THE ABORTION RATE OF LAZY REPLICATION PROTOCOLS

FOR DISTRIBUTED DATABASES

∗

Luis Ir

un-Briz, Francesc D. Mu

noz-Esco

ı, Josep M. Bernab

eu-Aub

Instituto Tecnol

ogico de Inform

atica

Universidad Polit

ecnica de Valencia

46071 Valencia, SPAIN

Keywords:

Replication, fault tolerance, reliability, distributed systems, databases, middleware, systems integration

Abstract:

Lazy update protocols have proven to have an undesirable behavior due to their high abortion rate in scenarios

with high degree of access conﬂicts. In this paper, we present the problem of the abortion rate in such protocols

from an statistical point of view, in order to provide an expression that predicts the probability of an object to

be out of date during the execution of a transaction.

It is also suggested a pseudo-optimistic technique that makes use of this expression to reduce the abortion rate

caused by accesses to out of date objects.

The proposal is validated by means of simulations of the behavior of the expression. Finally, the application

of the presented results to improve lazy update protocols is discussed, providing a technique to theoretically

determine the boundaries of the improvement.

1 INTRODUCTION

Nowadays, many distributed (i.e., networked) appli-

cations have to manage large amounts of data. De-

spite the increasing ubiquitousness of information,

the access patterns to distributed data often feature a

noticeable degree of geographical locality. Moreover,

many applications require a high degree of availabil-

ity, in order to satisfy the need of offering services

at any time, to clients that are either internal or ex-

ternal to the networked application. A predominance

of locality of access patterns usually suggests a parti-

tioning of the database (Gray et al., 1996). In many

scenarios, it may be convenient or even necessary to

replicate the information in a set of servers, each one

attending its local clients. The different replicas must

then be interconnected, a WAN being usually the best-

ﬁt architectural option.

The typical kind of applications we have in mind

are, for instance, widely distributed databases in

wide area intranets of medium and large enterprises,

for data warehousing or resource management, as

well as extranet service provisioning of such enter-

prises. Examples where such intranets of databases

∗

This work has been partially supported by the EU grant

IST-1999-20997 and the Spanish grant TIC2003-09420-

C02-01.

are deployed advantageously are enterprises with sev-

eral branch ofﬁces (e.g., banks, chains of retail-

ers, super- and hypermarkets), telecommunication

providers, travel businesses, logistics, etc. Examples

of extranet services which beneﬁt from replication

protocols as discussed in this paper are customer re-

lationship management, e-banking, virtually all kinds

of e-business as well as most e-government applica-

tions. Common to all of these applications is that

potentially huge amounts of data are maintained and

replicated on distributed sites, while access patterns

(or at least signiﬁcant contingents thereof) are highly

local. Efﬁciency and high availability of such services

is key to their acceptance and success.

The GlobData project (Instituto Tecnol

ogico de In-

form

atica, 2002; Rodrigues et al., 2002) strives to pro-

vide a solution for the kinds of applications just out-

lined. It does so by deﬁning a speciﬁc architecture

for replicated databases, together with an API and a

choice of consistency modes for data access. In the

GlobData architecture, a number of consistency pro-

tocols can be implemented and plugged, each one pro-

viding particular guarantees and behaviors.

During the development of the project, we encoun-

tered that the protocols necessities of our target sce-

nario (i.e. geographical distributed applications with

a high degree of locality) could be well-ﬁtted with a

130

Irún-Briz L., D. Muñoz-Escoí F. and M. Bernabéu-Aubán J. (2004).

THE ABORTION RATE OF LAZY REPLICATION PROTOCOLS FOR DISTRIBUTED DATABASES.

In Proceedings of the Sixth Inter national Conference on Enterprise Information Systems, pages 130-135

DOI: 10.5220/0002623301300135

 SciTePress

family of replication protocols classiﬁed as lazy up-

date protocols. However, we encountered that this

kind of protocols introduces a high number of abor-

tions in the system, because they propagate the up-

dates beyond the commit phase (in contrast to eager

update protocols, where the whole system is updated

inside the commit phase), making it possible for a

transaction to read out of date data, and thus, there

are consistency violations.

In (Mu

noz et al., 2002; Ir

un-Briz, 2003), we pre-

sented two consistency protocols, using different ap-

proaches for the update propagation.

