Dynamic Strategy Selection based on Evidence Theory. Application on a P2P-VoD system

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Dynamic Strategy Selection based Dynamic Strategy Selection based Dynamic Strategy Selection based Evidence Theory. Application on Evidence Theory. Application on EvidenceP2P-VoD Theory. Application on system P2P-VoD system P2P-VoD system

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Thibaud Rohmer ∗∗ Amir Nakib ∗∗ Abdelhamid Nafaa ∗∗∗ ∗∗ ∗∗∗ ∗ ∗∗ ∗∗∗ Thibaud Rohmer Amir Nakib Abdelhamid Nafaa Thibaud Thibaud Rohmer Rohmer ∗ Amir Amir Nakib Nakib ∗∗ Abdelhamid Abdelhamid Nafaa Nafaa ∗∗∗ ∗ ∗ Universite de Paris Est, Laboratoire LISSI,122 rue Paul Armangot, ∗ Universite Paris Laboratoire LISSI,122 rue ∗ Universite de Paris Est, Laboratoire LISSI,122 rue Paul Paul Armangot, Armangot, 94440de Vitry surEst, seine, France (e-mail: [email protected]). Universite de Paris Est, Laboratoire LISSI,122 rue Paul Armangot, 94440 Vitry sur seine, France (e-mail: [email protected]). ∗∗ 94440 Vitry sur seine, France (e-mail: [email protected]). Universite de Paris Est, Laboratoire LISSI,122 rue Paul Armangot, 94440 Vitry sur seine, France (e-mail: [email protected]). ∗∗ ∗∗ de Paris Est, Laboratoire LISSI,122 Paul Armangot, ∗∗ Universite Universite Est, Laboratoire LISSI,122 rue 94440 sur seine, France.rue Universite de de Paris Paris Est,Vitry Laboratoire LISSI,122 rue Paul Paul Armangot, Armangot, 94440 Vitry sur seine, France. ∗∗∗ 94440 Vitry sur seine, France. Google Inc, Business Intelligence, 345 Spear St, San Francisco, CA 94440 Vitry sur seine, France. ∗∗∗ ∗∗∗ Google Inc, Business Intelligence, 345 Spear St, San Francisco, CA ∗∗∗ Google 345 94105, USA Google Inc, Inc, Business Business Intelligence, Intelligence, 345 Spear Spear St, St, San San Francisco, Francisco, CA CA 94105, USA 94105, USA 94105, USA Abstract: Peer-to-Peer Video-on-Demand (VoD) systems are rising as a new dominant way Abstract: Video-on-Demand (VoD) systems are rising as a new way Abstract: Peer-to-Peer Video-on-Demand (VoD) systems are as dominant way to distributePeer-to-Peer video content over IP networks. While many works addressed the dominant broad area of Abstract: Peer-to-Peer Video-on-Demand (VoD) systems are rising rising as aa new new dominant way to distribute video content over IP networks. While many works addressed the broad area of to distribute video content over IP networks. While many works addressed the broad area of P2P communications, few work has been focused onto the resource allocation in P2P streaming to distribute video content over IP networks. While many works addressed the broad area of P2P few has onto resource allocation in streaming P2P communications, communications, few work workconstraint has been been focused focused onto the the resource to allocation in P2P P2PMost streaming systems, where the real-time adds another dimension the problem. work P2P communications, few work has been focused onto the resource allocation in P2P streaming systems, where the real-time constraint adds another dimension to the problem. Most work systems, where the real-time constraint adds another dimension to the problem. Most work on P2P resource allocation solve the problem static rules strategies are not robust systems, where the real-time constraint adds with another dimension to the problem. Most when work on P2P resource allocation solve the problem with static rules strategies are not robust when on P2P resource allocation solve the problem with static rules strategies are not robust when they are facing to the content demand (popularity) trends. In this paper, we use a dynamic on P2P resource allocation solve the problem with static rules strategies are not robust when they are facing the content demand (popularity) trends. this use a dynamic they to the (popularity) trends. In paper, we use dynamic approach, whichto selects the best strategy onIn givenpaper, time we period. the they are are facing facing toautomatically the content content demand demand (popularity) trends. Ina this this paper, we use aaWith dynamic approach, which automatically selects the best strategy on a given time period. the approach, P2P which automatically selects the abest best strategy on given time period. With the proposed resource allocation method, VoDstrategy service on provider cantime combine anyWith number approach, which automatically selects the aa given period. With the proposed P2P resource allocation method, a VoD service provider can combine any number proposed P2P resource allocation method, a VoD service provider can combine any number of resourceP2P allocation and