@article {Longo201737, title = {An approach for resiliency quantification of large scale systems}, journal = {Performance Evaluation Review}, volume = {44}, number = {4}, year = {2017}, note = {cited By 0}, pages = {37-48}, publisher = {Association for Computing Machinery}, abstract = {

We quantify the resiliency of large scale systems upon changes encountered beyond the normal system behavior. Formal definitions for resiliency and change are provided together with general steps for resiliency quantification and a set of resiliency metrics that can be used to quantify the effects of changes. A formalization of the approach is also shown in the form of a set of four algorithms that can be applied when large scale systems are modeled through stochastic analytic state space models (monolithic models or interacting sub-models). In particular, in the case of interacting submodels, since resiliency quantification involves understanding the transient behavior of the system, fixed-point variables evolve with time leading to non-homogenous Markov chains. At the best of our knowledge, this is the first paper facing this problem in a general way. The proposed approach is applied to an Infrastructure-As-A-Service (IaaS) Cloud use case. Specifically, we assess the impact of changes in demand and available capacity on the Cloud resiliency and we show that the approach proposed in this paper can scale for a real sized Cloud without significantly compromising the accuracy.

}, keywords = {Available capacity, Chains, Formal definition, Homogenous Markov chain, Infrastructure as a service (IaaS), Large scale systems, Markov processes, Non-homogeneous, Resiliency quantification, State - space models, State space methods, Stochastic models, Stochastic systems, Submodels, Transient behavior}, issn = {01635999}, doi = {10.1145/3092819.3092825}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85019853222\&doi=10.1145\%2f3092819.3092825\&partnerID=40\&md5=6266fffb7aad937fefad706e31fcd7da}, author = {Francesco Longo and Rahul Ghosh and Vijay K. Naik and A.J. Rindos and Kishor Trivedi} } @article {Longo2015280, title = {Dependability modeling of Software Defined Networking}, journal = {Computer Networks}, volume = {83}, year = {2015}, note = {cited By 6}, pages = {280-296}, publisher = {Elsevier}, abstract = {

Software Defined Networking (SDN) is a new network design paradigm that aims at simplifying the implementation of complex networking infrastructures by separating the forwarding functionalities (data plane) from the network logical control (control plane). Network devices are used only for forwarding, while decisions about where data is sent are taken by a logically centralized yet physically distributed component, i.e., the SDN controller. From a quality of service (QoS) point of view, an SDN controller is a complex system whose operation can be highly dependent on a variety of parameters, e.g., its degree of distribution, the corresponding topology, the number of network devices to control, and so on. Dependability aspects are particularly critical in this context. In this work, we present a new analytical modeling technique that allows us to represent an SDN controller whose components are organized in a hierarchical topology, focusing on reliability and availability aspects and overcoming issues and limitations of Markovian models. In particular, our approach allows to capture changes in the operating conditions (e.g., in the number of managed devices) still allowing to represent the underlying phenomena through generally distributed events. The dependability of a use case on a two-layer hierarchical SDN control plane is investigated through the proposed technique providing numerical results to demonstrate the feasibility of the approach. {\textcopyright} 2015 Elsevier B.V.

}, keywords = {Availability, Complex networks, Controllers, Degree of distributions, Distributed components, Electric network topology, Information dissemination, Markov processes, Networking infrastructure, Non-Markovian, Quality control, Quality of service, Random processes, Reliability, Reliability and availability, Software defined networking (SDN), Software reliability, Software-defined networkings, Stochastic models, Stochastic systems, Topology, Type expansions}, issn = {13891286}, doi = {10.1016/j.comnet.2015.03.018}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84946489290\&doi=10.1016\%2fj.comnet.2015.03.018\&partnerID=40\&md5=b4f32c89d2b7b79fefcaf97082764960}, author = {Francesco Longo and Salvatore Distefano and Dario Bruneo and Marco Scarpa} } @proceedings {Bruneo201598, title = {An SRN-based resiliency quantification approach}, journal = {Proceedings of the 36th International Conference on Application and Theory of Petri Nets and Concurrency (Petri Nets)}, volume = {9115 Lecture Notes in Computer Science}, year = {2015}, note = {cited By 0; Conference of 36th International Conference on Application and Theory of Petri Nets and Concurrency, Petri Nets 2015 ; Conference Date: 21 June 2015 Through 26 June 2015; Conference Code:119609}, pages = {98-116}, publisher = {Springer Verlag}, address = {Brussels, Belgium, 21-26 June 2015}, abstract = {

