Situated vs. Global Aggregation Schemes for Autonomous Management Systems

Transcription

1 4h IFIP/IEEE Workshop on Disribued Auonomous Nework Managemen Sysems Siuaed vs. Global Aggregaion Schemes for Auonomous Managemen Sysems Rafik Makhloufi*, Guillaume Doyen*, Gregory Bonne and Dominique Gaii* *ICDIERA, UMR Universie de Technologie de Troyes GREYCIMAD UMR Universie de Caen Basse-Normandie Absrac-In he conex of auonomous nework managemen, he Auonomic Managers (AMs) need o collec managemen informaion from oher elemens in order o infer an overall sae of he nework considered by he decision making process. Two concurren sraegies are commonly used o achieve his operaion. On one hand, approaches based on a siuaed view only gaher informaion in a bounded neighborhood, hus providing a high reaciviy o AMs for conrol operaions. On he oher hand, approaches based on a global view provide a good accuracy a he cos of a larger convergence ime. Being able o choose he bes approach in a given conex is crucial o ensure he efficiency of an auonomous managemen sysem. Thus, in his paper, we perform an exhausive performance analysis of hese approaches by considering ypical schemes of boh of hem, namely a one-hop and wo-hops siuaed view agains gossip- and ree-based global aggregaion schemes. Merics we consider are he convergence ime, communicaion and compuaion cos, scalabiliy and he accuracy of esimaed aggregaes. Given hem, we show under which condiions an approach ouperforms he ohers. Index Terms-Auonomous Neworking, Decenralized Aggregaion, Siuaed View, Managemen Informaion. I. INTRODUCTION The Auonomic Managers (AMs) of an auonomous managemen sysem need o collec managemen informaion from he nework elemens in order o infer an overall sae of he nework for he decision making process. Thus, he performance of he managemen sysem is direcly depending on he qualiy of colleced informaion ha mus mee some consrains such as accuracy, consisency and availabiliy. This informaion is colleced hrough aggregaion schemes according o a siuaed view (SV) where each node has he knowledge of a subse of he nework nodes or according o a global view (GV) where global aggregaes are compued on each node o infer he overall sae wihin he nework. Previous sudies show ha each aggregaion scheme is efficien in a given conex. For example, gossip schemes are less sensiive o fauls and dynamics han ree ones, bu hey need more communicaion, compuaion and ime o converge. Thus far, he exising evaluaions on he aggregaion schemes only propose o compare ree-based and gossip-based schemes. They do no include he siuaed schemes in heir comparisons. So, we do no know how his echnique behaves in comparison o he global schemes. Thereby, here is a need o sudy he performance of hese aggregaion caegories in order o learn exacly when using each of hem. In his paper, we propose a comparaive sudy of he performance of siuaed and global aggregaion schemes. For his we implemen hree ypical aggregaion schemes, one from he siuaed view wih wo global ones, a gossip and a ree aggregaion schemes. Then, we compare hem according o sandard evaluaion crieria ha are convergence ime, compuaion and communicaion coss, scalabiliy and accuracy. This paper is organized as follows. We firs presen he relaed work on he evaluaion of aggregaion schemes in Secion II. We give an overview of he exising global and siuaed aggregaion schemes and we describe he aggregaion schemes ha we have implemened from each caegory in Secion III. Subsequenly, we presen our evaluaion of he developed schemes in Secion IV. Finally, we conclude and we presen our perspecives in Secion V. II. RELATED WORK Because of he emergence of several decenralized aggregaion proocols, many sudies have been performed in order o compare heir performance. Bawa e al. [1] propose a se of aggregaion schemes for esimaing basic aggregaes on a P2P nework. They compare one gossip-based scheme Propagae2AII o wo ree-based schemes: SingleTree and MulipleTree. This sudy shows ha he ree ouperforms he gossip in erms of ime, communicaion and compuaion coss, bu he laer is more accurae under churn. The auhors compare hese global schemes, bu do no discuss he siuaed view in heir comparison. Wuhib e al. [2] presen G-GAP (Gossip-based Generic Aggregaion Proocol), a gossip proocol for coninuous monioring of aggregaes, where he radeoff beween he esimaion accuracy and he overhead can be conrolled. G-GAP is an exension of he push-synopses scheme of [8]. The auhors compare G-GAP o GAP (Generic Aggregaion Proocol), a ree-based aggregaion proocol ha we describe in he nex secion. Conrary o he firs presened sudy, his evaluaion shows ha GAP ouperforms he gossip proocol for comparaive overhead, boh in erms of accuracy and robusness. Birman [3] discusses he srenghs and limiaions of gossip schemes. On one hand, he auhor presens heir advanages: $ IEEE 1135