formulate different performance objectives its proposed resourcestrategies allocation method, a VoD service provider can combinethat any meet number of resource allocation and formulate different performance meet its of strategies and different objectives that meet its requirements. As part strategies of our effort develop algorithms that can beobjectives effectivelythat deployed of resource resource allocation allocation strategies andtoformulate formulate different performance performance objectives that meet by its requirements. As part of our effort to develop algorithms that can be effectively deployed by requirements. As part of our effort to develop algorithms that can be effectively deployed by broadband operators, we developed a full-scale emulator for P2P streaming that can support up requirements. As part of our effort to develop algorithms that can be effectively deployed by broadband operators, we full-scale emulator P2P streaming that support broadband operators, we developed developed a emulator full-scale includes emulatorafor for P2P streaming that can canalong support upa to 10,000 peers. The P2P streaminga VoD request generators, withup broadband operators, we developed a full-scale emulator for P2P streaming that can support up to 10,000 peers. The P2P streaming emulator includes a VoD request generators, along with to 10,000 peers. The P2P streaming emulator includes a VoD request generators, along with SuperNode (withThe backend DataBase)emulator that tracks and allocates networkgenerators, resources. In thiswith paperaaa to 10,000 peers. P2P streaming includes a VoD request along SuperNode (with DataBase) that tracks and allocates network In this SuperNode (with backend DataBase) that and network resources. In paper the goal is to usebackend a low complexity approach to enhance the resources. performance of a paper P2PSuperNode (with backend DataBase)learning that tracks tracks and allocates allocates network resources. In this this paper the goal is to use a low complexity learning approach to enhance the performance of the goal goal is to tobased use a aonlow low complexity learning approachapproach to enhance enhance the performance performance of aaa P2PP2PVoD system evidence theory. The proposed is compared to both static and the is use complexity learning approach to the of P2PVoD based proposed compared to static VoD system system based on on evidence theory. The proposed approach isapproach comparedallows to both both static and and dynamic solutions. Theevidence obtainedtheory. resultsThe show that theapproach proposedis to reduce the VoD system based on evidence theory. The proposed approach is compared to both static and dynamic solutions. The obtained results show that thewhile proposed approach allows to reduce dynamic The obtained results that approach allows to the complexity of selecting strategies, maintaining a low rejection rate.the dynamic solutions. solutions. The resource obtainedallocation results show show that the the proposed proposed approach allows to reduce reduce the complexity of resource allocation strategies, while maintaining aa low rejection rate. complexity of selecting selecting allocation strategies, while maintaining low rejection rate. complexity selecting resource resource allocation strategies, while maintaining low All rejection rate. © 2016, IFACof(International Federation of Automatic Control) Hosting by ElsevieraLtd. rights reserved. Keywords: FLearning system, Distributed application, Networks, Peer-to-Peer, Keywords: FLearning FLearning system, Distributed application, Networks, Peer-to-Peer, Keywords: system, Distributed application, Networks, Peer-to-Peer, Video-on-Demand, resource allocation, Evidence Theory, optimization. Keywords: FLearning system, Distributed application, Networks, Peer-to-Peer, Video-on-Demand, resource allocation, Evidence Theory, optimization. Video-on-Demand, Video-on-Demand, resource resource allocation, allocation, Evidence Evidence Theory, Theory, optimization. optimization. 