On the Impacts of Transitive Indirect Reciprocity on P2P Cloud

Federations

Eduardo L. Falc

, Ant

onio A. Neto

, Francisco Brasileiro

and Andrey Brito

Department of Computing and Systems, Federal University of Campina Grande, Campina Grande, Brazil

Department of Exact Sciences, Federal University of Para

ıba – Campus IV, Rio Tinto, Brazil

Keywords:

Reciprocity Mechanisms, Resource and Availability Asymmetry, Transitive Reciprocity, Cloud Federations.

Abstract:

Several P2P systems of resource sharing use cooperation incentive mechanisms to identify and punish free

riders, i.e., non-reciprocal individuals. A widespread approach is to use the levels of reciprocity, either di-

rectly or indirectly, to decide the extent to which an individual should trust other partners. One restriction

of direct reciprocity mechanisms is the inability to foster cooperation between individuals with asymmetrical

resources or availability incompatibility. In this work, we evaluate the performance of cloud federations ruled

by the combination of the well-known direct reciprocity with transitive reciprocity, a strategy that allows direct

reciprocity mechanisms to deal with asymmetry between individuals, while still keeping the beneﬁts of direct

reciprocity. For this, we implemented a simulator of resource bartering in cloud federations and experimented

it with workloads synthesized from traces of real systems. Our best results showed an average increase of

12.83% and 26.38% on the sharing level of the federation, in an optimistic but unrealistic mechanism setup.

When conﬁgured in a feasible and realistic manner, the transitive reciprocity was able to increase the sharing

level up to an average of 6.02% and 7.53%.

1 INTRODUCTION

One of the challenges with respect to the implemen-

tation of a cloud federation is to design a fair mar-

ket model that satisﬁes the participants and incen-

tivizes cooperation within the community. In gen-

eral, this resource exchange can be mediated through

monetary markets (Dhuria et al., 2017) or in a barter-

based approach that is often ruled by the tenets of reci-

procity (Haddi and Bencha

ıba, 2015).

Reciprocity mechanisms are categorized by the

way a resource provider assesses the resource re-

questers, which can be via a direct or indirect ap-

proach. In the direct reciprocity, a participant uses

the knowledge she acquired from her own experiences

to assess the past behavior (level of reciprocity) of the

requester. In the indirect reciprocity, however, third

party information can be used for this assessment as

well. Both approaches have advantages and disadvan-

tages that make them suitable for particular scenarios.

It is reasonable to state that the main advantage of di-

rect reciprocity is the integrity of the information an

individual keeps about the behavior of other partic-

ipants, which prevents peer collusion (Ciccarelli and

Cigno, 2011). Since it uses private history, direct reci-

procity mechanisms are more appropriate for small

and mid-sized communities, where repeated interac-

tion among peers is more likely, and also for com-

munities in which the type of resource provided is

the same as the one required, such as CPU, GPU and

storage – the case of cloud federations. On the other

hand, indirect reciprocity mechanisms are commonly

used in large-sized P2P systems with wide-ranging re-

sources (e.g., ﬁle sharing systems), where the chances

of a peer meeting another speciﬁc peer and satisfy its

requests are rather small.

However, scenarios with availability asymmetry

(Chuang, 2004) (when two peers can not cooperate

because the moments they are consumer and provider,

or vice versa, do not match) or with resource asymme-

try (Feldman et al., 2004) (or conﬂicts of interests –

when two peers can not cooperate because the type

of resource supplied by the provider is different from

the one required by the consumer) may lead to the

creation of credit chains

among some participants,

and thus some form of indirect reciprocity should be

Credit chains are created when, somehow, the re-

sources received by a peer are never reciprocated via direct

reciprocity, but may be returned indirectly (through another

peer), which yields a cyclic debt.

292

Falcão, E., Neto, A., Brasileiro, F. and Brito, A.

On the Impacts of Transitive Indirect Reciprocity on P2P Cloud Federations.

DOI: 10.5220/0007686402920299

In Proceedings of the 9th International Conference on Cloud Computing and Services Science (CLOSER 2019), pages 292-299

ISBN: 978-989-758-365-0

taken into consideration in such cases, even if the par-

ticipants cooperate repeatedly.

