linux has a policy that gives priority to throughput over fairness. Fig. 9 compares estimated throughputs and measured throughputs when the average seek distance in Table 2 is varied. The horizontal axis of the graph is the total average seek distance (l ave ) and the vertical axis is the total random read throughput. The marks in the graph represent the results under the conditions shown in Table 2. The total average seek distance in Xen VM environments is longer than that in a native Linux environment because the sequential access ratio is small in Xen virtual machine environments. Fig. 9 reveals that our method can estimate the total disk throughputs with no more than 1% error in all ranges. This is reasonable when the system administrators operate the virtual machine systems. SPECTS ISBN:

8 Read throughput [MB/sec] process 2 processes 4 processes 8 processes Estimate Average seek distance [GB] Read throughput [MB/sec] process 2 processes 4 processes 8 processes Estimate Average seek distance [GB] (a) Xen virtual machine (b) Native Linux Fig. 9: Comparison between estimated throughputs and measured throughputs 5. CONCLUSION In this paper we proposed a disk access throughput evaluation method for virtual machine environments. Our performance evaluation method is simple and practical, because it does not simulate every seek distance but analytically calculates seek distances between representative location of each file. To present these representative seek distances, we classified seek distances into two types, seek distance within a file and seek distance between files. In virtual machine environments, locations of s are limited by disk partitions. The two types of seek distances can be obtained easily. throughput was estimated based on probabilities of the two types of seek distances. To present the probabilities depending on the I/O scheduler, sequential access ratio was defined. Total average seek distance was derived from the two types of seek distances and the sequential access ratio. We evaluated our method experimentally. We measured the random read throughputs in Xen virtual machine environments and native Linux environments. We focused on random read accesses in our experiments, because disk throughput of other access patterns is greater than that of random read access due to the memory cache effect. The measured throughputs were compared with the throughputs estimated by our proposed method when the number of virtual machines and the files locations were varied. The experimental results show that our proposed method can estimate the total disk throughputs with a maximum of 1% error. This is reasonable for system administrators managing virtual machine systems. In this paper, virtual machines were created using Xen VMM, but our method can apply other VMMs. We took account of the case that disk access patterns of all virtual machines are the same in this paper. Considering a case in which each virtual machine has a different disk access pattern will be a subject of future work. ACKNOWLEDGEMENT We would like to thank a number of unnamed reviewers for their constructive comments and suggestions. This work was partly supported by Ministry of Internal Affairs and Communications (MIC). REFERENCES [1] J. Rolia, L. Cherkasova and A. Andrzejak, A Capacity Management Service for Resource Pools, in Proceedings of ACM WOSP 25, pp , 25. [2] M. Rosenblum and T. Garfinkel, Virtual Machine Monitors: Current Technology and Future Trends, in IEEE Computer, Vol. 38, No. 5, pp , 25. [3] [4] winfamily/virtualpc/default.mspx [5] P. Barham, B. Dragovic, K. Fraser, S. Hand, T. Harris, A. Ho, R. Neugebauer, I. Pratt, and A. Warfield, Xen and the Art of Virtualization, in Proceedings of ACM SOSP 23, pp , October 23. [6] [7] Y. Ding and E. Bolker, How Many Guests Can You Serve? On the Number of Partitions, in Proceedings of CMG conference, 26. [8] E. Bolker and Y. Ding, Virtual performance won t do: Capacity planning for virtual systems, in Proceedings of CMG conference, 25. [9] G. Khanna, K Beaty, G. Kar and A. Kochut, Application Performance Management in Virtualized Server Environments, in Proceedings of IEEE/IFIP NOMS 26, pp , 26. [1] C. Ruemmler and J. Wilkes, An Introduction to Drive Modeling, in IEEE Computer, Vol. 27, No. 3, pp , [11] [12] E. Varki, A. Merchant, J. Xu, and X. Qiu, Issues and Challenges in the Performance Analysis of Real Arrays, in IEEE Trans. Parallel and distributed systems, vol. 15, no. 6, pp , 24. [13] M. Uysal, G. A. Alvarez and A. Merchant, A Modular, Analytical Throughput Model for Modern Arrays, in Proceedings of IEEE MASCOTS 21, pp , 21. [14] A. Merchant and P. S. Yu, Analytic Modeling of Clustered RAID with Mapping Based on Nearly Random Permutation, in IEEE Trans. Computers, vol. 45, no. 3, pp , SPECTS ISBN: