先進的計算基盤システムシンポジウム SACSIS2012 Symposium on Advanced Computing Systems and Infrastructures SACSIS /5/18 VM 1 VM VM 0-1 1) 18% 50% 2) 3) Matching

Transcription

1 VM 1 VM VM 0-1 1) 18% 50% 2) 3) Matching-based Virtual Machine Packing Algorithm for Lower Power Consumption SATOSHI TAKAHASHI, ATSUKO TAKEFUSA, MAIKO SHIGENO, HIDEMOTO NAKADA, TOMOHIRO KUDOH and AKIKO YOSHISE VM (Virtual Machine)-based flexible capacity management, which consolidates multiple VMs into few physical machines and other physical machines are allowed to be put in stand-by mode, is an effective scheme to reduce total power consumption in a datacenter. However, there have been the following issues, reconcilement of power-saving and user experience, decision of VM packing in feasible calculation time and collision avoidance of VM migration processes. In order to resolve these issues, we propose a matchingbased VM packing algorithm (MBA), which enables to decide a suitable VM packing plan in polynomial time. In the experiments, we compare the proposed algorithm with 0-1 integer programming model, using optimization solvers, and a greedy algorithm. The results show that 1) the proposed algorithm MBA reduces the total power consumption by between 18% and 50% of when the packing plan does not work, 2) MBA enable to provide an optimal packing plan in feasible calculation time, and 3) there is a trade-off between the power-saving effect and the deterioration of the user experience. 1. IT University of Tsukuba National Institute of Advanced Industrial Science and Technology (AIST) 5 VM VM 1) 1 VM ACPI S3 333

2 VM VM (1) (2) VM VM (3) VM (1) VM VM VM (2) VM VM (3) 1) 1 VM [ ] VM MBA CPU VM 1 VM VM VM 0-1 IP (GREEDY) 4) VM CPU VM 1) 17% 31% 2)MBA 3) 2. VM 2),3) Entropy 15) Entropy VM VM CPU VM Stillwell 16) VM 3. (VM) VM (CPU ) VM CPU VM Web 3.1 VM VM VM 334

3 5) VM VM VM ACPI S3 ACPI S3 70w 5-7w VM VM CPU 5),6) VM 1 ACPI S VM 3.2 VM VM VM P V (VM) i P CPU m i, c i VM k V CPU vm k, vc k CPU z i( P ) cost i (z) i base i x 0 ik VM k( V ) k i( P ) 1 0 x ik (i P, k V ) y i(i P ) 0-1 { 1 ( i VM k ) x ik = (1) 0 () { 1 ( i ) y i = (2) 0 () (VMPP) (cost i ( vc k x ik ) + base i y i ) (3) x ik = 1, k V (4) vm k x ik m i, i P (5) vc k x ik c i, i P (6) x ik V y i, i P (7) x ik x 0 ik 1, i P (8) x ik {0, 1}, i P, k V (9) y i {0, 1}, i P (10) 7) (3) CPU (4) VM (5) (6) CPU (7) 1 VM (8) VM VM 1 (P, A) A = {(i, j) i, j P, i j} i i VM V i V i = {k V x 0 ik = 1} i VM k j 335

