Using a Potential Game for Power Reduction inDistributed Storage Systems
Koji Hasebe, Takumi Sawada, and Kazuhiko Kato
Department of Computer Science, University of Tsukuba
1-1-1 Tennodai, Tsukuba 305-8573, Japan
hasebe@cs.tsukuba.ac.jp, sawada@osss.cs.tsukuba.ac.jp, kato@cs.tsukuba.ac.jp

Abstract—We present a game-theoretic approach for power
reduction in large-scale distributed storage systems. The key
idea is to use distributed hash tables to dynamically migrate
virtual nodes, thus skewing the workload towards a subset ofphysical disks without overloading them. To realize this idea inan autonomous way (i.e., without any kind of central controller),virtual nodes are considered to be selfish agents playing a gamein which each node receives a payoff according to the workloadof the disk on which it currently resides. We model this setting
as a potential game, where an increase in the payoff to a virtual
node reduces the power of the system. This game consists of apair of global and private utility functions, derived by meansof the Wonderful Life Utility technique. The former function
evaluates the state of the system, and the latter provides criteria
for the migration of each node. The performance of our method ismeasured by simulations and a prototype implementation. Fromthese evaluations, we find that our method reduces the running
time of the disks in active mode by 12.7–18.7%, with an overall
average response time of 50–190 ms.

I. I NTRODUCTION
With the advent of cloud computing, power reduction in
datacenters has become a major concern. In particular, as ahigh percentage of the total computing system’s energy isused by data storage systems, there have been a number ofsuggestions for reducing the power consumption of massive
storage systems (cf. [1] for a comprehensive survey of thisresearch area). To reduce power consumption in storage systems, a commonly observed technique is to skew the workload(i.e., data accesses) towards a small number of disks, thereby
enabling the others to be in low-power mode. This idea can betraced back to some prominent early studies, such as MAID
[2] and EERAID [7]; however, when considering datacenterscale computing systems, scalability is of major importance.
In this paper, we propose a power-saving method for largescale distributed storage systems. As our prime interest is torealize a higher level of scalability, we investigate autonomic
control to skew data accesses in a storage array without any
kind of central controller. To achieve this objective, we use
distributed hash tables (DHTs) to provide a lookup service
for data accesses (e.g., Chord [14]). Data are stored in virtual
nodes of the underlying DHT, with each node dynamicallymigrating over physical nodes (disks) depending on the current
workload of the resident disk. Here, the criteria for migration
are as follows: for each disk, the higher the workload, thebetter it is for the system, although overload must be avoided.
In other words, the optimal state is that in which every