2 simpliciy, bounded load on nodes, opology independence and robusness o ransien nework disrupions. On he oher hand, according o him, he small bounded message sizes and he relaively slow periodic exchanges limi he informaion carrying capaciy of gossip. Furhermore, gossip scales well in some dimensions bu no for all. Gossip is also a communiy process where all he nodes are dependen upon he correc behavior of all oher nodes. Therefore, a malicious or malfuncioning node can delay or even defea he aggregaion. This paper does no provide quaniaive comparison resuls, bu only a qualiaive analysis of he gossip's limiaions and srenghs. In our previous work [4], we presened an overview of a se of decenralized aggregaion schemes and provided a mulicrieria classificaion of hem. The provided heoreical comparison resuls of his sudy were colleced from he lieraure. These resuls are limied, since he original experimens are performed under differen es condiions. To summarize, according o hese sudies, gossip schemes ensure faul-olerance. However, he large number of exchanged messages causes more colmnunicaion and compuaion overhead han ree-based schemes. Thereby, ree-based schemes execue hemselves in a beer convergence ime and a lower communicaion and compuaion cos due o heir opimizaion of he number of exchanged messages on he ree. However, heir hierarchical srucure wih a unique pah beween each node and he roo les hierarchical schemes be more sensiive o fauls han he gossip ones. Globally, hese evaluaion sudies show ha each of he aggregaion caegories is beer han he oher one in a given conex. All hese sudies consider only global aggregaion schemes. To he bes of our knowledge here is no work in he lieraure ha compares siuaed approaches wih global ones. Thus, we do no know he performance of he siuaed schemes in comparison o he global ones. So, i is necessary o clearly idenify when we need o use each of hese aggregaion caegories for collecing aggregaes. heir local aggregaes hrough a DHT o a single roo node. The laer compues an overall aggregae and uses a publishsubscribe mechanism o spread i on all nodes ha subscribed o he diffusion group concerning he moniored variable. A node does no know in advance he ree srucure and is children, bu i discovers i when messages are exchanged. As illusraed in Algorihm I, each node execues wo differen hreads: an acive and a passive one. The acive hread (Algorihm l.a), execued once on a node i, iniiaes he informaion exchange. The passive hread (Algorihm l.b) wais for messages (msg) sen by an iniiaor o process hem. Iniially, each node i uses he GeParenO mehod o selec is paren (line a.l) and sends i a couple (i, (Xrawi, 1)) including is Node! d, is raw value and is weigh (line a.2). A node i ha receives a message from a child j (line b.2), updaes is local sae over he updae(msg) mehod (line b.3) where i calculaes a new parial aggregae hrough hose of all is children. I hen forwards he new aggregae in a pair (i, (Xi, Wi» o is paren (lines b.4 and b.5). If node i is he roo (line b.6) hen i wais unil i receives all is children's aggregaes (line b.7), and i diffuses he global aggregae Xi over a publish-subscribe sysem on all he subscribed nodes (line b.8). Thus, each node ha receives Xi (line a.3) updaes is parial aggregae wih he global one (line a.4). Algorihm 1 Push ree scheme execued by a node i (a) Acive hread 1: p+---gepareno 2: send (i, (Xi, 1)) o p 3: msg+---receive(j, Xj) 4: saei+---updae(msg) (b) Passive hread 2: msg+---receive (j, (Xj, Wj)) 3: saei +---updae( msg) 4: p+---gepareno 5: send (i, (Xi, Wi») o p 6: if i is roo hen 7: wai unil receive all aggregaes 8: diffuse (i, ;) 9: end if' 10: end loop III. COMPARED AGGREGATION SCHEMES We develop and we implemen hree ypical and represenaive aggregaion schemes inspired from exising ones. In his secion, we give a brief overview of hem and we presen he algorihms we implemened in our sudy. A. Global view According o he global view, aggregaes can be colleced over a ree or hrough gossip. 