4 c(i, j, k) cost i ( vc k ) cost i ( vc k ) k V i k V i \{k} + base i max{0, 2 V i } + cost j ( vc k ) cost j ( vc k ) k V j k V j {k} + base j min{0, V j 1} (11) i j (5)(6) i j VM V i j vm l V i \{k} l m j, k V i vc l V i \{k} l c j, vm (12) l V j {k} l m j, vc l V j {k} l c j (i, j) A c(i, j) max{ c(i, j, k) k V i j } (13) c(i, j) = c(i, j, k) k σ c(i, j) = c(i, j, σ(i, j)) Ã = {(i, j) A V i j } VM 1 (P, A) 1 7 VM VM VM (5)(6) {i P i vc k > c i } {i P i vm k > m i } U U VM (P, Ã) U U- U 1. (P, Ã) c U- M (i, j) M i j σ(i, j) Proof. Ã U 1 i ˆV i 1 ˆM = {(i, j) i, j P, V i ˆV j } 1 ˆM (P, Ã) U- P + = {i P ˆV i \ V i } P = {i P V i \ ˆV i } i P + ˆV i \ V i = {k i } i P V i \ ˆV i = {k i} (cost i( vc k ) + base i min{1, V i }) i (cost i ( vc k ) + base i min{1, ˆV i }) k ˆV i = (cost i ( vc k ) cost i ( vc k )) + P i k ˆV i + base i (min{1, V i } min{1, V i 1}) + base i (min{1, V i } min{1, V i + 1}) + = (cost i ( vc k ) cost i ( vc k )) + i i {k i } + (cost i ( vc k ) cost i ( vc k )) i i \{k i } + base i max{0, 2 V i } + base i min{0, V i 1} + = c(i, j, k i) (14) (i,j) ˆM k i V i j c(i, j, k i) c(i, j) M U- (i,j) ˆM c(i, j) (i,j) M c(i, j) M M 336

5 (MBA) Step 1. Step 2. Step 3. (P, A) (i, j) A c(i, j) U = {i P i vc k > c i } {i P i vm k > m i } (P, Ã) U- M (i, j ) M σ(i, j ) i j Step 2 U- U = Edmonds 8) O( P 3 ) O( P Ã + P 2 log P ) 8) 10) 2. O( P 3 + V P ) Proof. Step 1 (i, j) c(i, j) O( V i ) i O( V i P ) Step 1 O( i V V i P ) = O( V P ) Ã =O( P 2 ) Step 2 O( P 3 ) U- Step 3 O( P ) 4.2 (GREEDY) GREEDY 1 VM (GREEDY) Step 1 Step 2 i( P ) VM CPU i vc k > c i i vm k > m i High( P ) Low( P ) High Low i util i util i util i = vc k /c i + vm k /m i (15) i i Step 3 h( High) util i h VM V h k Low l( Low) h( High) CPU oc h = max{0, h vc k c h } om h = max{0, h vm k m h } VMk (a) (b) (c) (d) Step 4 vc k oc h vm k om h diff1 k( V h ) vc k < oc h vm k om h diff2 k( V h ) vc k oc h vm k < om h diff3 k( V h ) vc k < oc h vm k < oc h diff4 k( V h ) diff1-4 diff1 = (vc k oc h )/c h + (vm k om h )/m h (16) diff2 = (oc h vc k )/c h + (vm k om h )/m h (17) diff3 = (vc k oc h )/c h + (om h vm k )/m h (18) diff4 = (oc h vc k )/c h + (om h vm k )/m h (19) l( Low) k ( V h ) Low\{l} Low l send l recv l recv V l send VM Low \{l recv } VM GREEDY 5. VM CPU 1 VM 200 MBA GREEDY VMPP IP 5.1 VM

6 1 MBA, GREEDY IP(CPLEX) VM CPU [MB] VM CPU avg. / max 0.5 / 1.0 VM avg. / max 2048 / 4096 [MB] VM CPU Sine ( : : 1/12π, ) base i / cost i (z) 53.0 / 47.0z CPU [MB] VM CPU / 0.5 / / 4096 [MB] VM Sine VM Sine 7) i P base i = 53.0 cost i(z) = 47.0z 1 VM Intel Core i7 CPU (3.4GHz, 8 ), MacOSX bit, 16GB CPLEX( IBM ILOG CPLEX Optimization Studio_Academic V12.3, 64bit ) MBA GREEDY CPLEX IP CPLEX Python pulp GLPK(Ver.4.47) 14) Python MBA step 2 9) O( P 3 ) J. van Rantwijk 11) U MBA GREEDY IP VMPP ((3)-(10) ) CPLEX VMPP (8) x ik x 0 ik 1 i VM k, (x ik + x 0 ik 2x ik x 0 ik) 1, i P (20) FIX MBA IP 1 GREEDY IP VMPP (5) (6) p i, q i vm k x ik m i p i, i P (21) vc k x ik c i q i, i P (22) (3) (cost i ( vc k x ik ) + base i y i ) + p i + (23) CPLEX IPr 300 MBA IP GREEDY MBA IP IP (600 ) IP IPr IPr GREEDY MBA IP MBA CPLEX 3 MBA GREEDY MBA GREEDY VMPP GLPK (=VM ) (sec.) (=VM ) q i 338