Lazy update protocols have proven to have a crit-

ical inconvenience in contrast to eager approaches:

the dramatical increase of the abortion rate in scenar-

ios with a high degree of access conﬂicts. This in-

convenience makes unusable the traditional lazy up-

date protocols in certain scenarios, because an unac-

ceptable number of started transactions will terminate

with an undesirable abort.

To understand the problem, this work presents a

set of expressions describing the abortion rate. In the

presentation, we model a complete system including

nodes, the sessions executed, and the objects accessed

by the sessions. Moreover, we use our LOMP algo-

rithm as an example of a lazy update protocol where

all these expressions may be directly applied. A full

description of this protocol may be found in Section

3.2 of (Ir

un-Briz, 2003).

Section 2 includes the description of such modeled

system, in order to formalize an analysis of the abor-

tion rate in section 3. In section 4, an empirical val-

idation of the model is presented, and section 5 will

provide a theoretical analysis of an improvement of

the lazy approach. Finally, section 6 describes some

related work, and section 7 includes some conclusions

about the applicability of the expressions.

2 THE MODELED SYSTEM

One of the problems solved by the GlobData architec-

ture(Mu

noz et al., 2002) (called COPLA) is to ensure

the consistency among transactions being executed in

different database replicas. Multiple implementations

of the consistency management are possible, thus al-

lowing that a GlobData system could change its con-

sistency protocol at will. So, we use the COPLA ar-

chitecture as a platform to experiment with different

consistency algorithms working on the top of a trans-

actional system (in fact, a database) and replicated

over a distributed system.

The target system of our analysis follows a number

of considerations, designed to conﬁgure a scenario as

close as possible to a general environment that, al-

though simpliﬁed, is able to ﬁt the requirements of

the kind of environment we are centered in. This en-

vironment was described in the introduction, and has

considerations about client applications, system load,

pattern of accesses, interconnection network, etc.

In summary, these adopted assumptions are the fol-

lowing:

• There are K COPLA managers running in the sys-

tem. Each one can be considered as a “node”

k=1..K

• Each node in the system manages a complete

replica of the database. This database contains N

objects.

• We assume that the objects stored in the database

have a identiﬁer that is unique in the entire sys-

tem. In addition, each write operation performed

in a node includes an storage for each written ob-

ject of the local time the operation is performed, as

well as a version number of the written object.

3 PROBABILITY OF ABORTION

We can deﬁne the probability for a session S to be

aborted as: P A(S) = 1 − (P C

conc

(S) · P C

outd

(S))

where:

• P C

conc

(S) is the probability that the session con-

cludes without concurrency conﬂicts.

• P C

outd

(S) is the probability that the session con-

cludes without accessing to outdated objects.

The goal of this section is to determine the value

of P C

outd

(S), in order to predict the inﬂuence our

LOMP has into the abortion rate in the system. To this

end, we can calculate this probability in terms of the

probability of a session to conclude with conﬂicts pro-

duced by the access to outdated objects (P A

outd

(S)):

P C

outd

(S) = P C

outd

)

taking nr as the number (in mean) of objects read by

a session,

P C

outd

(S) = P C

outd

)

(1)

moreover, P C

outd

) is the probability for an object

to have an updated version in the instant the session

accesses it. This probability can be expressed in terms

of the probability for an object to be accessed in an

outdated version (P A

outd

)) as:

P C

outd

) = 1 − P A

outd

)

now, let’s see the causes of these conﬂicts: we took r

as an asynchronous object in the active node that has

not been updated since ut(r

); the outdated time for

satisﬁes δ(r

) = t(r

) − ut(r

); it can be seen that

P A

outd

) depends on the number of sessions that

THE ABORTION RATE OF LAZY REPLICATION PROTOCOLS FOR DISTRIBUTED DATABASES

131

write r

having the chance to commit during δ(r

Let P C

T,r

be the probability for another concurrent

session T (that has success in its commit) to ﬁnalize

with r

6∈ W (T ). Then,

P A

outd

) = 1 − (P C

T,r

)

where C depends on the number of write-sessions that

can be committed in the system during δ(r

) . . .

P A

outd

) = 1 − (P C

T,r

)

wtps

×δ(r

)

(2)

now, we can reformulate P C

T,r

as P C

T,r

P [r

6∈ W (T )] and, considering W (T ) =

, w

, . . . w

nw(T )

}, then in mean, it will be satis-

ﬁed that:

P C

T,r

P [r

6= w

j∈{1..nw}

]

taking nw as the mean of |W (T )| for every write-

session in the system.