1) Tree: This involves he use of a hierarchical srucure for collecing aggregaed managemen informaion. The compuaion of aggregaes is done hierarchically in a boomup fashion. The aggregaion algorihm converges when he compued global aggregae is available on he roo of he ree [1]. In his caegory, we implemened a push ree-based aggregaion scheme ha is a combinaion of GAP [5] and he deploymen opology proposed in [6]. This scheme consiss in a srucured P2P overlay where all nodes communicae 2) Gossip: Unlike ree-based echniques, where nodes are organized ino a ree, gossip-based schemes do no require a paricular srucure o perform aggregaion. A each round of he aggregaion process, a node conacs one or more of is neighbors usually chosen randomly and exchanges informaion wih hem [3], [7], [8]. Iniially in he nework, each node has only is own raw managemen informaion. The aggregaion algorihm converges when he compued global aggregae is available across all he nework nodes. The aggregaion scheme developed here is based on he push-pull gossiping scheme [9] wih symmeric informaion exchanges where boh nodes send and receive heir esimaes. As illusraed in Algorihm 2, node i calls he GeNeighbors(l) mehod o selec uniformly a random one node j from he lis of is direc neighbors IDl; which is obained over he enire se of neworks nodes (line a.2). Then, i sends o j a message (i, Xi) conaining is local aggregae and wais for a response wih he remoe node j (line a.3). When i receives a couple (j, Xj) from j (line a.4), i updaes is local 1136

3 sae hrough he updae(msg) mehod ha compues a new parial aggregae according o he seleced aggregae funcion (line a.s). The node i repeas he same process a each round (line a.6). When he passive hread (Algorihm 2.b) of node i receives an exchange reques message (line b.2), i replies wih is local aggregae (line b.3) and hen i updaes is local sae hrough he updae(msg) mehod (line ba). Algorihm 2 Push-pull gossip scheme execued by node i (a) Acive hread 2: j+-geneighbors(l) send (i, Xi) o j 4: msg+-receive0, Xj) 5: saei +-updae(msg) 6: wai(round duraion) 7: end loop 3: B. Siuaed view (b) Passive hread 2: msg+-receive0, Xj) send (i, Xi) o j 4: saei +-updae(msg) 5: end loop In a concurren way, alernaive decenralized managemen approaches like [10], [11] propose o limi he view of each node o some nodes by using a siuaed view. Thus, he knowledge of a node is limied o is direc neighbors or a par of he nework nodes [12]. The size of his view is defined by a number of nodes or a number of hops. We have implemened a ypical siuaed scheme inspired from HyParView (Hyper Parial View) [10], where each node mainains a parial view of a par of nework nodes, bounded by a maximum number of hops. A node i can hen obain an aggregae of is view by collecing managemen informaion from is h-hops neighbors. As shown in Algorihm 3, he requesing node i ges he lis ]]J)i of all is direc neighbors hrough he GeNeighbors(all) mehod (line a.l) and sends hem a query message (i, h) (line a.2). Each node i ha receives an aggregaion reques message (line b.2) verifies if i does no previously answer o he same reques coming from j in he same aggregaion cycle. If so, i answers by sending is ID and is local raw value (i, XrawJ direcly o he requesing node (line b.3). Then, he node i decremens he number of hops conained in he received message (line ba). If he maximum number of hops is no reached (line b.s), hen he node i forwards he received reques (j, h) o all is direc neighbors (lines b.6 and b.7). When a requesing node i receives an answer (j, Xraw j ) from a neighbor (line a.3), i adds his pair of values o is mainained neighbors se lli and updaes is own sae by compuing a new parial aggregae (line aa). 3: IV. EVALUATION STUDY We presen in his secion our evaluaion sudy of he performance of hese siuaed and global aggregaion schemes. A. Experimenal framework We performed simulaions in he conex of he monioring service under he esbed and he scenarios described below. Algorihm 3 Pull siuaed view scheme on node i (a) Acive hread 1: j[])i+-geneighbors(all) 2: send (i, h) o j[])i 3: msg+-receive(j, Xraw) 4: saei+-updae(msg) (b) Passive hread 2: msg+-receive0, h) 3: send (i, XrawJ o j 4: h+-h - 1 5: if h > 0 hen 6: j[])i+-geneighbors(all) 7: send0, h) o j[])i 8: end if 9: end loop 1) Tesbed and Simulaion scenarios: We conduced our evaluaion in he FreePasry simulaor, an open-source Java implemenaion of he Pasry DHT [13]. In order o provide realisic resuls, we carry ou all our experimens wih he Euclidean nework opology model. We also rely for he reebased scheme on Scribe [14] o spread he roo's aggregaes on all he subscribed nodes. Based one he realisic parameers summarized in Table I, we run wihin a saic nework each of he developed aggregaion schemes o compue an average of randomly generaed values ranging beween 0 and 100. The siuaed scheme is execued wih a view limied o he direc neighbors (SV 1) and also wih wo-hops (SV2). The gossip process is execued wih rounds of duraion 600ms ha corresponds o he maximum ime for an informaion exchange. We consider a nework size varying from 2 o 1000 