disk has as high a workload as possible, while not being
overloaded. This idea was originally introduced in our previous
work [5]. However, in that study, the migration destinationof each virtual node was strictly predetermined in a specificway, and thus could not migrate freely to another disk that
may yield a better state. Moreover, owing to this restriction,
it was also difficult to change the system configuration byadding/removing disks (when extending the system or whennode failure occurs), as well as to deal with changes in the
distribution of popularity (i.e., data access frequency).
To overcome the flexibility issue, the key idea is to consider
the virtual nodes as selfish agents, playing a game in which
each of them receives a payoff according to the workloadof the disk on which it currently resides. Here, the payoff
is defined by satisfying certain migration criteria, and every
virtual node can move to any of the neighboring physical disks.
We model this setting as a potential game [9] by introducing
global and private utility functions based on the WonderfulLife Utility [4], [8] (cf. [11] for an overview of game theory).
In this model, increasing the payoff to any virtual node yields
a better system state with respect to power consumption.
The performance of our method is measured using botha simulation and a prototype implementation in terms ofthe number of active physical nodes, average response time,and migration cost. In the experiments, we consider various
changes in the environment that were difficult to deal within our previous method. From the experiments, we observethat the number of active physical nodes can be reduced by
12.7–18.7% relative to the configuration without any dynamic
migration. This result indicates that our method effectively
skews the workload while maintaining a preferred responsetime (with an overall average of 50–190 ms) by setting suitableparameters in the utility functions. In addition, the results
confirm that our method improves flexibility.
This paper is organized as follows. Section II discusses
related work, and Section III presents our game-theoretic
model for power-saving. Sections IV and V present evaluations
using simulations and a prototype implementation, respectively. Section VI concludes the paper and presents some ideas
for future work.
II. R ELATED W ORK
There have been a number of suggestions for power-saving
in storage systems. As explained in the previous section, theseare based on a similar idea, but are classified into the following
categories according to variations in their approach.
The first category, which includes MAID [2] and PDC [12],focuses on popularity by concentrating popular data on specificdisks. MAID provides specific disks to act as a cache to store
frequently accessed data, thereby reducing accesses to theother disks. PDC periodically reallocates data in the storagearray according to the latest access frequencies.
The second category uses non-volatile random-access memory (NVRAM) to extend the standby mode period by cachingdata to a write store. A typical example is Pergamum [15],which uses NVRAM to buffer write accesses and store data
signatures, reducing direct accesses to the disks.
The final category considers redundancy (i.e., data replication). In DIV [13], original and redundant data are separated
onto different disks, thereby allowing read/write requests tobe concentrated on those disks that contain the original data.
Hibernator [20] applies the idea of PDC to RAID and dynamic
rotations per minute (DRPM) systems. RIMAC [19] provides
two-layered caches, one for storing storage data and the otherfor parity conservation. PARAID [18], which is also a powersaving technique for RAID, allocates the replica in a specificway, meaning that data are collected/spread to adapt to changes
in operational workloads.
Although the above studies restricted their scope to storage
systems consisting of a relatively small number of disks(typically up to several dozen), in recent years the target of thisresearch area has shifted to datacenter-scale systems. Kaushik
et al. [6] proposed the idea of dividing disks in Hadoop
distributed file systems (HDFS) into hot and cold zones. Vermaet al. [16] developed sample-replicate-consolidate mapping(SRCMap), which gathers accesses to the replicas on active
disks, while Vrbsky et al. [17] proposed a replication approachcalled the sliding window replica strategy (SWIN). Finally,
Hasebe et al. [5] reported a power-saving method based on
the DHT technique that skews the workload by dynamicallymigrating virtual nodes in the storage array.
The motivation for this research follows that of the recent
studies mentioned above. In particular, this study can beconsidered as a direct successor to [5]. However, our main
aim is to increase scalability and flexibility by means of gametheoretic autonomic control, thereby making it possible to deal
with various changes in the system environment.
III. S YSTEM D ESIGN
A. Underlying System
Our proposed method targets storage systems consisting of
hundreds of physical disks with unique IDs. The basic lookup
service is provided by an underlying DHT mechanism, andthe stored data are managed by collaboration between virtual
nodes. Owing to the DHT mechanism, clients may access databy sending a request to any of the virtual nodes, regardless of
their location. In this setting, to reduce power consumption,
each virtual node can migrate to any of the neighboring
physical disks depending on their current workload. (Note thata similar idea for the dynamic migration of virtual nodes canbe found in [3] in the context of load balancing.) In the next
subsection, we introduce our modeling of this mechanism as
a potential game.
B. System Model as a Potential Game
Preliminaries. As preliminaries, we first introduce some notation and functions. In the following, N is used to denotethe set of natural numbers. Let P = {p1 , p2 , . . . , pn } be theset of physical nodes and V = {v1 , v2 , . . . , vm } be the set ofvirtual nodes. Time progress is represented as steps indicatedby a natural number t = 0, 1, 2, . . . ∈ T , where 0 indicates
the time of the initial state. Every virtual node is stored on aphysical node, with the allocation determined by the function
place : V × T → P . Intuitively, placet (v) = p means that
virtual node v is on p at time t. We also use this function to
denote the set of virtual nodes V ′ ⊆ V that are on physicalnode p, i.e., placet (p) = V ′ . In addition, the notation v ∈ P
is used to denote this relation. For each physical node, thecapacities of workload and volume are respectively determinedby the functions capload : P → N and capvol : P → N.
The current workload and total volume of stored data of avirtual node at any time are respectively determined by thefunctions load : V × T → N and size : V × T → N.
These functions are also used for physical∑ nodes according to
the following definitions:load(p,t)=v∈placet (p) load(v, t)∑size(v,t),respectively. Noteand size(p, t) =v∈placet (p)that no physical node is allowed to have virtual nodes whose
total stored data
∑ volume exceeds its volume capacity (i.e.,
capvol (p) ≤ v∈placet (p) size(vi , t) for any t). In addition,p is considered to be overloaded if load(p, t) > capload (p).
The central idea. Before giving a formal definition of ourgame-theoretic model, we briefly describe the central idea
behind our modeling approach. Our model can be regarded as apotential game, a kind of strategic game in which the incentive
for any player to change their strategy can be expressedby a single global function. More specifically, our model isdeveloped according to the following steps, in conjunction
with the Wonderful Life Utility technique.
In our model, virtual nodes are considered to be selfish
players who select their strategies to remain on the current
physical disk or move to another at regular intervals. Afterthe decision, each virtual node receives a payoff, and thus
every virtual node looks for a better location that will yielda higher payoff. In this setting, we first introduce the global
function for evaluating the state of the system with respect topower-saving and overloading. Next, using the Wonderful Life
Utility technique, we derive a local function, which determines
the payoff to virtual nodes, from the global function. This local
function satisfies the following criteria: if the workload of thedisk on which it resides increases, the payoff to the node also
increases, although the payoff is cut drastically if the resident
disk becomes overloaded. Moreover, the relationship between
the global and local functions can be regarded as a potential
game; that is, increasing the payoff to any virtual node causes
an increase in the value of the global function.