In order to deal with this particular source of prob-

lem some other works (cf. Section 3) conceived dif-

ferent forms of indirect reciprocity. In this work we

leverage the notion of transitive reciprocity, pre-

sented by Falc

ao et al. (2016), suggested as com-

plement to direct reciprocity. Transitive reciprocity is

a more restricted type of indirect reciprocity that can

be used in tandem with direct reciprocity mechanisms

with the purpose of mitigating the problems (credit

chains) arising from availability or resource asymme-

try but keeping the advantages of direct reciprocity.

Simulation results (Falc

ao et al., 2016) suggest

that the combination of transitive and direct reci-

procity increases the levels of cooperation among the

participants when compared to communities in which

only direct reciprocity is used. Yet, only scenarios

with simple workloads that cover a narrow spectrum

of the interesting cases were evaluated. The main re-

sults are that, when combined, transitive reciprocity

always enhance the performance of direct reciprocity.

However, the workloads experimented were too

simplistic and the results may not be representative

for real workload scenarios. This study extends such

investigation conducted by Falc

ao (2016), still in sim-

ulation lane, through the assessment of the impact

of transitive reciprocity in P2P cloud federations, but

this time using representative workloads that are syn-

thesized from traces of real systems. In addition, we

also investigate the impacts of transitivity in credit

chains involving different numbers of peers.

Our main outcomes are the actual performance

improvements a cloud federation may experience

through transitive reciprocity, and also that in some

speciﬁc setups, the transitive reciprocity may degrade

the overall federation performance (in contrast to re-

sults presented earlier). In face of that, this work high-

lights the main care the member of a cloud federation

should take to setup its transitive mechanism properly,

to avoid performance degradation.

The rest of this paper is organized as follows. Next

section presents the existing reciprocity mechanisms,

detailing their main features and drawbacks, to em-

phasize in what they differ from transitive reciprocity.

In Section 3 we show the most relevant related work.

The transitive reciprocity is described in Section 4.

Section 5 details the reciprocity mechanism used in

our simulations, the Transitive FD-NoF. In Section 6

we present the simulation model and the description

of the evaluated scenario. The simulation results and

their corresponding analysis are presented in Section

7. Finally in Section 8 we put forward the main con-

clusions.

2 RECIPROCITY MECHANISMS

Reciprocity-based incentive mechanisms are strate-

gies that aid providers in prioritizing the most re-

ciprocal consumers for granting its resources. Obvi-

ously, this encourages cooperation because free rid-

ers (i.e., individuals that consume resources from the

community with no compensation) will hardly suc-

ceed when there is contention on resources. This de-

cision is made in accordance with the transactions his-

tory, which indicates the level of reciprocity of a given

peer. Such mechanisms are categorized as direct reci-

procity or indirect reciprocity.

Direct reciprocity takes place on interactions be-

tween two individuals – B helps A because A has

helped B before, or because B expects A to return

this favor in the future (Haddi and Bencha

ıba, 2015).

On the other hand, indirect reciprocity takes place

on interactions involving at least three individuals,

and may happen via pay-it-forward (Floyd, 2017) or

reputation-based systems (Li and Su, 2018). Pay-it-

forward reciprocity is a so called altruistic strategy

that, in face of free riders, is quite utopic and unfea-

sible: A donates to B and B returns this favor to C,

which is a third party chosen randomly. Note that, in

this case, either A, B or C are not expecting something

in return. Reputation systems are often used in large-

scale P2P systems. In these systems, individuals are

encouraged to cooperate in order to render itself as a

collaborative and valuable member, and thus be recip-

rocated by its reputation. Therefore, if A helps B, C

will indirectly know that A is cooperative and reward

her for her good reputation. The direct reciprocity and

pay-it-forward reciprocity can take place via immedi-

ate or delayed exchange, whereas reputation systems

rely mainly on a delayed exchange since all the in-

formation about the reputation of the other peers is

collected in the past. Figure 1 illustrates a summary

of both types of reciprocity.

The main drawback of reputation systems is that

an individual will base their donation decisions on

third party information, which may be tampered with

by malicious peers to beneﬁt themselves. If on the

one hand, the way this information is collected in rep-

utation systems can give room for peer collusion as

a disadvantage, on the other hand, the speed in which

these pieces of information are diffused by the partici-

pants of the system is its main advantage. This feature

enables newcomers to collect a reasonable amount of

information about the behavior of other participants

in a short period of time so that they can properly se-

lect whom they should cooperate with. In addition,

this speed in which the information is spread enables

the community members to swiftly discover the repu-

On the Impacts of Transitive Indirect Reciprocity on P2P Cloud Federations

293

Figure 1: Types of reciprocity mechanisms.

tation of other peers they have never interacted with,

what may allow cooperation with unknown peers in

a less vulnerable way, as opposed to only interacting

with known peers as recommended by the direct reci-

procity. Therefore, it is possible to state that indirect

reciprocity is also suitable for communities with high

levels of resource asymmetry, and not only for com-

munities in which the participants have common in-

terests as required in direct reciprocity — if repeated

interaction is not necessary, common interests should

not be mandatory after all.

