An Elastic Cache Infrastructure through Multi-level Load-balancing

Carlos L

ubbe and Bernhard Mitschang

IPVS, University of Stuttgart, Universit

atsstraße 38, 70569 Stuttgart, Germany

Keywords:

Load-balancing, Spatial Cache, Spatial Data Processing, Peer-to-Peer System.

Abstract:

An increasing demand for geographic data compels data providers to handle an enormous amount of range

queries at their data tier. In answer to this, frequently used data can be cached in a distributed main memory

store in which the load is balanced among multiple cache nodes. To make appropriate load-balancing deci-

sions, several key-indicators such as expected and actual workload as well as data skew can be used. In this

work, we make use of an abstract mathematical model to consolidate these indicators. Moreover, we propose

a multi-level load-balancing algorithm which considers the different indicators in separate stages. Our eval-

uation shows that our multi-level approach signiﬁcantly improves the resource utilization in comparison to

existing technology.

1 INTRODUCTION

Geographic data is becoming increasingly important,

since the rapid proliferation of Internet-ready mobile

devices have made location based services (LBS) ac-

cessible to a large crowd of users. As LBS typically

operate on data referring the user’s current vicinity,

data providers need to be able to cope with a massive

amount of requests for data of speciﬁc geographic re-

gions. A lot of these requests can be cached in a

distributed main memory store which provides efﬁ-

cient access to most frequently used data. Key play-

ers make use of similar concepts to cope with massive

load, e.g. Facebook uses Memcached to cache fre-

quently used data in main memory and many others

make highly requested data on dedicated edge servers

available. In such a distributed system, it is essential

to balance incoming load among participating cache

nodes to provide high throughput during the entire ex-

ecution process. For that matter, speciﬁc challenges

have to be considered.

First of all, spatial data is not spread uniformly

across the world but rather relates to the density of

geographic features or the degree of development of

represented areas. As obviously more cache mem-

ory is needed to cover regions with high data density

than sparsely occupied areas, it is essential to con-

sider data skew to adequately allocate cache memory

during load-balancing. Furthermore, the workload is

not equally scattered throughout the data space. In

fact, large areas are likely to be not requested at all,

as approximately 70% of the world is covered by wa-

ter being typically of little interest by the majority of

people. Thus, it is crucial to consider the expected

workload and reserve resources for those areas which

are most likely to be requested. Finally, effective

load balancing must also react to dynamic load peaks

when the actual workload deviates from anticipated

patterns.

Existing load-balancing mechanisms are limited

to one of the three above-mentioned indicators. For

instance, (Aberer et al., 2005), focuses on data skew

only, (Scholl et al., 2009), addresses only expected

workload and many other approaches, such as (L

ubbe

et al., 2012; Wang et al., 2005), solely focus on dy-

namic load-peaks. Fully relying on a single indica-

tor can lead to inadequate resource allocation during

load-balancing.

To substantiate our argument, we use an example

of a maritime region comprising little islands and a

huge offshore portion. In this area, the data is dis-

tributed nonuniformly with higher concentration in

insular regions. An oil spill, ship wreckage or any

other critical event will suddenly raise disproportion-

ately high interest in the area around the event’s lo-

cation. In consequence, a purely dynamic approach

clusters a huge amount of memory to cache data in

the sea area around the accident, although at that lo-

cation only marginal data exists. This overcompensa-

tion can lead to poor resource utilization which com-

promises the overall performance of the system, as the

resources would have been needed elsewhere, e.g., to

183

Lübbe C. and Mitschang B..

An Elastic Cache Infrastructure through Multi-level Load-balancing.

DOI: 10.5220/0004486001830190

In Proceedings of the 2nd International Conference on Data Technologies and Applications (DATA-2013), pages 183-190

ISBN: 978-989-8565-67-9

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Overview.

load

(a) Land mass ρ

load

(b) Data density ρ

load

(d) Holistic distribution ρ

Figure 2: Examples for distribution functions (L

ubbe et al., 2013).

cache data of insular regions.