P C

T,r

P [r

6= w

j∈{1..nw}

]

(3)

The next step consists of the calculation of P [r

j∈{1..nw}

]. To do this, we must observe the number

of objects in the database (N ). The probability that

an accessed object is a given one is

, thus: P [r

j∈{1..nw}

] = 1 −

Finally, the complete expression can be rewritten as

follows:

P A

outd

) = 1 −

1 −

wtps

×δ(r

)

(4)

This expression provides a basic calculation of the

probability for an object access to cause the abortion

of the session by an out-of-date access.

The expression can be calculated with a few param-

eters. Only nw

and wtps

must be collected in the

nodes of the system in order to obtain the expression.

Thus, it becomes possible for a node to estimate the

convenience for an object to be locally updated be-

fore being accessed by a session. This estimation will

be performed with a certain degree of accuracy, de-

pending on the “freshness” of the values of nw

and

wtps

the node has. The way the expression can be

used, and an adequate mechanism for the propagation

of these parameters has been presented in (Ir

un-Briz,

2003).

4 EXPERIMENTAL VALIDATION

OF THE MODEL

We have validated the algorithm presented above by

implementing a simulation of the system. In this sim-

ulation, we have implemented nodes that concurrently

serve sessions, accessing to different objects of a dis-

tributed database. We have also modeled the concur-

rency control, and the lazy update propagation used

by LOMP.

4.1 Assumptions

The assumptions for the implementation of the sim-

ulation (Chandy and Misra, 1979; Bagrodia et al.,

1987) are compatible with the ones taken for the

model calculation, and the values have been estab-

lished to increase the number of conﬂicts produced

by the transactions executed in the system (i.e., this

conﬁguration shows a “worst-case” scenario for our

system):

• There are 4 nodes in the system, each holding a

full replica of the database, that contains 20 ob-

jects. Each node executes transactions, accessing

the database.

• For every object, a local replica holds the value of

the object, and the version corresponding to the last

modiﬁcation of the object. That is, the only syn-

chronous replica for each object is its owner node.

• There are three kinds of transactions, with a prob-

ability to appear of 0.2, 0.4, and 0.4 respectively:

”Type 0” (read-only): reads three objects; ”Type 1”

(read-write): reads three objects, then writes these

three objects; ”Type 2” (read&read-write): reads

six objects, then writes three of the objects read.

• The model supports the locality of the access by

means of the probability for an accessed object to

be owned by that node (i.e. the node where the

transaction is started). For read-only transactions,

this is 1/4, (this models no locality for read-only

transactions). For ”type 1” and” type 2” transac-

tions, the probability is 3/4.

• The simulation time has been set at 1,422 t.u., dis-

carding the ﬁrst 2 t.u. as stabilization time for the

simulation. This allows to start up to 60,000 trans-

actions.

4.2 Accuracy of the Prediction

When the expression exceeds the established thresh-

old for an object, and an update request is sent, it is

possible for the response of this request to contain the

same version for the requested object (e.g. when the

object was, in fact, up to date). We name this situation

“Inaccurate prediction”.

The more accurate the predictions are, the less

overhead the algorithm introduces in the system. This

accuracy of the predictions will be given by the set

threshold: higher values for the threshold should pro-

vide more accurate predictions. In general, we ob-

served that higher values for the threshold increase

the accuracy of the prediction.

The evolution of the inaccuracy in respect to the

amount of LocalUpdate messages is shown in the ﬁg-

ure 1. The optimum line is also shown, and corre-

sponds with the diagonal. The more accurate the pre-

diction is, the closest the curves are. The studied im-

ICEIS 2004 - DATABASES AND INFORMATION SYSTEMS INTEGRATION

132

100

0 0.2 0.4 0.6 0.8 1

% outdated

PA_outd

Completeness of the prediction

Predicted abortions

Actual abortions

Figure 1: Evolution of the inaccuracy for different

P[update]

plementation differs from the ideal line with a lower

bound pattern, and it is shown that is quite proximal

to the ideal.

5 THEORETICAL BOUNDARY

OF AN IMPROVEMENT

The ﬁrst sections of this paper has been dedicated to

the study of an statistical expression determining the

probability for a particular object access, to obtain an

out to date value, thus causing the abortion of the re-

questing transaction.