Two closely related problems common to both

reciprocity mechanisms are: i) how to treat newcom-

ers and ii) how to mitigate the advantages obtained by

whitewashers (individuals that leave and return to the

system with a new identity in order to dodge from the

consequences of a past in which they acted in a non-

cooperative way (Haddi and Bencha

ıba, 2015)). If the

rules to join the system are too strict, the individuals

may feel discouraged to join the community, but if, in

contrast, these rules are too liberal, the participants

would be able to leave the system and appear as a

newcomer. Alternatives to this issue could be an entry

fee or a proof of work that newcomers should be sub-

mitted to be able to join the system (da Costa Cordeiro

et al., 2016). Another solution is to disregard negative

values for credit/reputation systems (Andrade et al.,

2007), thus making no sense for any peer to leave and

return to the system since this fact does not change

the way other participants value him.

In general, it is possible to state that the main

advantage of the indirect reciprocity is the quick

growth of the database containing information about

the behavior of other participants. On the other hand,

the main advantage of direct reciprocity is the in-

tegrity of this same information kept in database. Ta-

ble 1 presents the characteristics of both mechanisms

thus allowing a quick comparison between the main

features of each one.

Table 1: Characteristics of direct and indirect reciprocity.

Characteristic Direct Rec. Indirect Rec.

database growth slow fast

database integrity guaranteed not guaranteed

supply and demand symmetrical symmetrical and asymmetrical

frequency of interactions repeated repeated and occasional

bootstrapping speed slow fast

collusion impossible possible

identity changing possible possible

2.1 The Asymmetry Problem

Direct reciprocity presents the following two restric-

tions when put into practice individually: time and

resources asymmetry. In order to better understand

this issue, one must picture a federation consisting of

3 peers (A, B and C) with a conﬂict of interest, as fol-

lows: A has a high processing capacity but insufﬁcient

storage, B has enough storage but often needs an extra

bandwidth, and C has bandwidth but often needs more

processing capacity. This cooperation setup, concern-

ing the types of resource required and offered, leads

to the following situation: A always provides to C,

B always provides to A, and C always provides to B.

In such cases, no resource is directly returned to the

providers, and even though all participants involved

in this cooperation chain receive what they request,

some of them may be seen as free riders.

For explanation purposes, one must consider that

peers A, B and C cooperate through a direct reci-

procity mechanism in which the balance of B from the

perspective of A would be computed by the function

γ(A, B,t) = υ(B, A, t)− υ(A, B, t),

where υ(A, B, t) denotes the total amount of resources

A provided to B until time t. Figure 2 depicts the

interactions via immediate exchange between three

peers with conﬂicts of interest (the case described on

the previous paragraph), and their corresponding bal-

ances. It is assumed that γ(A, B, t

) = γ(B,C,t

) =

γ(C, A, t

) = 0, t

< t

, and that each peer receives

and provides 10 units of resource per time unit.

As shown in Figure 2, as the individuals interact

with one another the balances decrease to negative

values, what naturally brings distrust. In such cases, it

is extremely hard to distinguish between cooperators

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294

Figure 2: The interests asymmetry problem.

and free riders, since both will have a negative bal-

ance for returning no favors, either intentionally (free

riders) or unintentionally (asymmetry).

Next section depicts how some related work ad-

dress this issue.

3 RELATED WORK

The main indirect reciprocity mechanisms typically

use reputation systems, transitive credit systems, or

the pay-it-forward principle.

Regarding the cryptography technique, there ex-

ists Dandelion (Sirivianos et al., 2009) and T-Chain

(Shin et al., 2017), based respectively on a global

credit system with tit-for-tat and on pay-it-forward,

both thought for ﬁle sharing systems. The cryptog-

raphy applied on Dandelion and T-Chain is efﬁcient

in promoting cooperation even in the face of free rid-

ers. However, this idea is only feasible for ﬁle sharing

systems, since ﬁles are encryptable.