The different load-balancing indicators data skew,

expected workload and dynamic load peaks can all

be consolidated into a comprehensive mathematical

model (L

ubbe et al., 2013). In this work, we im-

plement a distributed and elastic main memory cache

supporting multi-level load-balancing which consid-

ers the different indicators of the abstract model in

separate stages. The ﬁrst stage prepares the cache net-

work for expected workload while the second adapts

to unexpected load peaks. We systematically evalu-

ate the approach in the above-mentioned realistic sce-

nario. Our evaluation shows that our implementation

signiﬁcantly improves the resource utilization in com-

parison to a conventional algorithm.

2 FOUNDATIONS

As this paper builds upon the ideas of previous work

ubbe et al., 2011; L

ubbe et al., 2012; L

ubbe et

al., 2013), this section outlines their major contribu-

tions. First, we describe the general architecture of

the distributed main memory cache. Then, we present

a strategy to to control the overall cache content of

participating cache nodes. Finally, we summarize our

abstract load-balancing model.

Overview. (L

ubbe et al., 2011) introduced data struc-

tures and algorithms to store spatial data on a single

node. The work bases on a general data model com-

prising objects which contain an obligatory attribute

delineating the spatial extend of the object and arbi-

trary additional non-spatial attributes. Thus, a single

node can use the cached objects of previous queries

to process a given range query. Combining multi-

ple of these cache nodes to a distributed spatial main

memory cache, allows scalable access to frequently

used data. Figure 1 depicts the general architecture

of such a system. In the distributed infrastructure,

cache nodes process requests cooperatively using the

cached data of previous queries and may fetch miss-

ing data from the data back-end which stores the com-

plete data set. Due to the considerable high spatial and

temporal overlap between succeeding queries, most

requests can be served by the distributed spatial cache

which leads to a reduction of back-end accesses. To

achieve a high cache hit-rate during execution, it is

essential to control the cache content of participating

nodes as elaborated in the following.

Cache Content Control. To control the overall cache

content of the distributed spatial cache, (L

ubbe et al.,

2012) introduced a dedicated replacement strategy,

denoted as focused caching. In this strategy, we as-

sign each cache node a point in space, denoted as its

cache focus. Once the capacity of a node has been

reached, the node replaces the data with the highest

Euclidean distance to its cache focus in order to free

up space for new data. As a single node will thus

rather keep data near its cache focus, the overall cache

content can be controlled by moving the cache foci of

participating nodes into certain regions. Increasing

the density of cache foci in a geographic area also en-

larges the amount of memory allocated for that region

and thus raises the cache hit-rate for queries which

request data of that particular region. This observa-

tion forms the basis of this paper’s approach which

positions the cache foci according to dedicated distri-

bution functions characterized in the following.

Abstract Distribution Model. In (L

ubbe et al.,

2013), we introduced an abstract mathematical model

to describe load distributions as probability density

functions. Formally, such a distribution function can

be deﬁned as a two-dimensional function ρ : R

→ R

which maps geographic coordinates to an abstract

measure representing load. To balance load, we can

use such distribution functions to distribute the re-

sources, i.e. the cache foci, in the same way.

Load distribution functions can be classiﬁed into

anticipated, dynamic and holistic distributions. An-

ticipated distributions express statistical analysis of

previous workloads, heuristic assumptions about the

expected workloads or prior knowledge on data skew.

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(z)

uniform distribution

custom distribution

(a) Cumulative distribution

0 1 4 5

2 3

8 9 12 13

10 11 14 15

(b) Z-Curve

Figure 3: Generate custom distributions of cache foci.