Formal definition of the global function. We first introduce
the global function G to evaluate the state of the system.
However, to respond to rapid changes in the system workload,
it estimates the expected state at some later step provided thatthe rate of change in the workload during the past j steps
is the same in the future. The formal definition of the global
function is as follows:s ∑∑2
G(placet ) =(load2pred (p, i, t) − c · overpred(p, i, t)).

bandwidth in a system, it is difficult to allow all virtual nodes
to migrate as they wish. Thus, we introduce a priority orderaccording to the degree of contribution to improving the valueof the global function (i.e., the amount by which the value ofthe global function increases).
As the degree of contribution, we consider the increasein the payoff of migration divided by the time required tocomplete the migration. The formal definition is as follows:
M igeval (v, pfrom , pto ) =i=0 p∈P

Here, the function loadpred (p, i, t) indicates the expected
workload of p at time i + t (i.e., i steps later), and is defined
as follows:i
loadpred (p, i, t) = load(p, t) + (load(p, t) − load(p, t − j)).
j
The function overpred (p, i, t) indicates the level of overload
for p, and is defined as follows:
overpred (p, i, t) = β · capload (p) − loadpred (p, i, t),where β (with 0 < β ≤ 1) is a coefficient indicating the
proportion of capacity that may be devoted to migration. For
example, β = 0.6 means that the physical node may spare
60% of its capacity to respond to data access requests, while
the remainder (i.e., 40% of its capacity) is kept
∑ for migration.
c is a weighting constant with c > (s + 1) p∈P cap2load (p).
In the definition of G, load2pred (p, i, t) gives a positive
evaluation for effectively skewing the workload, whereas
2−c · overpred(p, i, t) gives a negative evaluation according to
the level of overloading. We note that the argument of G (i.e.,
placet ) determines the allocation of virtual nodes at time t.
Thus, in game-theoretic terminology, it is a strategy profile ofthe virtual nodes.
Formal definition of the local function. Next, in terms of the
Wonderful Life Utility technique, the global function defined
above can be used to derive a local function Lv for node v ∈ V
as follows.
s∑
Lv (placet ) =[(load2pred (placet (v), i, t)
i=0−load′2
pred (placet (v), i, t))2−(c · overpred(placet (v), i, t)′2−c · overpred(placet (v), i, t))].
′(p, i, t) denote the values
Here, load′pred (p, i, t) and overpred
obtained from loadpred (p, i, t) and overpred (p, i, t), respectively, by removing v from p.