Apart from the cryptography strategy, which

clearly is not applicable to cloud federations, we may

also cite, still in the context of ﬁle sharing, the Clus-

ter Based Incentive Mechanism (CBIM) (Zhang and

Antonopoulos, 2013), the K-Cycle (Eidenbenz et al.,

2012) and Menasch

e et. al. (2010). CBIM and K-

Cycle organize peers with asymmetric resources in

what the authors call barter rings or barter cycles,

forcing the peers comprising the ring to cooperate be-

fore consuming. Menasch

e et. al. (2010) suggest that

cycles of indirect reciprocity cooperation should be

converted into direct reciprocity.

When it comes to mechanisms that could be

straightforwardly applied to P2P cloud federations

and computational grids, but without relying indis-

criminately on third-parties (such as the transitive

reciprocity we rely on), there are the following rel-

evant work: CompactPSH (Bocek et al., 2009),

PledgeRoute (Landa et al., 2009) and Scrivener

(Nandi et al., 2005). In these mechanisms, in-

direct reciprocity is broken down into two steps:

credit transfer and direct reciprocity. The idea is to

strengthen the economy of the system since the trans-

fer of credits allows interactions that would not hap-

pen between peers with asymmetric resources.

4 TRANSITIVE RECIPROCITY

Transitive reciprocity is a more limited form of in-

direct reciprocity, which is designed to be put into

practice in tandem with direct reciprocity but while

still keeping the integrity of database with transac-

tions history (which is not the case for reputation sys-

tems). For instance, when A requests resources from

B, and somehow the latter can not meet A’s request, B

can ask other peers that are in debt with him (e.g., C)

to do A this favor as a kind of repayment to B. Further,

once A receives the resources, she must be informed

by C that that favor was done under B’s request. Also,

A will increase the balance of B in proportion to the

time period and amount of resources provided by C,

but obviously A will not credit C and C will not debt

With the aid of transitive reciprocity, the distrust

raised by the asymmetry problem (Fig. 2) would

be solved. The decrease of balances that took place

on each time period due to the cooperation chain

(A → C → B → A) would give place, in face of transi-

tive reciprocity, to a balance stability. At the end of t

γ(A, B, t

) = γ(B,C, t

) = γ(C, A,t

) = 0, as well as at

the end of t

, γ(A, B, t

) = γ(B,C,t

) = γ(C, A, t

) = 0,

instead of −10 and −20 for t

and t

respectively,

since for each time period the resource provision

would be indirectly reciprocated and all the debts

would be paid.

From the related work we may note that the

main differences are the protocol to enable cooper-

ation among peers with asymmetry, and the appli-

cation context, which may require special treatment.

The change of the protocol may not entail signiﬁcant

changes in the results of the performed simulations,

since the protocols are only enablers of the same in-

teraction through different approaches/idea of indirect

reciprocity. However, transitive reciprocity is more

efﬁcient in terms of amount of exchanged message –

to allow interaction through transitive reciprocity be-

tween three peers, its protocol only needs 5 messages,

while Scrivener and CompactPSH needs respectively

6 and 10 messages (cf. (Nandi et al., 2005; Bocek

et al., 2009)).

On the Impacts of Transitive Indirect Reciprocity on P2P Cloud Federations

295

5 THE TRANSITIVE FD-NoF

In the Fairness-Driven Network of Favors (or FD-

NoF, for short), the most reciprocal participants are

prioritized for the concession of favors through a sys-

tem of balances that, considering functions deﬁned in

Section 2.1, are calculated by the following equation:

γ(A, B, t) = max

{

0, υ(B, A, t) − υ(A, B, t) + log υ(B, A, t)

}

By preventing the balances from being negative, this

deﬁnition does not allow malicious peers to manipu-

late their balances by changing their identity to pre-

tend to be a newcomer. Furthermore, it takes into

consideration an amortized and historical portion of

donations that A has received from B in the past. This

enables A to distinguish a peer C that has never pro-

vided resources from a cooperative peer B that has

provided to A in the past but has received from A at

least the same amount of resources provided.