1. INTRODUCTION of those systems implement a central node, which has the 1. INTRODUCTION INTRODUCTION of those systems implement central node, which has the 1. of those systems central which has task of managing the wholeaaanetwork. As the SuperNode 1. INTRODUCTION of those systems implement implement central node, node, which has the the task of managing the whole network. As the SuperNode task of managing the whole network. As the SuperNode receives VoD requests and fulfill them by allocating conVideo-on-Demand (VoD) systems present many advan- task of managing the whole network. As the SuperNode requests and fulfill them by conVideo-on-Demand (VoD) systems present many advan- receives receives VoD VoD requests and the fulfill them by allocating allocating contributing peers to stream VoD session, peers uplink Video-on-Demand systems present many advantages, both for the(VoD) users and for the content providers. VoD requests and fulfill them by allocating conVideo-on-Demand (VoD) systems present many advan- receives tributing peers to stream the VoD session, peers uplink tages, both for the users and for the content providers. tributing peers to stream the VoD session, peers uplink resources are committed for the duration of the movie. tages, both for the users and for the content providers. Therefore, during the past decade, such systems have been tributing peers to stream the VoD session, peers uplink tages, both for the users and for the content providers. resources are committed for the duration of the movie. Therefore, during the past past decade, decade, such systemsNowadays, have been been resources committed for the the each peer typicallyof wide Therefore, the such systems rising as a during new solution content delivery. resources are arethat committed forwould the duration duration ofstore the amovie. movie. Therefore, during the pastfor decade, such systems have have been Considering Considering that each peer would typically store a wide rising as a new solution for content delivery. Nowadays, Considering that each peer would typically store a range of content parts, the resource allocation decision rising as a new solution for content delivery. Nowadays, though, providers areforfacing a quickly growing num- Considering that each peer would typically store a wide wide rising astitle a new solution content delivery. Nowadays, range of content parts, the resource allocation decision though, title providers are facing a quickly growing numrange of of critical content for parts, the resource resource allocation decision becomes maximizing the network utilization, though, title are facing ber of clients, and find needaa quickly for new,growing highly numscal- range content parts, the allocation decision though, title providers providers arethe facing quickly growing numbecomes critical for maximizing the network ber of of clients, clients, and find find the need need for new, highly scalcritical for the utilization, and minimizing requests rejection rates. Asutilization, the peers ber and the new, highly scalable, architecture designs. Manyfor work Janardhan and becomes becomes criticalVoD for maximizing maximizing the network network utilization, ber ofVoD clients, and find the need for new, highly scaland minimizing VoD requests rejection rates. As the peers able, VoD architecture designs. Many work Janardhan and and minimizing VoD requests rejection rates. As uplink capacity gets saturated, all content parts they able, designs. Janardhan and Schulzrinne (2007) have shownMany the work interests of using a and minimizing VoD requests rejection rates. As the the peers peers able, VoD VoD architecture architecture designs. Many work Janardhan and uplink capacity gets saturated, all content parts they Schulzrinne (2007) have shown the interests of using a uplink capacity gets saturated, all content parts contain become unavailable to satisfy new VoD requests. Schulzrinne (2007) have shown the interests of using a Peer-to-Peer (P2P) have architecture solution to capacity gets saturated, all content parts they they Schulzrinne (2007) shown as thea interests of improve using a uplink contain become unavailable to satisfy new VoD requests. Peer-to-Peer (P2P) architecture as a solution to improve contain the become unavailable to algorithm satisfy new newshould VoD requests. requests. Ideally, resource allocation carefully Peer-to-Peer architecture as solution to the scalability(P2P) of such video delivery become unavailable to satisfy VoD Peer-to-Peer (P2P) architecture as aasystems. solution Approaches to improve improve contain Ideally, the resource resource allocation algorithm should carefully the scalability scalability ofLiao suchetvideo video delivery systems. Approaches the carefully weigh which peer toallocation commit algorithm so as to should leave necessary the delivery Approaches such as AnySeeof al. (2006) andsystems. PROMISE Hefeeda Ideally, Ideally, the resource allocation algorithm should carefully the scalability of such such video delivery systems. Approaches weigh which peer to commit so as to leave necessary such as AnySee Liao et al. (2006) and PROMISE Hefeeda weigh which peer to commit so as to leave necessary resources available to satisfy the most probable future VoD such as