3.4 The Extended Arbitrary Tree Protocol
3.4.4 The Arbitrary versus Extended Arbitrary Tree Protocols
In this section, we compare the availability of read and write operations of the Arbitrary as well as Extended Arbitrary Tree protocols. The comparison is performed by setting up four different configurations and considering a replication-based system composed of 15, 31, 63, 127 and 255 replicas respectively. The tree structure of the configuration Arbitrary Tree (“AT”) is constructed using Algorithm 3 whenever possible such that the root is a logical node whereas the tree of Extended Arbitrary Tree (“EAT”) has the same structure as that of “AT” however with a physical root node. On the other hand, the tree structure of Square Arbitrary Tree (“SAT”) is constructed by setting |Kphy| '
√
n and mphy,k '
√
n ∀k ∈ Kphy such that the root is a logical node whereas
the tree of Extended Square Arbitrary Tree (“ESAT”) has the same structure as that of “SAT” however with a physical root node. The followings are the tree representations of
3.5 Conclusion 87
“SAT” for the above-mentioned number of replicas respectively:1-3-4-4-4, 1-5-5-5-5-5-6, 1-7-8-8-8-8-8-8-8, 1-11-11-11-11-11-11-11-11-11-11-17 and 1-15-16-16-16-16-16-16-16-16- 16-16-16-16-16-16-16. Keep in mind that such a representation of the arbitrary tree was followed in section 3.2.
The availability computations of read and write operations of “AT” and “SAT” configurations are based on the equations (3.2.1) and (3.2.3) respectively whereas those of “EAT” and “ESAT” configurations are carried out by considering the equations (3.4.2) and (3.4.1) respectively. We suppose that the replicas are individually available with a probability p = 0.6 and 0.7 respectively whereas we assume that the root replica for “EAT” and “ESAT” configurations has an availability of g = 0.95.
Figure 3.7 illustrates the availability of read operations of the (Extended ) Arbitrary Tree protocols. We can notice that, the availability of “EAT” and “ESAT” configura- tions (Extended Arbitrary Tree protocol) is always superior to that of “AT” and “SAT” configurations (Arbitrary Tree protocol) when p = 0.6. However, as p becomes greater than 0.65, the read availability of the Arbitrary Tree protocol becomes comparable to that of the Extended Arbitrary Tree one.
Figure 3.8 illustrates the availability of write operations of the two protocols. In this figure, we can observe the big amelioration in availability of “EAT” and “ESAT” configurations (Extended Arbitrary Tree protocol) with respect to “AT” and “SAT” configurations (Arbitrary Tree protocol), due to the fact that, every time the write operation is incapable of being carried out normally (because of replica failures), the root replica is accessed which is almost always available.
3.5
Conclusion
I
n this chapter, we introduced the Arbitrary Tree protocol whose tree structure can be configured appropriately by taking into account the frequencies of read and write operations of the system. We identified a configuration which has the best combined read and write communication costs of 2√n and has the least system load of √1nimposed
by write operations compared to the other (previously existing) tree-structured replica control protocols. This proposal enables the shifting from one configuration into another by just modifying the structure of the tree. There is no need to implement a new protocol whenever the frequencies of read and write operations of the system change.
Also, an approach was presented that integrates the perfect failure detector P into the Arbitrary Tree protocol in order to ameliorate the availability of read and write operations. We showed that such a proposal has better availability for its read and write operations which is achieved by considering the root of the tree a physical node instead of assuming it a logical one as it is the case for the Arbitrary Tree protocol.
Figure 3.7: The availability of read operations of the Arbitrary and Extended Arbitrary Tree protocols for different number of replicas n.
Figure 3.8: The availability of write operations of the Arbitrary and Extended Arbitrary Tree protocols for different number of replicas n.
SUMMARY
Dans ce chapitre, nous ´evaluons la performance du protocole Arbitrary Tree en util- isant un syst`eme de Grille [ViSaGe07]. ViSaGe est l’acronyme de “ Virtualisation du Stockage appliqu´ee aux Grilles informatiques” et a pour objectif le partage et la mobil- isation des ressources de stockage distribu´ees dans un environnement Grille.