These indicators play an important role in ﬁnding an

adequate resource allocation, as they enable to pre-

pare for expected situations before the actual load

strikes the system. For instance, assuming that users

mainly request onshore data we can deﬁne ρ

which

returns 1 in onshore regions 0 otherwise, as depicted

in Figure 2(a). A resource allocation according to this

function distributes the cache foci uniformly within

land parts and cuts out the sea areas. This coarse

model can be reﬁned by function ρ

which returns

the number of objects per area. As shown in the bot-

tom part of Figure 2(b) this clusters the cache foci

in regions with high density and thus increases the

cache memory for data-intensive areas. Dynamic dis-

tributions measure the actual workload at a certain

point in space. Our example ρ

uses the positions of

the cache foci to situate the node’s current workload

(queries per second) in space. Due to unforeseen load

peaks, the actual workload may deviate from antici-

pated patterns, as visualized by the high peak in the

middle of Figure 2(c). With regard to the negligible

amount of data present in this area, we can observe a

clear oversupply of cache memory. For this reason, it

can be beneﬁcial to fuse multiple aspects into a sin-

gle holistic distribution. Our example ρ

incorporates

and ρ

in equal shares. Thus, we obtain an allo-

cation which prioritizes regions where both workload

and data density is high, as observable in Figure 2(d).

3 IMPLEMENTATION

This section describes the concrete implementation of

the abstract load-balancing model. For that we inte-

grated the example distribution functions of the ab-

stract model into our system (see Section 3.1). Based

on link structures among the nodes of the cache net-

work, we propose a ﬂexible reorganisation scheme

supporting multi-level load-balancing (see Section

3.2). Finally, we implement an algorithm which uses

the distribution functions of the abstract model to re-

alize multi-level load-balancing (see Section 3.3).

3.1 Integrating Distributions

The distribution functions of Figure 2 form an ex-

ample of a concrete load-balancing model which is

likely to be needed by a service provider of an LBS.

Other application domains may require different mod-

els, however. For this reason, our system supports ar-

bitrary load-balancing models by the inclusion of cus-

tom distribution functions. From these custom distri-

bution functions, we derive resource allocations (i.e.

distributions of cache foci) which are tailored towards

the service provider’s speciﬁc needs. In the follow-

ing, we present a method to calculate the positions of

cache foci using custom distributions. During our ex-

ample, we use a two-dimensional Gaussian distribu-

tion, denoted as ρ

, as representative for an arbitrary

custom distribution.

With probabilistic methods, a standard uniform

random number generator can be extended to do this

task. Best practices for the one-dimensional case can

be found in (Grinstead et al., 2006). However, ad-

ditional efforts are required for our two-dimensional

functions. For this reason, we applied a z-ordering

(Morton, 1966) to discretize a given distribution func-

tion ρ

and to map the two-dimensional coordinates

to one dimension. For each of the z-numbers, we

precomputed the corresponding function values of

and composed the cumulative distribution func-

tion C

(z) =

∑

i=z

i=0

, y

), where x

, y

represent

the two-dimensional coordinates of the z-number z

The inverse of C

can be used to obtain random z-

numbers according to the original distribution func-

tion ρ

. As depicted in Figure 3(a), the z-numbers

which correspond to the uniform samples of the or-

dinate have the same frequencies as deﬁned by our

Gaussian distribution function ρ

. Thus, for a given

uniform random number r with 0 ≤ r < 1, we used

−1

to retrieve the corresponding the z-number z

. To

obtain the ﬁnal result, we generate a uniformly dis-

tributed random point within the corresponding cell

of z

(see Figure 3(b)). These points closely match

the distribution function ρ

(minus a negligible dis-

cretization error). With this method, we can produce

scattered point sets of any distribution function, such

as our examples of Figure 2. Note, that any space-

ﬁlling curve could have been used for this task. We

used a z-ordering because it is straightforward to im-

plement and yet very efﬁcient to compute. For our

evaluation scenario (see Section 4) we achieved sufﬁ-

cient results in terms of transformation accuracy with

a 5th order z-curve which comprises 32 cells in each

dimension, i.e., 1024 cells in total.

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3.2 Network Structure

In our system model, we assume the cache nodes to be

connected via a communication protocol such as the

Internet Protocol (IP), i.e., nodes can send or receive

messages using distinct network addresses. On top

of this communication structure, we assume a large

number of nodes that can unexpectedly join or leave

our network of cache nodes. Each node keeps the net-

work addresses of a respectably small subset of nodes,

thus limiting the impact of unexpected node join or

departure to local parts of the cache network. When

two nodes mutually know their network addresses, we

say they are connected via a link. Similar to com-

mon peer-to-peer models such as (Stoica et al., 2001),

every node in the cache network can be reached via

multiple-hop routing over the links. We continue with

a detailed description of distributed request process-

ing, describe how to maintain the cache network and

ﬁnally propose a mechanism to reorganize the net-

work structure during load-balancing.