AnySee Liao et al. (2006) and PROMISE Hefeeda et al.as(2003) were to overcome the scalability which peer to commit so as to leave necessary such AnySee Liaoproposed et al. (2006) and PROMISE Hefeeda weigh resources available to satisfy the most probable future VoD et al. al. (2003) (2003) werewhen proposed to overcome overcome the scalability scalability resources available to satisfy the most probable future requests. Different resource allocation strategies have been et were proposed to the issues that arise delivering live streams to a very available to satisfy the most probable future VoD VoD et al. (2003) were proposed to overcome the scalability resources requests. Different resource allocation strategies have been issues that arise when delivering live streams to a very requests. Different Different resourceliterature, allocationwith strategies havedesign been published in the relevant different issues that when streams to very large of receivers. Those live systems provide resource allocation strategies have been issues number that arise arise when delivering delivering live streams to aa great very requests. published in the relevant literature, with different large number number of receivers. receivers. Those systems provide great in the literature, with different design focuses and performances. al Zoudesign et al. large of Those systems great scalability at lower cost, thus proving quiteprovide efficient for published published in different the relevant relevant literature, Zou withet. different design large number of receivers. Those systems provide great focuses and different performances. Zou et. al Zou et al. scalability at lower cost, thus proving quite efficient for focuses and different performances. Zou et. al Zou (2002) presented multiple selection algorithms, most of scalability at lower cost, thus proving quite efficient for large delivery networks. those systems are based and different performances. Zou et. al Zou et et al. al. scalability at lower cost,Most thus ofproving quite efficient for focuses (2002) presented multiple selection algorithms, most of large delivery networks. Most of those systems are based (2002) presented multiple selection algorithms, most which are based on peer uplink capacity. Koo et al. Koo large delivery networks. Most of those systems are based on Peer-to-Peer (P2P) architectures, where titles are dipresented multiple selection algorithms, most of of large delivery networks. Most of those systems are based (2002) which are based on peer uplink capacity. Koo et al. Koo on Peer-to-Peer (P2P) architectures, where titles are diwhich are based based on peer peera uplink uplink capacity. Koo Koo et al. al. This Koo et al. (2004) presented neighbor-based approach. on titles divided into parts,(P2P) whicharchitectures, are stored atwhere the peers. Then, are on capacity. et Koo on Peer-to-Peer Peer-to-Peer (P2P) architectures, where titles are are di- which et al. (2004) (2004) presented neighbor-based approach. This vided into into parts, which are stored at Then, al. aaa neighbor-based approach. This approach triespresented to group peers into classes based upon their vided parts, which are from storeda dedicated at the the peers. peers. Then, instead of streaming content server, the et et al. (2004) presented neighbor-based approach. This vided into parts, which are stored at the peers. Then, approach tries to group peers into classes based upon their instead of streaming content from a dedicated server, the approach tries to group peers into classes based upon their similarities. More recently, Fouda et al. Fouda et al. (2012) instead of streaming content from a dedicated server, the peers contribute to the video from sessions. Furthermore, tries to group peers into classes based upon their instead of streaming content a dedicated server,some the approach recently, Fouda et al. peers contribute contribute to the the video sessions. sessions. Furthermore, some some similarities. similarities.aMore More recently,and Fouda et al. al. Fouda Fouda et etsystem. al. (2012) (2012) introduced localization congestion-aware In peers More recently, Fouda et al. Fouda et al. (2012) peers contribute to to the video video sessions. Furthermore, Furthermore, some similarities.  introduced a localization and congestion-aware system. Thanks to UCD Dublin, Irland for funding this work. introduced aa localization localization and and congestion-aware congestion-aware system. system. In In introduced In  to UCD Dublin, Irland for funding this work.  Thanks  Thanks Thanks to to UCD UCD Dublin, Dublin, Irland Irland for for funding funding this this work. work.