ViSaGe est organis´e autour de cinq composants de base: un composant de gestion de fichiers pour grille (VisageFS), un composant de virtualisation des ressources de stockage pour agr´eger les ressources physiques de stockage (VRT), un composant de gestion de la concurrence et de la coh´erence (VCCC), un composant d’administration et de mon- itoring (MonAmin) pour contrˆoler et piloter le syst`eme, ainsi qu’un composant g´erant la communication pour les messages de contrˆole et le transfert des donn´ees (VCOM). Une op´eration de lecture ou d’´ecriture est g´en´eralement initi´ee par l’application qui en- voie sa requˆete au composant VisageFS. Ce dernier s’occupe de g´erer les droits d’acc`es aux fichiers et aux r´epertoires. Il s’occupe ´egalement de g´erer la concurrence des acc`es par le biais de la librairie VCCC. Une fois que l’objet de stockage qui correspond au fichier demand´e a ´et´e trouv´e par l’op´eration de lookup, une demande d’acc`es `a cet ob- jet est envoy´ee par VisageFS au VRT. Le VRT s’occupe de l’agr´egation des ressources physiques distribu´ees sur la grille et doit fournir `a VisageFS une vue de ces ressources sous la forme d’un espace de stockage virtuel. Au sein de cet espace virtuel, le VRT peut appliquer diverses politiques de placement et de migration de donn´ees afin d’am´eliorer les performances d’acc`es `a ces donn´ees. Pour cela, il manipule des objets de stock- age qui peuvent ˆetre r´epliqu´es parmi les ressources physiques distribu´ees. Lorsque les donn´ees sont r´epliqu´ees, le VRT assure la coh´erence des acc`es en lecture/´ecriture par le biais de la librairie VCCC. L’architecture de ViSaGe ´etant sym´etrique, tous les com- posants logiciels sont distribu´es sur les diff´erentes ressources de stockage. Le composant VCOM permet `a deux composants situ´es sur deux nœuds distants de communiquer sans se soucier des probl`emes de s´ecurit´e. Le composant MonAdmin est d´ecompos´e en un module d’administration et un module de monitoring. Ces modules sont utilis´es par tous les composants de ViSaGe. La partie monitoring de MonAdmin doit collecter les informations relatives `a l’´etat de chacun des composants ainsi que l’´etat de la ressource repr´esent´ee par la couche fabrique. La partie administration de MonAdmin permet de contrˆoler les autres composants afin d’optimiser l’acc`es aux ressources de stockage. Ce composant d’administration sert ´egalement d’interface de gestion pour tous les com- posants de ViSaGe.
L’´evaluation des performances est effectu´ee en tenant compte deux facteurs: le temps de r´eponse des op´erations de lecture et d’´ecriture ainsi que la fraction des op´erations de
consid´erant que toutes les r´epliques se trouvent dans le mˆeme site local ainsi que de localiser certains d’entre eux dans un site diff´erent. Plusieurs modes et taux de lecture et d’´ecriture sont prises. Les r´esultats exp´erimentaux obtenus confirment fermement aux r´esultats th´eoriques qui ont ´et´e fournis avec preuves math´ematiques dans [BBG08].
CHAPTER IV
PERFORMANCE EVALUATION OF THE ARBITRARY
TREE PROTOCOL
In this chapter, we evaluate the performance of the Arbitrary Tree protocol by making use of a grid-wide system ViSaGe1[FM04, TFM05], which aims at facilitating the sharing
and the mobilization of distributed storage resources within a grid environment. The performance evaluation is performed by taking into account two factors: the read and write operations’ response time as well as the fraction of read and write op- erations each replica of the system received. For this purpose, we set up three different configurations and carry out the experiments under different circumstances such as by considering that the replicas are found in the same local site as well as by locating some of them in a different site. Several different patterns of read and write operation interleavings are taken with varying read-write ratios.
The obtained experimental results firmly confirm the theoretical ones whose math- ematical proofs are provided in Appendix A. Additionally, they show that among the studied configurations, some have the ability to evenly distribute read operations among replicas of the system whereas others can do it for write operations. Furthermore, the experiments show that, for certain configurations, the distribution of read operations among the replicas depends on the used pattern of read and write operation interleav- ings as well as on the number of read quorums in the system.
In section 4.1, we introduce ViSaGe and its relevant components and give its ar- chitectural design whereas the experimental results of the Arbitrary Tree protocol is provided in section 4.2.1.