C. Migration algorithm
In our proposed method, every virtual node independently
checks its current payoff at regular intervals, and migrates toanother physical disk if it yields a better payoff. Because themodel introduced above is a potential game, any migrationthat improves a virtual node’s payoff increases the value of the
global function. However, owing to the limitation of network

Lv (place′ ) − Lv (place),
M igtime (v, pfrom , pto )where pfrom and pto (∈ P ) denote the source and destinationof migration, respectively, and M igtime represents the timerequired to migrate v from pfrom to pto . This function is defined
as follows:diff(v, pfrom , pto )M igtime (v, pfrom , pto ) =min{bw(pfrom ), bw(pto )},where diff denotes the total amount of data that must be transferred for the migration of v from pfrom to pto , and bw represents the bandwidth of p, defined as bw(p) = (1−β)capload (p)(with 0 < β ≤ 1). Note that β is the same predefined constantas in the global function.
In a real system, the evaluation of payoffs and migration
are autonomously controlled by the physical nodes on thebasis that the virtual nodes behave as selfish agents. Roughly
speaking, every physical node (denoted by p) independently
collects information to evaluate the payoffs from its neighboring nodes. (As we shall see in Section IV, the set ofneighbors for each physical node is predetermined. This set
consists of 100 neighbors in our simulation.) Then, p selects
the best migration, and sends a request to the destination.
The destination node decides whether to accept or reject therequest. If it is accepted, the migration starts immediately;otherwise, it is rejected. Note that, to reduce the migration
cost, physical nodes are allowed to send or receive one virtual
node at a time.
More precisely, every physical node (denoted by p ∈ P )independently executes the following steps at regular intervals.
(Here, the current time is indicated by t ∈ T .)1) p obtains the following information from each of its
neighboring nodes (denoted by p′ ∈ P ).
′• Estimated workload: loadpred (p , i, t);′′• Amount of free space: capvol (p ) − size(p );• The value of the migration that p is executing:M igeval (v, pfrom , pto ), where v is the virtual nodethat is currently migrating from/to p′ .
2) Among all possible migrations for the virtual nodes inp and the migrations previously requested to p, find thebest migration (whose virtual node is denoted by v)
yielding the largest M igeval (v, p, p′ ). If there is no such
v (i.e., M igeval (v, p, p′ ) ≤ 0 for any v), then p quits andreturns to Step 1 in the next time interval. Note that thecurrently migrating virtual node is also included as a
candidate.
3) Execute one of (3-a)–(3-d) according to the current state:In closing this section, we comment on the migration cost.
Instead of moving all data stored in a virtual node, there is analternative that reduces the volume of data to be migrated.
That is, when a virtual node is removed from a disk, thestored data remain in the disk and are reused at the time of
the next migration. This enables the migration to proceed bycopying only those data that are different from the previous
residence at that physical node. Indeed, the advantage of thistechnique is the trade-off with the disk space. However, if thesystem has enough space on the disk and can afford to create
some redundancy, this technique can be useful for effective
migration. We adopt this technique in our simulation andexperiments, as reported in later sections.
IV. S IMULATION R ESULTS
To understand the scalability of our method for storage
systems consisting of thousands of physical nodes, we conducted a series of simulations in various environments. Theseevaluated the performance by observing the change in thenumber of active physical nodes, average response time, andcumulative number of migrations.
A. Parameters and Settings
In the evaluation, we considered a system consisting of
1,000 physical nodes whose volume and workload (i.e., maximum transfer rate of data access) capacities are 500 GB and 55
MB/s, respectively. As per the suggestion in [14], the numberof virtual nodes is 10 times the number of physical disks.
The system stores 200 million files, each of size 500 KB, andthese are randomly allocated between the virtual nodes. In
the intended usage environment, we assumed that the system
workload varies over a day.
During the course of a day, as modeled by discrete timeintervals t (s) with 0 ≤ t ≤ 3, 600 ∗ 24, the workload of all
virtual nodes is initially at its lowest, then increases until the
middle of the day, before decreasing until the end, where thegap is 4-fold. As suggested by many studies (e.g., [3], [12],[10]), we assumed that the data access frequency conforms
to a Zipf distribution [21]. According to this law, the accessfrequency of the r-th most popular file is determined by the