In order to assure fairness, the ratio between

the total amount of resources received and the to-

tal amount of resources provided up to a particular

point in time, the FD-NoF suggests that each par-

ticipant should manage the amount of resources of-

fered to other peers of the federation. Each partici-

pant is provided with a feedback control loop mech-

anism and must deﬁne a minimum (τ

min

) and max-

imum threshold (τ

max

), thus determining an interval

[τ

min

, τ

max

] that represents the desired levels of fair-

ness. One must assume that the amount of resources

that A offers to any other peer B in time t is expressed

by the function α(A, B, t). If at any moment the fair-

ness of A in relation to a peer B is lower than τ

min

the controller will continuously subtract a ﬁxed value

∆ from α(A, B,t) over the subsequent periods of time

until the fairness of B under the perspective of A gets

higher than τ

min

. On the other hand, if the fairness

of A in relation to B is superior to τ

max

, the controller

will add ∆ to the value of α(A, B,t) over the subse-

quent periods of time until the fairness of A in relation

to B assumes an inferior value to τ

max

— at this stage,

once the desired level of fairness is reached, A will try

to have an accumulated balance in the perspective of

this participant. Finally, when the fairness of A in re-

lation to B is within the interval [τ

min

, τ

max

], the con-

troller will run a Hill Climbing algorithm that uses

the latest values of fairness to decide whether there

should be an increase or decrease in α(A, B,t + 1) to

maximize the fairness of B perceived by A within the

interval [τ

min

, τ

max

This brief discussion aims to make this work self-

contained with respect to the the FD-NoF mechanism.

Additional information about the algorithm and its

performance can be found in (Falc

ao et al., 2016).

The goal of transitive reciprocity is to enable co-

operation between participants that show any type

of asymmetry. Therefore, whenever a peer has idle

resources and the FD-NoF mechanism suggests this

peer should not share them, the transitive reciprocity

must be put into practice to verify if there is any credit

chain between the requester and the provider, what

could enable cooperation through transitivity. Each

peer is free to setup its own mechanism autonomously

by choosing the maximum allowed length of chain

(χ ∈ N

≥3

) and also the percentage of peers consid-

ered for trying cooperation at each level of the chain,

η ∈ [0, 1]. Obviously, the higher are χ and η the higher

will be the probability of cooperation, but also more

congested will be the federation network.

The FD-NoF mechanism with this additional en-

abler is what we call the Transitive FD-NoF.

6 EVALUATION OF THE

TRANSITIVE FD-NoF

In order to assess the performance of the Transitive

FD-NoF in P2P cloud federations, we advanced the

simulator built by Falc

ao et. al. (2016) to allow the

experimentation of realistic workloads, and also to en-

able cooperation in transitive chains with more than

three peers. The simulation model with these addi-

tional features is described next.

6.1 Simulation Model

The federation F consists of a community comprised

by N peers. The simulation proceeds in discrete steps

and, therefore, the balance (γ : F × F × N → R

≥0

) and

quota (α : F × F × N → R

≥0

) functions are best de-

scribed in the form of step functions.

Assume that each peer has a total resource capac-

ity of C ∈ R

≥0

. A peer in consumer state at any step

t will have a total resource demand D

total

= D + C ,

of which C units are provided by the local resources

and D units are requested to the federation. A peer is

in provider state when D

total

< C , which means that

it can provide up to C resource units to the federation.

For two-party interactions, a peer A in a provider state

at time step t may provide up to α(A, B,t) units of re-

sources to any peer B in consumer state at step t.

When cooperating through transitive reciprocity

and the number of peers involved in the credit chain

is three (χ = 3), the amount of resources provided is

computed as follows. A peer C in a provider state at

step t may provide to a peer A in a consumer state

on behalf of a peer B up to the minimum between

α(C, B, t) (the amount that C would provide directly

to B) and α(B, A, t) (the amount that B would provide

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296

to A, since B would not require C to provide more re-

sources to A than B itself would provide). The same

logic is applied for χ > 3. Roughly, this means that

the peers involved in the transitive reciprocity never

donate more than the limit imposed by the controller.

Whenever a peer is in a consumer state, ﬁrst she

will send requests to participants she knows she has

credit with, in a direct reciprocity basis. If none of

them can meet her request, then she will send requests

to peers that could meet requests via transitive reci-

procity, with the aid of any credit chain. Let us call

these intermediate individuals the transitive peers.

Then, each transitive peer, which will denote one level

of the chain, should forward this request only to a por-

tion (η) of the participants of the federation. Finally,

if none of these requests are met, the consumer sends

direct requests to unknown peers, randomly chosen,

for establishing new links. At each time step, upon

receiving the requests from consumer peers, the sim-

ulator randomly selects a peer in a provider state,

and this peer prioritizes the granting of resources to

consumer peers according to the protocol established

by the NoF — peers with higher balances are prior-

itized, and if there is more than one requester with

the same balance, the provider distributes its idle re-

sources equanimously among them.