We can make use of such expression, in order to de-

termine the achievable improvement for a transaction,

in terms of abortion rate, when the average outdate

time of the objects is decreased.

Unfortunately, this decrement in the outdate time

will cause a degradation in the service time of the ex-

ecuted transactions, and this must also be taken into

account.

In this section, we present a theoretical boundary

for the reduction of the abortion rate that an adequate

exploit of the expression can provide.

5.1 Preliminaries

The used expression for the probability of an access

to be an stale-access was presented in 4. In the ex-

pression, the elapsed time between two consecutive

updates of the object r

is expressed as δ(r

We can perform a serial analysis in order to de-

termine the mean value for P A

outd

). The analy-

sis can be easily performed applying differentiate cal-

culus to the expression. The obtained expression is

showed to be:

P A

outd

= 1 −

1 −

wtps

×δ

(5)

where δ is the mean value for the δ(r

) in a sys-

tem execution, and P A

outd

is the mean value for the

P A

outd

) in the same system execution.

Now, we can obtain P C

outd

= 1 − P A

outd

, being:

P C

outd

= P C =

1 −

nwwt×wtps×δ

(6)

5.2 Average Outdate Time

To simplify, let’s suppose that transactions are dis-

tributed homogeneously along the system history.

Imagine the system execution history as a line,

where a number of transactions are sequentially ex-

ecuted. For a certain object o

, the probability for a

executed transaction to read o

will be

, where nr

is the number, in mean, of objects read by any exe-

cuted transaction (either read or write transactions are

included here), and N is the number of objects in the

database.

The probability of the object o

to be updated by

a lazy replication protocol depends on the probability

for a transaction that read o

to be aborted by an stale-

access (i.e. P A

= P A

). Thus the probability for

an object to be updated by a generic transaction will

be:

P A

Now, let tps be the number of transactions executed in

the system per second. Thus, there will be up(o

) =

tps × P A

updates of o

per second. Finally,

we can express δ(o

) as

up(o

)

, and, in mean:

δ =

tps × P A

(7)

If the accessed objects are updated along the transac-

tion, the value for δ will be decreased proportionally

to the amount of updates performed during the trans-

action execution.

To model this, a simple approach can be expressed

with the following expression:

= P C × d

+ (1 − P C) × δ (8)

where d

is the duration of a transaction when the

updates are performed along its execution. For the

aborted transactions, (i.e. (1 − P C)), the mean out-

date time is unchanged (δ). In contrast, for committed

transactions, the new outdate time is decreased to d

(i.e. the duration of the transaction).

Now, the duration of a transaction when the updates

are performed will depend on the number of requested

accesses that are actually updated along the transac-

tion execution (nr × P

UP D

), and the cost of each of

these updates (K

UP D

). Note that P

UP D

is the prob-

ability for a requested object to be updated. Thus, if

UP D

, there will be forced to be updated the

half of the objects requested by a transaction.

THE ABORTION RATE OF LAZY REPLICATION PROTOCOLS FOR DISTRIBUTED DATABASES

133

In summary, the expression for d

can be com-

posed by:

= d

+ nr × P

UP D

× K

UP D

(9)

Replacing 9 in 8, the new outdate time will follow the

expression:

= δ × (1 − P C) + P C × d

(10)

This result will be useful in section 5.3, where the

achievable abortion rate is speciﬁed in terms of δ

5.3 Abortion Rate

In mean, we can say that the achievable commit rate

will be, observing equation 6:

P C

1 −

nwwt×wtps×δ

(11)

Replacing δ

in the expression, we obtain:

P C











1 −

nwwt×wtps×δ×(1−P C)

1 −

nwwt×wtps×P C×d

(12)

That can be rewritten as:

P C

= P C

1+P C

−1

(13)

Now, we can replace δ with the expression obtained

in (7), the resulting expression is:

P C

= P C

P C

(

×(tps×(1−P C)

)−1

)

(14)

From the equation 14 we obtain that the improvement

of the probability for an object to be accessed in an

adequate way (i.e. not an stale access), is determined

P C

, and it will be beneﬁtted from the decrease of

the established value or any of the following expres-

sions:

• d

, the duration of the transactions.

• nr × P

UP D

× K

UP D

, the number of updated ob-

jects, and the computational cost of each of these

updates.

• tps, the amount of committed transactions per sec-

ond (including both read-only and read-write trans-

actions).