Distributed Query Processing. To enable efﬁcient

processing of range queries, the geographic relation

of the data being cached by the nodes has to be re-

ﬂected in the link structure of the cache network. A

Delaunay triangulation of the cache foci constitutes

such a link structure which preserves the topological

relationship. Figure 4 depicts a Delaunay triangula-

tion where triangle vertices (black dots) represent the

cache foci and the triangle edges (bold lines) repre-

sent links between the corresponding nodes. The De-

launay property is met when no vertex exists which is

inside the circumcircle of any other triangle (a formal

deﬁnition can be found in e.g. (de Berg et al., 2000)).

In a Delaunay-based link topology, it is possible to

apply greedy routing, i.e., a node forwards a given

query to the neighbor that has the closest cache focus

to the requested query region until no closer neighbor

is found. The node at which greedy routing termi-

nates processes the query, as it has the closest cache

focus and thus most likely keeps the requested data in

its cache. In case of cache misses, the node fetches

missing data from the data back-end. On an arbitrary

graph greedy routing does not always ﬁnd the global

optimum, but prematurely terminates at a local opti-

mum which is not closest to the query region. How-

ever, it is proven in (Bose et al., 1999) that greedy

routing always succeeds to ﬁnd the closest node for

Delaunay-based link topologies.

For performance reasons, we do not force the

whole link topology to be coherent to the Delaunay

property all the time, but occasionally allow minor

deviations from that property in certain parts of the

link structure. Consequently, the accuracy of greedy

(a) Greedy routing

(b) Delaunay test

Figure 4: Move a node’s cache focus position.

routing will degrade, as the global optimum can not

always be found in a non-perfect Delaunay triangu-

lation. Nevertheless, this does not inﬂuence the cor-

rectness of the query results as every node is able to

request missing data from the data back-end. Yet, in-

accurate routing may decrease the cache hit-rate, as

a mislead query will be processed by a node whose

cache focus is not closest to the query region and thus

may not have cached as much of the requested data

as the optimal node. In our system, the movement

of cache foci may violate the Delaunay property in

certain regions and thus decrease the cache hit-rate.

Therefore it is necessary to reorganize the link struc-

ture once the routing accuracy has been decreased too

much.

Network Maintenance. Particularly for application

ﬁelds that can cope with partial routing inaccuracy, a

set of protocols were devised which are able to estab-

lish and maintain a Delaunay-based link topology in a

distributed setting under node churn, so that nodes can

join or leave unexpectedly (Lee et al., 2008). More-

over, it has been shown that the topology converges to

an accurate Delaunay topology once the churning has

stopped. In particular, this property is extremely use-

ful for our purposes, as it ensures that the system’s

efﬁciency returns to normal after adapting to node

churn or repositioned cache foci. Thus, this mainte-

nance protocol can be used for node joins and depar-

tures. However, to provide the ﬂexibility needed for

our multi-level load-balancing, we extend this proto-

col in the following section.

Network Reorganisation. The maintenance protocol

outlined in the previous section can be extended by a

new primitive MOVE which moves a node’s cache fo-

cus to a certain position and updates the link structure

if required. Figure 4(a) depicts an exemplary network

before a node has moved. Suppose that the cache fo-

cus of node a ought to be moved into the center of

triangle (c, d, e). With greedy routing (visualized as

red arrows) we are able to ﬁnd the closest node to

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the destination position which is node d in our exam-

ple. Node d splits the destination triangle into three

new triangles and checks whether the new triangles

violate the Delaunay property. In our example it dis-

covers that the triangles (c, a, d) and (a, e, d) violate

the Delaunay property as b and f are contained by the

circumcircle as shown in Figure 4(b). Then node d

ﬂips the edges (c, d) and (d, e) to obtain a triangula-

tion as depicted in Figure 4(c). As the ﬂipped edges

may in turn violate the Delaunay property of differ-

ent triangles this process is recursively repeated until

no violations are found anymore. Then node d in-

forms the involved nodes (i.e., nodes b, c, e and f )

about the changed link structure. As the ﬂipped edges

may in turn violate the Delaunay property of different

triangles this process is recursively repeated until no

violations are found anymore.