In simulations in which χ > 3, the consumer will

always try to ﬁnd the credit chain with lowest length

possible to the provider. In other words, if for instance

χ = 5, the consumer will ﬁrst try to ﬁnd a provider

through a chain with a single level (χ = 3), and in case

it is not possible, she will increment χ until she ﬁnds a

chain to a provider. This process is repeated until her

demand has been fully met or until the requester has

explored chains of length χ = 5 and no credit chain

has been found.

The source code of the Transi-

tive FD-NoF simulator is available at

https://github.com/antonionetto20/Transitive-FD-

NoF.git.

6.2 Workload Synthesized from Real

Traces

In terms of client applications, cloud federations may

have similar applicability to that of P2P opportunis-

tic computational grids, suitable for fault tolerant ap-

plications such as Bag-of-Tasks (BoT). Therefore, we

used a workload generator presented by Carvalho and

Brasileiro (2012), a software that uses traces from real

systems, provided by the Grid Workload Archive at

http://gwa.ewi.tudelft.nl/, in order to synthesize real-

istic workloads based on parameters such as number

of peers, users, maximum duration of a job and dura-

tion of the whole workload.

With the aid of this software, we generated a

workload of 72 hours, comprising a federation of 60

organizations (peers) and 10 users per organization.

Since the simulator models the exchange of re-

sources in discrete turns, it was necessary to map the

jobs generated by the workload to the turns of the sim-

ulation. This was done considering time grains, i.e.,

mapping all jobs that start and/or ﬁnish in a given time

slot for one turn of the simulation. In our simulations,

to approximate the duration of a turn to the jobs run-

ning time, the grain was deﬁned as the average of the

total duration of all jobs: 942 seconds. The factors

are the reciprocity mechanism (direct or transitive),

the total resource capacity of each peer (C ) and, if

the transitivity is enabled, the maximum length of the

credit chain (χ) and the percentage of peers consid-

ered at each level of the chain (η) – recall that the

peers’ demands comes from the workload generator.

We varied the resource capacity of the peers to under-

stand the impact of the transitivity in scenarios with

different levels of resource contention. In addition,

we also changed χ and η to analyze the trade-off be-

tween the cost of increasing the number of peers in-

volved in the transitive cooperation (which would in-

crease the amount of messages sent, possibly congest-

ing the network) and its beneﬁts (which would be the

increase in the amount of shared resources thanks to

the number of transitive peers).

Once the difference in performance between the

FD-NoF and the Transitive FD-NoF in a turn tends

to be marginal, the evaluation metric is computed by

the total amount of resources donated in the Transitive

FD-NoF minus the total amount of resources donated

in the FD-NoF, in all turns of the simulation. With this

value we can measure the percentage of increase in

donation brought by the transitive reciprocity.

In all simulations, the FD-NoF mechanism is set

with ∆ = 0.05 · C , τ

min

= 0.75 and τ

max

= 0.95, values

suggested by Falc

ao et. al. (2016) for performing

well in wide range of scenarios.

7 RESULTS AND DISCUSSION

Figure 3 presents the percentage of increase in to-

tal donation when comparing the same scenarios ran

with Transitive FD-NoF and the FD-NoF. We simu-

lated scenarios in which all the peers are set only with

C = 50 and scenarios in which they are all set with

C = 100. In addition, we also changed the maximum

chain length when the transitive reciprocity is enabled

between χ ∈ {3, 4, 5}. We ﬁrst explore transitivity to

its edge — the percentage of peers tried on each chain

On the Impacts of Transitive Indirect Reciprocity on P2P Cloud Federations

297

level is 100% (η = 1). Each box-plot presents the dis-

tribution of the percentage of increase in donation

in 30 replications, where the seed for generating ran-

dom numbers is modiﬁed, which affects the order in

which providers and consumers are selected by the

simulator for the provision of resources. The conﬁ-

dence intervals for these distributions are plot with a

95% conﬁdence level.

Figure 3: Distribution and conﬁdence intervals of percent-

age increase in resource donation provided by transitivity in

scenarios with χ ∈ {3, 4, 5}, C ∈ {50, 100} and η = 1.