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P2P-VoD systems, demand evolves over time. The content popularity and other characteristics change over time, which suggests it has to be seen as a dynamic environment. In this paper, we use an adaptive resource allocation strategy. It aims to dynamically adapt the resource allocation strategy to fit the demand. We present three main strategies (RA), and performance evaluation metrics for those strategies. Then, by constantly evaluating the performances of each strategy, we select and use the best fit for the current demand. Our solution, Adaptive Resource Allocation (ARA), adapts to the demand by automatically using the best strategy available, at any time. Over the last decade, optimization in dynamic environments has attracted a growing interest, due to its practical relevance. Many real-world problems are dynamic optimization problems (DOPs), i.e. their objective function changes over time. For dynamic environments, the goal is not only to locate the optimum, but to follow it as closely as possible. A dynamic optimization problem can be expressed by (1). min f (x, t) x

(1)

where x is the vector of inputs, f the function that models the optimization problem, and t the time period on which it is evaluated. In this work, the selection strategy problem is seen as a dynamic optimization problem with constant time constraints. We propose to solve this problem with the Evidence Theory, and possibility estimations. We compare our results to another dynamic strategy selection approach, based on bayesian inference, and posterior probability estimation. This paper is organised as follows. Section II presents the P2P-VoD system used and presents the issue at hand as a resource allocation problem, before introducing three static strategies used. Then Section III presents Evidence Theory, and our new dynamic resource allocation selection method. Section IV compares the performances of our approach and other strategies. Finally, we conclude this paper. 2. P2P STREAMING RESOURCE ALLOCATION In this section, we introduce P2P streaming, and present the resource allocation problems associated. The peerassisted architecture is here casted for a broad network operator, but can otherwise be deployed as an over-the-top (OTT) solution delivering VoD services on top of Internet Services such as VuDu. Our P2P-VoD system works as follows. All peers of the system contain a predefined number of chunks, and are ready to seed their contents at any time. Whenever a peer requests a content, the Super Node, a central entity, selects the best fit peers to seed the chunks of the content to the requesting peer. Then, the Super Node responds with the list of peers, and the requesting peer starts streaming from its neighbor. Whenever a content is unavailable through the network of peers, we consider the request a failure. These failures may be caused by parts of the contents not stored in any of the currently online peers, or by the fact that peers holding those parts have reached their maximal uplink capacity. 776

If the requesting peer encounters a failure, the file then comes from the cache, which is always online. To evalute the performances of a P2P-VoD system we considered two criteria: the rejection rate and the entropy that expresses peers’ participation and streaming load over active peers. Their description is presented in the following. Rate of VoD sessions rejected Whenever a peer requests a title, if all of the parts are available then this VoD request is deemed successful. If a part of this title is not available in the network, the VoD request is rejected. The rejection rate of our system is calculated by: R(δ) =

r(δ) d(δ)

(2)

where R(δ)is the VoD rejection rate over a time period δ, r(δ) the number of sessions rejected over the time period δ, and d(δ) the total number of VoD requests received over the time period δ. The entropy criterion In a P2P network, each peer contributes to the system by streaming parts of titles to other peers. To evaluate the peers participations level, we use the entropy of the partici- pation of every peer during the considered emulation time. It allows to define how well spread the participation is among the peers. Clearly, one of our objectives in designing a P2P-VoD system is to make sure that all peers are equally taped, which should increase the system utiliza- tion. The definition of entropy is introduced in information theory, which describes entropy as a way to express the level of heterogeneity of a variable. We express the participation rate of a peer by: Rj = rj /(Σ( k = 0)N rk )

(3)

where Rj is the participation probability of peer j, and rj the number of times peer j participated. Then, the Entropy (H(N )) is calculated by : H(N ) = −ΣN j=0 [Rj ∗ log(Rj )]

(4)

where H(N ) is the entropy for N peers, and Rj the participation rate of peer j. Then, the aim is to maximize the entropy, meaning that all peers participated equally. The objective of any P2P streaming resource allocation strategy is to maximize the success rate, Sω (T ). This success rate, computed for a given period T , depends on the strategy ω used in that previous period. The number of titles and the number of peers are fixed during the evaluation. Characteristics such as the number of sessions available at each peer, and the number of sessions necessary to seed stream each title, are also fixed parameters. Every period of time T , we evaluate the performance of each strategy ω, and select the one that maximises Sω (T ). Parameters : • Sω (T ): Success Rate of strategy ω on period T • xk : Success of demand k: 1 if success, else 0 • d: Total number of VoD requests this is the aggregated demand level Variables : • ω : Id of the resource allocation strategy selected, with ω ∈ [1, N ], N number of strategies considered.

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Metric : We select the strategy ω ∗ that maximises Sω (T ), the success rate on period T : Sω (T ) =

Σdk=0 xk d

(5)

Resource allocation strategies aim to define a ranking function f , to select the best peer θ∗ from the the set of peers Θ that can satisfy the current VoD request. f is defined in 6. θ∗ = argj max(f (θj ))

(6)