The number of active physical nodes(3-a) If v is currently migrating from p to p′ , thenthe migration continues;(3-b) If v ∈ p and p is asking its neighbor to receivev, but this has not yet been approved, then pcontinues to wait for a response;(3-c) If v ∈ p and p has not asked its neighbor toreceive v, then p drops its current request thatwas previously sent to a neighbor, and asks thedestination to receive v.
(3-d) If v ̸∈ p, then p drops the request that waspreviously sent by p to a neighbor and themigration currently being executed, and thenapproves the migration of v;
4) Reject all other requests from the neighbors.

1000
800
600
400
200
0
2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Time (day)Fig. 1.

Number of active physical nodes

following formula:1

loadr (t) = loadsys (t) ∑Frα1i=1 iα,where F is the total number of files, loadsys indicates thetotal number of data accesses, and α is a coefficient. In
our simulation, we consider the case where α = 0.7. Thus,
the workload of the system is determined by the following
formula:{3t
22, 000 ∗ ( 12∗3,600+ 1)(0≤t<12∗3,600)
loadsys (t) =3t22, 000 ∗ (− 12∗3,600 + 7) (12∗3,600≤t<24∗3,600).
For example, the total number of accesses is 22,000 during
the off-peak period, rising to 88,000 at peak time. Note that if
we consider a static configuration (i.e., without our method),
it is necessary to make 800 physical nodes active to deal withthe workload in this setting.
As mentioned in Section III, after migrating a virtual node,
the stored data remain at the source physical disk unless it
overflows. Thus, we reuse the remaining unchanged data whenthe virtual node returns to its original position. We assumed
that 10% of files are rewritten by write accesses during thecourse of a day.
Finally, the remaining parameters were as follows: In the
global function defined in Section III-B, we set s = 30 ∗ 60,
β = 0.9, j = 15. The neighbors for each physical node pi are{pj | i − 50 ≤ j ≤ i − 1, i + 1 ≤ j ≤ i + 50}. Note thatthe future workload was estimated using only the workloads
of 15 and 30 minutes ago.
B. Number of Active Physical Nodes
Fig. 1 indicates the change in the number of active physical nodes for the 5 days following the initial configuration.
(Throughout this section, we omit results from the first 2 days,
because from the 3rd day, reusable data are spread across thesystem by the migrations in the first 2 days.) Fig. 1 showsthat the number of active physical nodes, indicating the total
running time, was reduced by an average of 17.3% relative tothe static configuration.

400

40000

200

20000

0

0
2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Cumulative number of VN migrations

60000

Average response time
Maximum response time

Maximum response time (ms)Average response time (ms)600

300000250000200000150000100000
50000
0
2

2.5

3

3.5

Time (day)Fig. 2.

Num. of Nodes [%]
14.4
12.7
18.7
16.9

Response time

Ave. Res. [ms]
142
190
130
128

4.5

5

5.5

6

6.5

7

Time (day)Fig. 3.

TABLE IS IMULATION RESULTS FOR C ASES 1–4
Case 1Case 2
Case 3
Case 4

4

Max Res. [ms]79,638159,358
157,345
56,124

C. Response Time and Migration Cost
Figs. 2 and 3 indicate the change in the overall averageand maximum response time and the cumulative number of
migrations during the 5 days, respectively. Fig. 2 shows thatthe overall average response time was 121 ms, although the
maximum was 44,134 ms. The results of this experiment showthat roughly the same number of virtual nodes were migrating
regardless of the system workload. For each virtual node, there
were an average of 5.27 migrations. In our previous work [5],the number of migrations required of each virtual node wasabout 2 in a similar environment, which is fewer than half thenumber required using this method.
Our method has room for improvement in the response timeat peak times, as well as in reducing the number of migrations.
On the whole, however, our method effectively skews theworkload while keeping a preferred overall average responsetime in a large-scale system.
D. Flexibility toward Various Environments
To evaluate our method in various environments, we considered the following cases, which cannot be treated using ourprevious method [5]:Case 1:Peak times of some virtual nodes are different fromothers.
Case 2:Distribution of popularity changes over time.
Case 3:Some physical nodes are added to the system.
Case 4:Some physical nodes are removed from the system.
For Case 1, we considered the environment where 80% of
the virtual nodes encounter peak time at noon, while for theothers this occurs at midnight. For Case 2, we changed thedifference in workload between peak and off-peak times tobe 8-fold for 10% of the virtual nodes, and to be a factor of
32/9 for the other 90%. For Cases 3 and 4, we added 50 andremoved 30 physical nodes, respectively.