•

, the relation between the amount of objects

accessed per transaction (read-only or read-write

transactions) and the total number of objects con-

tained in the database.

To simplify the expression 13, we can denote as ∆ to

the existing relation between d

and δ (i.e. ∆ =

The resulting expression is:

P C

= P C

1+P C×(∆−1)

=⇒

P C

= P C

P C×(∆−1)

(15)

Let’s see an example for the improvement achiev-

able in an extremely simple system, where nr = 1. In

such system, we can establish as a parameter the prob-

ability for a requested object to be previously updated

(i.e. P

UP D

), and then study the achieved improve-

ment for different values of ∆ (and, consequently, dif-

ferent computational overheads).

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability of Commit

PC (probability for an object to be up-to-date)

Comparison PC’ vs. PC

PC’ for Delta=0.5

PC’ for Delta=0.1

PC’ for Delta=0.01

Figure 2: Evolution of the improvement varying ∆

Figure 2 shows the commit probability for a ses-

sion accessing only one object. There is shown how

the commit probability can be improved, when the

update-time is decreased to the half, up to the 120%

of the original commit time. When the update-time

is decreased ten times, the improvement reaches the

140%. Lower values of ∆ provides marginal im-

provements, at a higher computational costs.

When more than just an object is accessed in a

session, the results shows higher differences between

the commit promise, due to the factorization of such

probabilities.

These results points to the convenience, in the sce-

narios ﬁtting the parameters described above, to apply

the techniques postulated by the presented discussion.

6 RELATED WORK

Current work in consistency protocols for replicated

databases can be found using either eager (Agrawal

et al., 1997) and lazy protocols (Breitbart and Korth,

1997; Holliday et al., 1999) using either optimistic

and pessimistic consistency control.

Each one has its pros and cons, as described in

(Gray et al., 1996). Eager protocols usually hamper

the update performance and increase transaction re-

sponse times but, on the positive side, they can yield

serializable execution of multiple transactions with-

out requiring too much effort. On the other hand,

lazy protocols may allow a transaction to read out-

dated versions of objects, hamper the abortion rate,

but they can improve transaction response times.

ICEIS 2004 - DATABASES AND INFORMATION SYSTEMS INTEGRATION

134

Pessimistic consistency control for distributed

databases (Bernstein et al., 1987) is based on the prin-

ciple of “locks” in order to avoid concurrent transac-

tions to access to the same object in an inadequate

mode. The use of “locks” minimizes the number of

aborted transactions, but degrades the performance of

the system, because the complexity introduced by the

management of the locks.

On the other hand, the traditional approach for op-

timistic consistency control was presented in (Kung

and Robinson, 1981), and its main advantage consists

on the reduction of the blocking time of the transac-

tions, using “versions” (or “timestamps”) as the basis

for its implementation. The main disadvantage of op-

timistic consistency protocols consists of the increase

in the abortion rate.

The presented approach uses a optimistic consis-

tency control, with lazy replication, and has been im-

plemented in a real environment (COPLA).

7 CONCLUSIONS

Lazy update protocols have not been widely exploited

due to its excessive abortion rate on scenarios with

high probability of access conﬂicts. Nevertheless,

such protocols can provide important improvements

in the performance of a distributed system, when the

abortion rate can be kept low, and the locality of the

accesses is appreciable.

We have presented an statistical study of the abor-

tion rate (as disadvantage of lazy protocols), in or-

der to provide an expression for the probability for an

accessed object to be out of date (P A

outd

)), and

cause a further abortion of the accessing transaction.

An statistical analysis has been performed in this

paper, in order to provide an expression for the prob-

ability for a requested access to obtain a stale value of

the required object.

The application of the expression has been also dis-

cussed, in order to determine the convenience, using

a general algorithm, to update along the execution of

a transaction the objects predicted to be stale. This

discussion has provided a set of conditions, in base

to a number of parameters, where these generic algo-

rithms can improve the abortion rate of a lazy update

protocol.

Consequently, the improvement has also studied, in

base to the established decrement of the update-time

of the accessed objects, giving as conclusion that such

reductions may considerably improve the probability

for an object to be updated, thus reducing dramati-

cally the abortion rate of lazy update protocols.

Thus, this work theoretically validates the imple-

mentation of not-so-lazy update protocols based on

statistical prediction of stale accesses to reduce the

abortion rate. These protocols conform possible im-

plementations of the mentioned generic algorithm, as

a real improved update algorithm.

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