3.3 Multi-level Load-balancing

Our multi-level load-balancing approach operates in

two stages. The ﬁrst stage determines a node’s ini-

tial cache focus when joining the cache network. The

second stage organizes the continuous repositioning

of cache foci during run-time.

Initial Cache Focus Positions. When a node joins

the cache network, we use an anticipated distribution,

such as our examples ρ

or ρ

of Figure 2 to calculate

the initial position. Greedy routing ﬁnds the closest

node which inserts the new node into the encircling

triangle of the calculated position. We assume that

each node determines its initial cache focus position

individually. Thereby it is crucial that all nodes use

the same anticipated distribution to determine their

initial position. In this manner, the nodes can au-

tonomously organise the positions of their cache foci

during the network construction and thus prepare the

system layout for anticipated load patterns.

Cache Focus Update. The general idea is that nodes

use ρ

of Figure 2 to periodically calculate a new po-

sition and move their cache focus towards it. To avoid

rapid zig-zag movements of cache foci and to ob-

tain a smooth distribution of resources, we base upon

standard k-means (Macqueen, 1967), which we ex-

tended to our distributed environment. Subsequently,

we sketch the procedure in pseudo code:

1: procedure UPDATEPOSITION(P =

, p

, . . . p

})

2: Initialize indices i

← 1, ∀ j = 1, 2 . . . k

3: repeat

4: r ← Random point according to ρ

5: Find the closest point p

∈ P to r

6: p

←

∗p

7: i

← i

+ 1

8: until Average distance of the last λ move-

ments is lower than threshold τ

9: Initiate topology re-organisation for all

changed p

10: end procedure

Each node periodically executes UpdatePosition,

where P comprises the position of its cache focus

and all the cache foci of its direct neighbors. In the

interpretation of k-means, these positions resemble

the centers of k clusters. In each iteration, the al-

gorithm generates a random point r according to ρ

ﬁnds the closest cluster and updates the cluster cen-

ter p

. The iteration stops when the average distance

of the last λ movements is lower than a threshold τ.

In other words, the algorithm converges when our ac-

curacy criterion deﬁned by λ and τ is met. This is

the state in which the points are smoothly distributed

according to ρ

. If the position of a node’s cache fo-

cus has changed during the computation, it initiates

a topology re-organization using the MOVE primitive

(see Section 3.2). Empirical analysis exposed that

the algorithm produces sufﬁcient results for the val-

ues λ = 20 and τ = 50 m which we used throughout

all our experiments. In addition, we obtained accept-

able adaption rates using an update period of 5 s.

4 EVALUATION

In this section, we focus on examining the system

properties in respect to adequate resource allocation.

To measure the quality of resource allocation, we

begin with characterizing the adequateness of our

caching strategy in respect to given data requests. To

measure this aspect, we use the cache hit-rate. For a

given query, we deﬁne the hit-rate as the number of

objects retrieved from the cache divided by the num-

ber of objects satisfying the query. If no object sat-

isﬁes the query, nodes can often avoid sending a re-

quest to the data back-end, as they internally mark

empty regions. Thus, to avoid undeﬁned values in the

empty result case, we deﬁne the cache hit-rate as 1 if

no back-end request was sent and 0 otherwise.

Furthermore, we look into the distribution of

workload among the nodes. Thereupon, we measure

the deviation of all nodes from the average workload

in the system. Let avg

be the average workload of all

n nodes at a time t and ω

t j

the workload of node j at

time t, then the average deviation can be deﬁned as:

dev(t) =

∑

j=1

|ω

t j

− avg

(1)

From that we obtain

AnElasticCacheInfrastructurethroughMulti-levelLoad-balancing

187

(a) Resource initialization with ρ

(b) Resource initialization with ρ

Figure 5: Visualization of the cache network.

dev(t) =

1 + dev(t)

(2)

which constitutes our normalized optimality measure

for workload distribution.