where θ∗ is the best peer for the current VoD request, f the ranking function, and θj is the peer j from the set of peers Θ. In this Section we introduce three resource allocation (RA) strategies we consider, explaining the characteristics of every strategy and the performance objectives behind their respective designs. We will particularly emphasize the ability of RA strategies to accommodate varying content popularity distribution, fairness among content popularity categories, high demand for VoD services, etc. We present the considered resource allocation strategies and their respective ranking function f . It is worth noting that resource allocation algorithms can be classified into two distinct categories: passive and active. In the passive the resource allocation algorithm use pre-calculated metrics to select appropriate contributing peers for an incoming VoD request. While in the second class, an active resource allocation will rely on performance metrics that vary over time. More details on this problem can be found in Rohmer et al. (2013). In order to achieve a good performance, the strategy of choosing peers must be dynamic. Then, each of the considered strategies can be suited for a particular situation Rohmer et al. (2012). Since a typical P2P streaming system deployment will be exposed to all different realistic scenarios, it is important to design an algorithm able to efficiently switch between different strategies to achieve the highest performance. A simple method would be to directly combine the sorting algorithms used in each strategy, by using a combination Vogt and Cottrell (1999) of the decision criteria. However, in this approach did appear many drawbacks. Fixed weights for the different RAs are required. Obviously, one can fix weights for each of the RA strategies to achieve the best performances over a given period. Then, this fixed strategy will fall when the working conditions will change, and the aggregation parameters must be fitted again. To solve this problem and to enhance the performance of the VoD-P2P system, we propose a dynamic strategy that will be presented in the next section. All demand variations will lead to a different pattern of VoD requests arrival rate and a different distribution of popularity over the content library. In this context, multiple resource allocation strategies would lead to various performances in terms of VoD system utilization, timing and frequency of the saturation. Therefore, our dynamic approach proposes to automatically switch between strategies over time, in order to adapt to each demand pattern. In our previous work Rohmer et al. (2013), we introduced an algorithm for peer resource allocation selection based 777

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on a bayesian approach. At the core of this dynamic RA switching scheme is the ability to predict the most likely trends shifts in the content popularity. The VoD system operation time is split into discrete time periods and the popularity trends are constantly observed within each one of these time periods. In this experiment we use a 4-hour time period, but this can be changed in practice to match specific VoD consumption trends observed in the target audience. ARA essentially uses long-term popularity trends as the aggregate point to which the average popularity should eventually revert. In other words, ARA assumes a relatively stable long-term popularity trends and treats the popularity distribution within the individual 4-hour time periods as deviations from the mean. The method is baed on the prediction of the popularity to let the system takes a good idea of the likely frequency and intensity of VoD requests for every title in the content library ARA will assess how every basic RA strategies would perform in terms of both success rates and entropy. In Rohmer et al. (2013), we used a Bayesian approach to effectively blend together both performance objectives (success rate and entropy) and use the result to compare how the different RA strategies would perform in the following time period. However, the complexity of the Bayesian approach is high, especially, when montecarlo simulation is used to get the maximum a posteriori. Then, herein, we introduce a new fast approach based on Evidence Theory, to select the best strategy by mixing multiple performance objectives.

3. A PLAUSIBILITY-BASED APPROACH TO STRATEGY SELECTION In this section, we start by presenting the Evidence theory. This theory can be viewed as an extension of probability theory. It is suitable for characterizing uncertainty when evidence is imprecise because it allows one to estimate probabilities of intervals instead of probabilities of specific values. We then explain how this approach can be used to efficiently dynamically select a peer resource allocation strategy.

3.1 From Bayes to Dempster-Schafer Although some aspect of probability like the Bayesian probability are closely related with possibility theory, both differ in some major aspects. The Bayesian approach requires to make strong assumptions to estimate the likelihood of the available evidence. Because it is based on posterior probability evaluation, it is sensitive to imprecision in our predictions. Furthermore, this approach is quite heavy, due to the need to keep prior values stored in memory, in order to compute the new posterior probabilities. On the other hand, the Evidence theory approach does not require the user to assume anything beyond what is already available. This approach treats uncertainty due to imprecision differently than uncertainty due to randomness. It is lighter to set up, and even computes faster.

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3.2 Dempster-Schafer Theory The idea of the Dempster-Schafer Theory is that numerical values of uncertainty may be assigned to overlapping sets and subsets of hypotheses, as well as to individual hypothesis. Basic Probability Assignment Measures of uncertainty are known as basic probability assignment. Let Θ = {h1 , h2 , ..., hn } be a finite set of hypotheses (frame of discernment). A basic probability assignment (bpa) is a function m : 2Θ → [0, 1] such that : m(∅) = 0 (7) and



m (x) = 1

(8)

x∈2θ

All of the assigned probabilities sum to unity and there is no belief in the empty set. Any subset x of the frame of discernment for which m(x) is non-zero represents the exact belief in the proposition depicted by x. Belief function The belief represents the confidence that a value lies in A or any subset of A. Therefore, a belief measure is a function Bel : 2Θ → [0, 1], computed from the sum of probabilities that are subsets of the probabilities in question. We have :  m (B) (9) Bel (A) = B⊆A

for all A ⊆ Θ, with A a subset of Θ, B the subsets of A, and m(B) the basic probability assignment of B. Plausibility function The plausibility of a subset A represents the extent to which we fail to disbelieve A. It is a function P ls : 2Θ → [0, 1], defined by:  P ls (A) = m (B) (10) B∩A=∅