Cumulative number of migrations

The results for each case are summarized in Table I. (Here“Num. of Nodes”, “Ave. Res.”, “Max Res.” denote the resultsof reducing the number of active physical nodes relative tothe static configuration, overall average response time, andmaximum response time, respectively.) Overall, although insome cases the performance worsened, our method was able
to effectively skew the workload, adapting to various changes
in environment.
V. I MPLEMENTATION E XPERIMENTS
We conducted experiments with the current prototype implementation to evaluate the applicability of our method toreal systems. In the experiments, we measured the change in
the number of active physical nodes and the response time inan environment with a variable system workload.
Our prototype consisted of 28 PC servers, each of which
was equipped with Intel Core i7 2.67 GHz × 8 CPUs,
11.8 GB memory, and a single 500 GB ATA disk. In this
implementation, we omitted the DHT mechanism.
A. Parameters and Settings
The system consisted of 300 virtual nodes, each of which
stored 5.6 million files of size 500 KB. In this experiment,
the distribution of data access frequency was also assumed toconform to Zipf’s law. At off-peak times, the system workload
was 1,209,600 accesses/s, and this increased to 4,838,400
accesses/s at peak times, similarly to the simulations.
For this setting, if we consider a static configuration, it isnecessary to make 23 physical nodes active to deal with theworkload.
B. Number of Active Physical Nodes
Applying this configuration, we observed the performancefor 24 h. Fig. 4 indicates the change in the number of active
physical nodes. The figure shows that our method reduced
this number by an average of 14.1% relative to the static
configuration. This result shows that our method adjusts thenumber of physical nodes to changes in workload, and reduces
power consumption effectively.

The number of active physical nodes

response time in a large-scale distributed environment.
In future work, we will improve the migration algorithm
so as to reduce the latency at peak-time. We are also interested in an evolutional mechanism to allow virtual nodes toautonomously change the parameters of local payoff functions
according to the current environment, with the aim of achieving a better optimization.

30

20

10

R EFERENCES

0
0

4

8

12

16

20

24

Time (hour)

Average response time (ms)200

Number of active physical nodes
8000

Average response time
Maximum response time

150

6000

100

4000

50

2000

0

Maximum response time (ms)Fig. 4.

0
0

4

8

12

16

20

24

Time (hour)Fig. 5.

Response time

C. Response Time
Fig. 5 indicates the change in the average and maximum
response times. This figure shows that the overall average
response time was 50 ms, while the maximum was 6,573 ms.
We observed some long delays in responses at peak time, buton the whole, our method retains an intended latency in thereal system.
VI. C ONCLUSIONS AND F UTURE W ORK
In this paper, we presented a game theoretic approachfor reducing power consumption in datacenter-scale storage
systems. To enhance the scalability in a commonly-observed
technique, our method was based on DHTs to dynamicallymigrate virtual nodes, thereby skewing the workload andavoiding overloads. Moreover, to improve the flexibility problem in the method of [5], we investigated a technique thatallowed virtual nodes to freely migrate to any neighboringdisks, thereby enabling autonomous adaptation to various
changes of environment, such as changes in the popularity
distribution, extension of a system, and node failures. For thisobjective, the idea behind our method was to consider virtual
nodes as selfish agents, and play a game in which each node
receives a payoff according to the workload of the disk onwhich it currently resides. This idea was modeled as a potential
game using the Wonderful Life Utility technique. We also evaluated the performance of our method using simulations and a
prototype implementation. The results showed that our method
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