7 2 1 (sec.) (=VM ) FIX MBA IP GREEDY IPr MBA IP GREEDY IPr (sec.) (=VM ) FIX MBA GREEDY MBA GREEDY MBA IP GREEDY IPr (=VM ) (=VM )250 FIX, MBA, GREEDY, IP, IPr FIX MBA GREEDY IP IPr FIX MBA, GREEDY, IP, IPr 4 18% 50% 5 (=VM ) MBA IP GREEDY IPr CPU (24) i( P ) VM V i max{0, vc k c i }/c i i + max{0, vm k m i }/m i (24) i 5 5 MBA MBA IP IPr IPr MBA 1 VM NP- 339

8 3 VM VM VM 6. VM CPU CREST( ) ( ) 1) T. Hirofuchi, H. Nakada, S. Itoh and S. Sekiguchi. Reactive Consolidation of Virtual Machines Enabled by Postcopy Live Migration, Proc. of the 5th Int. Workshop on Virtualization technologies in distributed computing, pp.11 18, (2011). 2) H. Nakada, T. Hirofuchi, H. Ogawa and S. Itoh. Toward Virtual Machine Packing Optimization Based on Genetic Algorithm, Distributed Computing, Artificial Intelligence, Bioinformatics, Soft Computing, and Ambient Assisted Living (Proc. of Int. Symposium on Distributed Computing and Artificial Intelligence), LNCS, Vol. 5518, pp , Springer, (2009). 3) (CPSY: ) Vol.110, No.167, pp , (2010). 4) (CPSY: ) Vol.110, No.167, pp.73 78, (2011). 5) T. Hirofuchi, H. Nakada, S. Itoh and S. Sekiguchi. Enabling Instantaneous Relocation of Virtual Machines with a Lightweight VMM Extension, The 10th IEEE/ACM Int. Conference on Cluster, Cloud and Grid Computing (CCGrid2010), pp , (2010). 6) (2010-OS-115), pp. 1 13, (2010). 7) T. Hirofuchi, H. Nakada, S. Itoh and S. Sekiguchi. Making VM Consolidation More Energy-efficient by Postcopy Live Migration, Proc. of the 2nd Int. Conference on Cloud Computing, GRIDs, and Vidualization, pp , (2011). 8) B. H. Korte, and J. Vygen. Combinatorial optimization: theory and algorithms, Springer, (2004). 9) Z. Galil. Efficient Algorithms for Finding Maximum Matching in Graphs. ACM Conputing Serveys, Vol.18, 1, pp.23 38, (1986). 10) J. Edmonds. Paths, trees, and flowers, Canadian Journal Mathematics, Vol. 17, pp , (1965). 11) J. van Rantwijk. Joris VR, 12) M.R. Garey and D.S. Johnson. Computeres and Intractability - A Guide to the Theory of NP- Cpmpleteness, A Series of Books in the Mathematical Science, 22nd printing, W.H. Freeman and Company, New York, (2000) 13) IBM ILOG CPLEX, software/integration/optimization/cplex-optimizer/. 14) GLPK, 15) F. Hermenier, X. Lorca, J-M. Menaud, G. Muller and J. Lawall. Entropy: a consolidation manager for clusters, Proc. of the 5th Int. Conference on Virtual Execution Environments, pp.41 50, (2009). 16) M.L. Stillwell, F. Vivien and H. Casanova. Dynamic Fractional Resource Scheduling for HPC Workloads. Proc. of Int. Parallel and Distributed Symposium (IPDPS), pp.1 12, (2010). 340