We evaluated our approach by simulation using

PeerSim (Montresor et al., 2009), which bases on a

discrete event-driven simulation model. PeerSim is

able to simulate peer-to-peer networks. We extended

PeerSim in order to simulate our density-based spatial

cache network. The simulation bases on real world

data of the Italian island Giglio and its surroundings

extracted from OpenStreetMap. The data set com-

prises a total number of 36 777 objects. It covers

an area of roughly 32 × 35 km, in which data is not

spread evenly, but rather resembles the density of ge-

ographic features in the land parts of the coastal re-

gion. On top of this data, we emulate range queries

(500 x 500 m) at a rate of approximately 83 queries

per second. I.e. every 12 ms a query is sent to a ran-

domly chosen node in the cache network. The cache

network comprises a total number of 100 nodes which

are initialized with empty caches.

To compare our multi-level load-balancing al-

gorithm with a purely dynamic approach, we used

the load-balancing mechanism of our previous work

ubbe et al., 2012) which bases upon a particle-

spring model. In this model, the particles represent

the cache foci which are interconnected by springs.

Load-balancing is achieved by spring contraction in

regions with high load. Furthermore, we initialized

the particle-spring system by distributing the cache

foci uniformly across the space in rows of 10 cache

foci in each dimension. The optimization goal of the

load-balancing algorithm can be tuned towards work-

load and cache occupancy. Workload is deﬁned as

queries per second, while cache occupancy is deﬁned

as the number objects cached by a single node divided

by the area it covers. For spatial data sets that do

not contain vast empty areas this is a good approxi-

mation of the data density. However, in our scenario

which contains huge empty regions, this measure is

imprecise which leads to faulty load-balancing. For

that reason, we used a workload-only setting for all

our experiments. Through a speciﬁc parameter, β, the

stiffness of the particle-spring system and thus inﬂu-

ences the adaption speed of the load-balancing algo-

rithm can be inﬂuenced. For each of the following

experiments, we empirically determined the most ad-

vantageous setting for β and compared the best results

of this parameter setting with the results of our multi-

level approach. In the following, we ﬁrst examine the

system behavior when the actual load matches antici-

pated workload patterns. Then we study the effects of

deviation from the anticipated workload patterns.

4.1 Anticipated Workload

To examine the system behavior under anticipated

workload, we initialized our system with a node ca-

pacity of 800 objects per node and distributed the

cache foci according to ρ

, i.e. a uniform distribution

within land parts as visualized in Figure 5(a), and ρ

i.e. a data density-based distribution as depicted in

Figure 5(b). Then we emulated a uniform distribution

of 5 000 queries within the land parts. The simulation

lasts for 1 min of simulation time. Figure 6(a) depicts

the hit-rate during the simulation. One can observe a

slightly better hit-rate for the data density-based dis-

tribution ρ

. The reason for this is the concentration

of cache memory in regions with a lot of data which

is a more suitable resource allocation strategy for our

data set. As it can be observed in Figure 5(b) data is

not distributed evenly within land parts, but is slightly

denser on the western island. Obviously, the more

non-uniformly the data is spread within land parts, the

better the data density-based resource allocation will

get. Moreover, we examined the optimality of work-

load distribution in Figure 6(b). The geometry-based

resource allocation slightly outperforms the density-

based allocation, as it distributes the resources uni-

formly within the land parts which match exactly

our expected workload. Alongside, we examined

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0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

hit-rate

simulation time [min]

(a) width=3.5cm

0.52

0.54

0.56

0.58

0.6

0.62

0 0.2 0.4 0.6 0.8 1

dev(t)

simulation time [min]

(b) Workload distribution

Figure 6: System parameters under anticipated workload

[capacity=800].