for all A ⊆ Θ, with A a subset of Θ, B the subsets of Θ that do not intersect with A, and m(B) the basic probability assignment of B. The plausibility measure is clearly related to the belief function : P ls (A) = 1 − Bel (¬A) (11) for all A ⊆ Θ, with A a subset of Θ, and ¬A the rest of the subsets of Θ. Bel(¬A) is also referred to as the doubt in A, in the litterature. 3.3 Proposed evidential approach Several methods use Evidence Theory for modeling uncertainty with consideration on the analysis of computed measures in expert systems Walley (1996). There, the analysis is basically the comparison of the measures, i.e. possibility measures, coherent lower previsions, additive probabilities and belief function. Method of uncertainty is also known to be useful in the analysis of prognostics Baraldi et al. (2010). 778

The aim here is to select the best strategy ω ∗ in a set Ω, based on multiple criteria. Fig.1 presents an analytical hierarchic modelisation of this problem. Focus%

Best%Strategy%

Success%% Rate%

Criteria%

Decision%% Alterna6ves%

HUF%

LCS%

Par6cipa6on% Entropy%

LPS%

HUF%

LCS%

LPS%

Fig. 1. Analytical Hierarchy Process modelisation of the strategy selection process. Problem formulation In our approach, we select the best strategy using the maximum of plausibility estimator. We express the problem as follows: Find ω ∗ ∈ Ω such as : ω ∗ = argω∈Ω max (P ls(ω))

(12)

where ω ∗ is the best strategy, Ω is the set of all strategies, ω a strategy, and P ls(λ) the plausibility of strategy λ. Plausibility estimation In order to select the best strategy, we need to estimate the plausibility for each strategy. To do so, we combine the basic probability assumptions, obtained for each strategy with each criteria, by using :  B∩A=x m1 (A) · m2 (A)  [m1 ⊕ m2 ] = (13) 1 − B∩A=∅ m1 (A) · m2 (A)

An important feature in the above formula is in the denominator, which can be interpreted as a measure of conflict between the sources. It is directly taken into account in the combination as a normalisation factor. The measure represents the mass which would be assigned to the empty set if masses were not normalised. It is important to note that, with a larger set of criterias and strategies, the number of solutions to evaluate increases, thus increasing the complexity. In such cases, a genetic algorithm can be used to reach an optimal solution in fewer iterations. 4. EXPERIMENTAL PLATFORM OVERVIEW

Our emulator is a very close approximation of the behavior of a full-scale peer-assisted VoD streaming system. First, we have a full-scale implementation in Python of the central server, called the Super Node (SN). The SN can process VoD requests in real-time. Each VoD request targeting a specific title leads the SN to lookup the database for peers with the content parts and enough uplink capacity to stream the content parts. The SN then returns a list of peers that can satisfy the VoD request by contributing a specific part to the multi-source streaming session. The SN keeps the database up-to-date by reflecting changes after processing every new VoD request. Fig.2 illustrates the process at the highest level, and more details can be found in Rohmer et al. (2013). To evaluate each resource allocation strategy, we generate a trace file corresponding to the upcoming demand, and

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Database$

779

uses LCS (Lowest Critical Score), then, finally switches back to HUF for the last time period.

Peer$Resource$Alloca/on$

Server$

Peer$Request$

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Fig. 3. Strategies selected by ARA-Evidence over time. Fig. 2. Overview of our P2P-VoD Architecture. test each strategy with that trace file. Every 4 hours, the prediction centre (here located at the Super Node) generates a trace file of the upcoming demand covering the next 4 hours. Then, it contacts the simulator with the trace to request a Strategy Update. At this point, the simulator determine the best RA strategy to used using the ARA algorithm and the Evidence Theory approach as explained above. Our simulations rely on real content popularity data from a Youtube, a large consumer digital media offering. This data was originally collected from YouTube by Xu Cheng et al., and it is publically available online. Youtube service reach is broad enough and can thus be considered a fairly good proxy for consumers expected demand for a large VoD library. Furthermore, we integrated the Youtube content popularity traces with Carsten et al.s approach to content demand evolution in order to better reproduce real-world content popularity shifts.