nodes. To give a sufficien saisical significance o he resuls, each value presened here is an average of he values obained on 100 execuions of he aggregaion algorihms. TABLE I SIMULATION PARAMETERS Parameer Aggregae funcion B. Evaluaion resuls Nework opology model Topology mainaining frequency Values changing ftequency Toleraed error (E) 0 Neighborhood degree 8 Gossip round duraion Value Average Euclidean 200ms 20sec 600ms Number of nodes (N) [2;1000] Number of hops in SV (h) [1;2] Since in he lieraure, he acknowledged sudied evaluaion crieria for aggregaion schemes are convergence ime, communicaion and compuaion cos, scalabiliy and accuracy [1], [2], [3], [4], we propose here o carry ou a comparison of he developed schemes according o hese crieria. 1) Convergence ime: I is he elapsed ime for boh he communicaion and he compuaion of a global aggregae [1]. Therefore, i is he necessary ime beween he iniializaion of he aggregaion process and he ime when all nodes hold he aggregaion resuls. Thereby, Tconv=Tagg-Tini (equaions 1,2 and 3). Thus, in he case of global view, Tconv corresponds o he ime when all nodes hold he same global aggregae. In he 1137

4 Number of Nodes (,) Number of Nodes (b) Number of Nodes (e) Fig. 1. Simulaion resuls on: (a) Convergence ime; (b) Communicaion cos; (c) Compuaion cos [log-log scale] siuaed scheme, his condiion canno be reached because each node rerieves only he values of is h-hops neighbors. So, we measure he required ime for each node o collec informaion from is neighbors and o calculae a parial aggregae. = Tini Tagg(GV) = Tagg(SV) = 'Vi E {I, "., N}, xf = Xra w i (1) 'Vi,j E {l,,,.,n}, IX; -Xjl < E(2) 'Vi, 'Vj E {I, "., K}, Xrawj E lli (3) We observe in Figure 1.a a large convergence ime for he gossip scheme followed by he ree, hen a relaively low ime for he siuaed view. Under a nework of 1000 nodes, he gossip's convergence ime is abou 6 imes higher han he one of he ree and abou 23 imes he one of SV2. This high delay is explained by he blind communicaion used o exchange messages a each round of he gossip. For he ree, he convergence ime is he delay required o send all he values o he roo node and o spread he compued aggregae on all he subscribed nodes. The siuaed scheme requires a low ime o converge because a one ime each node sends simulaneously one reques message o all is direc neighbors and hen compues a parial aggregae of he received values o wo-hops nodes. This ime is lower in SV1 when only direc neighbors are conaced. Thus, in erms of convergence ime, he siuaed scheme scales beer and converges more quickly han he global ones. 2) Communicaion cos: The communicaion cos [1] is he sum of sizes of messages sen beween any node pairs (i, j) during he aggregaion process. The communicaion cos for he developed algorihms is considered as he number of messages sen by all nodes because all messages have approximaively he same size, in he sense ha each message conains only wo or hree numerical values. Thus, Ccomm = 2::1 Ccommi' where Ccommi is he he number of messages sen by node i and N is he number of nework nodes. In Figure 1.b, we see ha he colmnunicaion cos is proporional o he number of nodes. Under a nework of 1000 nodes, he communicaion cos of SV2 is almos 3 imes higher han he one obained in he case of gossip and abou 42 imes he one of he ree. This high colmnunicaion cos is explained by he fac ha he laer is based on a broadcas algorihm where each node floods is reques message on all is h-hops neighbors. SV1 causes more communicaion overhead han he ree and less han he gossip. In he laer, a node exchanges is value wih only one oher node, so i causes abou 9 imes less overhead han SV2. The ree scheme causes he lowes communicaion overhead ha corresponds o he messages sen in a boom-up fashion o he roo and hose used by Scribe o spread he global aggregae. For he gossip scheme, i involves more messages o converge han he ree because i uses a blind communicaion over muliple rounds. Thus, SV2 involves more messages exchanges han he aggregaion hrough he global schemes. This overhead can be reduced by limiing he view size of nodes o he direc neighbors. 