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5 1 1.5 2

hit-rate

simulation time [min]

δ=1.0

δ=0.5

δ=0

(a) Hit-rate

0.48

0.49

0.5

0.51

0.52

0.53

0.54

0.55

0.56

0.57

0 0.5 1 1.5 2

dev(t)

simulation time [min]

δ=0

δ=0.5

δ=1.0

(b) Workload distribution

Figure 7: System parameters under deviated workload [ca-

pacity=300].

our purely dynamic particle-spring approach (PS) of

previous work (L

ubbe et al., 2012) under the given

workload using β = 13. The results show the clear

supremacy of static load-balancing provided that the

actual workload meets the anticipated patterns.

4.2 Deviated Workload

To examine the system performance when the actual

workload deviates from anticipated patterns, we emu-

lated a hot spot of 5 000 queries in the sea area accord-

ing to a Gaussian distribution with a standard devia-

tion of 1 500 m. The hot spot workload comes on top

of anticipated workload, thus adding up to total work-

load of 10 000 queries. Moreover, we inspect the im-

pact of scarce resources on the system performance.

For that reason, we reduced the node capacity to 300

objects per node, i.e. with a total number of 100

nodes, the overall capacity of the cache memory sums

up to 30 000 objects which is approximately 80 % of

the complete data set size. We initialized our sys-

tem with ρ

(uniform distribution within land parts)

and used ρ

continuous adaptation towards the actual

load. In our example ρ

incorporates both ρ

and ρ

The parameter δ allows weighting between these two

aspects. Figure 7(a) depicts the hit-rate during the

simulation. The most obvious result is that compared

to Figure 6(a) all hit-rates have decreased. This is due

to the reduced node capacity. However, the best hit

rate is achieved by δ = 1, i.e. when the system favors

anticipated workload during load-balancing. This is

because most of the cache memory is preserved for

land parts where it is needed most. The hit-rate de-

grades slightly for lower values of δ. Contrary results

can be observed for the optimality of workload dis-

tribution in Figure 7(b) where low values of δ lead to

better results. In this case more nodes are assigned to

process the workload of the sea area which leads to

a better overall distribution of the workload between

the nodes. The particle-spring approach (β = 4) per-

forms quite well in terms of optimality of workload

distribution, as it is solely focused on distributing the

workload evenly among the nodes, but completely ig-

nores other aspects. The consequence is a disastrous

hit rate provoked by inadequate memory allocation.

5 CONCLUSIONS

The key aspects of load-balancing – data skew, antici-

pated workload and dynamic load peaks – can be con-

solidated into a single abstract mathematical model.

Static load-balancing techniques can only handle the

ﬁrst two aspects, but are useless in the face of un-

predictable load peaks. Dynamic approaches solely

focus on the last issue and suffer from inadequate re-

source allocation.

In this paper, we take advantage of an abstract

load-balancing model to implement a distributed and

elastic cache infrastructure which supports multi-

level load-balancing. Through multi-level load-

balancing, the advantages of both static and dy-

namic approaches can be exploited to achieve supe-

rior load-balancing facilities. We examined our ap-

proach in a scenario of skewed data, anticipated and

unpredictable workload. Compared with the purely

dynamic approach of previous work (L

ubbe et al.,

2012), we achieved signiﬁcantly better resource uti-

lization. In our concrete scenario, we could save up

to 40 % of back-end accesses in comparison to the dy-

namic approach.

We conducted our work with focus on the appli-

cation ﬁeld of spatial data processing. Beyond that,

our approach can be generalized to other application

ﬁelds which require high scale processing of data re-

quests over ranges, e.g., eScience applications in the

ﬁeld of astrophysics. In principle, the only require-

ment is that the data can be numerically ordered and

a distance metric exists. Thus, it is even possible to

consider high-dimensional data with more than two

dimensions. For future work we plan to explore dif-

ferent application ﬁelds and to analyse the impact of

high dimensionality on our mechanism.

AnElasticCacheInfrastructurethroughMulti-levelLoad-balancing

189

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DATA2013-2ndInternationalConferenceonDataManagementTechnologiesandApplications

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