It is important to recall that the main drivers of ARA strategies selection are: (i) most likely popularity pattern and intensity in the following time period. This is estimated based on the recently observed popularity deviations from the long-run popularity pattern-intensity; (ii) the current content availability in the network which is the consequence of past RA decisions. Fig. 4 presents the evolution of the rejection rate over time. It appears clearly that both dynamic strategies greatly reduce the rejection rate. Indeed, when all static strategies reach a higher than 0.5 rejection rate at 13 hours, both dynamic approaches maintain a close to 0 rejection.

4.1 Simulation parameters In order to assess the performances of resource allocation strategies in large Peer-to-Peer deployments, our simulations feature a system with 100,000 peers. Each peer can simultaneously seed up to 5 simultaneous VoD sub-streams to other peers, and can hold up to 500 movie parts, which means the system can store up to 50,000,000 parts. We use a content library containing 50,000 different video titles. Each title in the library is characterized by a different popularity behavior as illustrated in Figure 3, and the overall popularity distribution over the entire content library follows a Long Tail model. It is worth recalling that the different 50,000 titles are duplicated in the network based on their expected popularity. Each duplicate is split into 5 complementary parts before storage in the network. In order to evaluate the performances of each strategy, we propose two metrics : rejection rate, and entropy. 5. RESULTS AND DISCUSSION In this section, we present the results obtained with ARA using the Evidence Theory, labelled ”ARA-Evidence”. We compare those results to the ones obtained with static strategies, and with the ones obtained with ARA using a Bayesian Approach, labelled ”ARA-Bayes”. Fig. 3 shows the strategies selected over time by the ARAEvidence algorithm based on the Evidence Theory statistical analysis. First, ARA starts the first time period with HUF(Highest Uplink First) before switching to LPS (Lowest Popularity Score)for the following time period, then 779

Fig. 4. Rejection rate over time for each approach. This can also be oserved in Fig.5, which displays the total (meaning the sum of all rejection rates, from the start, up to time t) rejection rate over time. All three static RA rise quickly to 2 and higher, while the dynamic approaches manage to stay near 0 rejection, rising up to 1.5 towards the end of the simulation.Fig. 6 presents the evolution of the entropy when using each strategy. Here, HUF is clearly the most efficient. This is due to its design : HUF automatically selects the least participating peers, and, therefore, tends to spread the participations to all peers. On the other hand, the dynamic strategies aim to maintain a low rejection rate, while maintaining a good peer participation entropy. Table 1 presents the overall results for all strategies. Both ARA strategies tend to perform similarly, greatly reducing the overall rejection rate. Table 1. Average Rejection Rate and Entropy Results. Strategy LPS LCS HUF ARA-Evidence ARA-Bayes

Rejection 0.289 0.225 0.099 0.063 0.063

Entropy 6.403 6.648 8.013 6.441 6.461

IFAC MIM 2016 780 June 28-30, 2016. Troyes, France

Thibaud Rohmer et al. / IFAC-PapersOnLine 49-12 (2016) 775–780

ple would be to keep the same resource allocation strategy as long as the demand does not present an important shift, and request a new strategy as soon as it occurs. REFERENCES

Fig. 5. Cumulated rejection rate over time for each approach.

Fig. 6. Peer participation entropy evolution over time for each approach. Both dynamic approaches perform better than the static ones, from a rejection point of view. Although HUF performs better in terms of entropy, it is important to note that, while the entropy is a key parameter to define the efficiency of a strategy, it is not the main parameter for our resource allocation problem, defined in II.A. The overall goal is to reduce the rejection rate, which is successfully obtained by both dynamic approaches. Because those two strategies dynamically select the best choices, and switch accordingly, they both obtain very similar results. However, this approach does not require posterior probability estimation, whereas the Bayesian approach is based on it. Therefore, the bayesian approach is a heavier approach to strategy evaluation. By using Evidence Theory, we managed to keep the results obtained with a Bayesian Approach, but with a lighter algorithm. 6. CONCLUSION In this paper, we introduced a new approach for a resource allocation selection strategy. We used Evidence Theory to select the most efficient strategy, in a dynamic context. The proposed algorithm switches between multiple resource allocation strategies, in order to adapt to the upcoming demand scenario, and use the best strategy. Our main contribution is the strategy selection method. While a Bayesian approach requires posterior probability estimation, this approach does not. Therefore, the algorithm, based on Evidence theory and using the Maximum Plausibility estimator, is easier to implement. In this work, we adapt the strategy every considered number of hours. In work under progress, we dynamically request a strategy update, based on live observed demand shifts. The princi780

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