From Figure 3 one may observe that the transi-

tive reciprocity increased the percentage of donation

in vast majority of the scenarios simulated with η = 1,

speciﬁcally, 97.2%. The remaining scenarios, conﬁg-

ured with C = 100 and χ = 3, showed performance

degradation as can be seen on Figure 3 (a few blue

points below zero). This fact was not perceived before

in (Falc

ao et al., 2016), perhaps because it was used

a very simple workload that didn’t generate coopera-

tion scenarios with higher complexity. This degrada-

tion may be experienced when speciﬁc interactions,

that occur at a given moment, depend on the oc-

currence of previous interactions, since the existence

(or not) of a past interaction that happened through

the presence (or absence) of the transitive reciprocity

may alter the disposition of balances and quotas be-

tween the peers, in such a way that prevents certain

donations. However, when the length of the transi-

tive chain (χ) is increased, augmenting the chances

of transitive cooperation, there is a considerable in-

crease in the amount of resources shared. For sce-

narios in which the peers have C = 100, the aver-

age increase in donation was 12.83% and 26.38% for

χ ∈ {4, 5}. Finally, we observed that the increase in

donation brought by the transitive reciprocity in sce-

narios with different resource contention (different C )

may differ signiﬁcantly for χ ∈ {4, 5}, although with

no clear pattern since for χ = 4, C = 100 underper-

formed scenarios with C = 50 but for χ = 5, C = 100

overperformed C = 50.

However, exploiting all possibilities of transitive

chains between the provider and the consumer may

not be realistic depending on N , χ, and η. Scenarios

with N = 60, χ = 5 and η = 1 allow a number of com-

binations up to 59+ (59· 58)+ (59· 58· 57) = 198530

between a single provider and all the other partici-

pants. Considering all the providers at a given time,

the amount of messages sent would surely congestion

the network, besides the delay on decision of each in-

termediate peer on whether it should cooperate or not.

For this reason, we also evaluated scenarios in

which the transitive reciprocity considered a reduced

amount of participants at each level of the chain,

η ∈ {

}. The increase in donation of such simu-

lations are presented in the box-plots of the Figure 4.

Figure 4: Percentage increase in resource donation provided

by transitive reciprocity in scenarios with χ ∈ {3, 4, 5}, C ∈

{50, 100} and η ∈ {

In scenarios setup with χ = 3 and η ∈ {

} there

were some scenarios with performance degradation

due to the low value of η. Further, we may also

note that when χ = 3, there is no meaningful differ-

ence on increasing η from

. However, when

χ ∈ {4, 5} the amount of peers considered for coop-

eration increases substantially, and then increasing η

incurred in a higher level of resource provision. Sce-

narios set with χ ∈ {4, 5} and η =

, for instance, had

solely performance improvements, 6.02% and 7.53%,

on average. Therefore, χ = 4 and η =

can be con-

sidered and interesting setup for presenting a good

cost-beneﬁt, at least for the workload experimented,

since to explore all cooperation possibilities a con-

sumer would only need to send 420 messages.

CLOSER 2019 - 9th International Conference on Cloud Computing and Services Science

298

8 CONCLUSIONS

This work evaluates the impact of transitive reci-

procity in P2P cloud federations with workload syn-

thesized from traces of real systems. To this goal,

a simpliﬁed simulation model was conceived to al-

low the investigation of the performance of transitive

reciprocity in different scenarios. To the best of our

knowledge, only the present work evaluates the im-

pacts of the chain length and the amount of peers con-

sidered for cooperation on each level of the chain.

Simulation results showed that in some scenarios

(2.8%) in which all interactions are tried (η = 1) tran-

sitive reciprocity may degrade the federation overall

performance – the amount of shared resources is de-

creased, a result not seen in any related work. How-

ever, our main ﬁndings are that transitive reciprocity

can actually increase the sharing level in a more re-

alistic scenario in which less transitive combinations

between consumer and provider are considered —

Transitive FD-NoF increased the percentage donation

in 6.02% and 7.53% in scenarios setup with η =

and χ ∈ {4, 5}, respectively.

ACKNOWLEDGMENT

This research was partially funded by the EU-BRA

SecureCloud project (EC, MCTIC/RNP, and SERI,

3rd Coordinated Call, H2020 Grant agreement no.

690111) and by the EU-BRA ATMOSPHERE project

(EC and MCTIC/RNP, 4th Coordinated Call, H2020

Grant agreement no. 777154).

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