3) Compuaion cos: The compuaion cos [1] is he maximum compuaion cos among all he nodes in he nework. For a single node, he compuaion cos is he number of seps aken by he aggregaion process ha is execued on he node. Thus, Ccomp = max(ccompj, i E {l,.'" N}. We noice in Figure 1.c ha when we have a large number of nodes, he compuaion cos of he siuaed view is less imporan han he ree one and less han he gossip one. In he laer, exacly one updae operaion is execued on a node in each round. For he siuaed scheme, he compuaion cos depends on he view size of each node, since in one round an updae operaion is execued a each recepion of a neighbor's value. We observe a higher compuaion cos for he ree-based scheme because according o he developed algorihm, he wors case is regisered a he roo node where he compuaion cos is equal o he number of nodes. A lower compuaion cos was expeced which is no he case. I is due o he reacive mechanism in which each node of he ree direcly sends he received messages o is paren. Thus, a node does no wai o receive messages from all is children before sending he compued parial aggregae. The siuaed view causes less compuaion overhead han he he global schemes. I is also more scalable han hem, according o his crierion. 4) Accuracy of esimaed aggregaes: When messages are exchanged beween nodes, he iniial average is redisribued 1138

5 among hem. Thus, he aggregaion process does no change he global average bu i decreases he variance over he se of all esimaes in he sysem. Thus, in order o show he disribuion of esimaes over all he nework nodes and o show how far hese values lie from he average value, we compue he variance over all he esimaes (equaion 4). N 1-2 V(X) = - L (Xi - X). (4) N i=1 In order o evaluae he accuracy of esimaed aggregaes for each aggregaion scheme, we fix he size of he nework o 1000 nodes and we measure he variance over he parial nodes's aggregaes afer each cycle of duraion 200ms. V. CONCLUSION AND FUTURE WORK This paper compares siuaed aggregaion schemes o he global ones. I provides quaniaive resuls on he use of hese schemes for collecing aggregaes. We evaluae he performance of each scheme according o convergence ime, communicaion and compuaion coss, scalabiliy and he accuracy of esimaed aggregaes. Through he obained simulaion resuls, we confirm ha none of he proocols is beer han anoher. Their performance depends on he conex in which hey are deployed. The siuaed scheme ouperforms boh gossip and ree in erms of convergence ime, compuaion cos and scalabiliy. However, for he accuracy of esimaed aggregaes, he global schemes ouperform he siuaed one. Finally, he colmnunicaion cos of he siuaed view depends on he view size of nodes. In an effor o enhance his sudy, we are currenly working on he esablishmen of realisic models o represen he level of informaion dynamics and nework dynamics. This will allow us o evaluae he faul-olerance of each scheme by measuring he impac of boh he nework and informaion dynamics on he decision making process qualiy. We also plan o pursue his work by designing an adapive managemen sysem able o combine he use of global and siuaed schemes by selecing he suiable scheme o use according o he curren conex of he managemen informaion and is environmen. Cycle (200ms) Fig. 2. Accuracy of esimaed aggregaes [semi-log scale]; We see in Figure 2 ha he variance beween he disribued aggregaes decreases wih an increase in he number of cycles. For he siuaed scheme, he minimal variance is always greaer han O. Thus, i is less accurae han he global schemes. This is caused by he compuaion of parial aggregaes on each node, conrary o gossip or ree where a global aggregae is compued. When we resric he view size in he siuaed view o he direc neighbors of nodes, his minimizes he overhead and he convergence ime. Alhough, we ge less accuracy on he esimaion of global aggregaes. Thus, he global schemes ensure more accuracy han he siuaed one in he aggregaion. Globally, he wo-hops siuaed scheme involves less convergence ime and less compuaion cos han he global ones. I is also more scalable han hem regarding hese crieria, wih a comparable communicaion cos. Bu, i provides less accuracy in he esimaion of aggregaes han he global schemes. Thus, i is more preferable o use he global schemes when we need more accuracy and exaciude and o use he siuaed one when we need o reduce he ime, communicaion and compuaion coss. When we limi he view size of nodes o he direc neighbors, we reduce he differen coss of he siuaed scheme bu we lose in erms of he accuracy of he esimaed aggregaes. Moreover, concerning he global schemes, one can noe ha we obained consisen and comparable evaluaion resuls wih hose presened in he relaed work for he common crieria. REFERENCES [1] M. Bawa, H. Garcia-Molina, A. Gionis, and R. Mowani, "Esimaing aggregaes on a Peer-o-Peer nework," Tech. Rep., [2] F. Wuhib, M. Dam, R. Sadler, and A. Clem, "Robus monioring of nework-wide aggregaes hrough gossiping," TNSM, vol. 6, no. 2, pp , [3] K. Birman, "The promise, and limiaions, of gossip proocols," SIGOPS Oper. Sys. Rev., vol. 41, no. 5, pp. 8-13,2007. [4] R. Makhloufi, G. Bonne, G. Doyen, and D. 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