Resiliency is often considered as a synonym for faulttolerance and reliability/availability. We start from a different definition of resiliency as the ability to deliver services when encountering unexpected changes. Semantics of change is of extreme importance in order to accurately capture the real behavior of a system. We propose a resiliency analysis technique based on stochastic reward nets that allows the modeler: (1) to reuse an already existing dependability or performance model for a specific system with minimal modifications, and (2) to adapt the given model for specific change semantics. To automate the model analysis an algorithm is designed and the modeler is provided with a formalism that corresponds to the semantics. Our algorithm and approach is implemented to demonstrate the proposed resiliency quantification approach. Finally, we discuss the differences between our approach and an alternative technique based on deterministic and stochastic Petri nets and highlight the advantages of the proposed approach in terms of semantics specification. {\textcopyright} Springer International Publishing Switzerland 2015.

}, keywords = {Analysis techniques, Deterministic and stochastic Petri nets, Model analysis, Performance Model, Petri nets, Resiliency, Semantics, Stochastic models, Stochastic reward nets, Stochastic systems}, isbn = {9783319194875}, issn = {03029743}, doi = {10.1007/978-3-319-19488-2_5}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84937428490\&partnerID=40\&md5=7d0bbe99afba1a79df65b4e35e86a02c}, author = {Dario Bruneo and Francesco Longo and Marco Scarpa and Antonio Puliafito and Rahul Ghosh and Kishor S. Trivedi} } @article {Longo20151540, title = {Two-layer symbolic representation for stochastic models with phase-type distributed events}, journal = {International Journal of Systems Science}, volume = {46}, number = {9}, year = {2015}, note = {cited By 2}, pages = {1540-1571}, publisher = {Taylor and Francis Ltd.}, abstract = {

Among the techniques that have been proposed for the analysis of non-Markovian models, the state space expansion approach showed great flexibility in terms of modelling capacities.The principal drawback is the explosion of the state space. This paper proposes a two-layer symbolic method for efficiently storing the expanded reachability graph of a non-Markovian model in the case in which continuous phase-type distributions are associated with the firing times of system events, and different memory policies are considered. At the lower layer, the reachability graph is symbolically represented in the form of a set of Kronecker matrices, while, at the higher layer, all the information needed to correctly manage event memory is stored in a multi-terminal multi-valued decision diagram. Such an information is collected by applying a symbolic algorithm, which is based on a couple of theorems. The efficiency of the proposed approach, in terms of memory occupation and execution time, is shown by applying it to a set of non-Markovian stochastic Petri nets and comparing it with a classical explicit expansion algorithm. Moreover, a comparison with a classical symbolic approach is performed whenever possible. {\textcopyright} 2013 Taylor \& Francis.

}, keywords = {Decision diagram, Decision theory, efficient memory occupation, Many valued logics, Markov processes, Non-Markovian, Petri nets, phase type distributions, Stochastic models, Stochastic systems, symbolic representation}, issn = {00207721}, doi = {10.1080/00207721.2013.822940}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84928644988\&partnerID=40\&md5=3f853e6fcb8bddeebf2e890076ff798d}, author = {Francesco Longo and Marco Scarpa} } @proceedings {Distefano2014255, title = {Non-Markovian modeling of a BladeCenter chassis midplane}, journal = {Proceedings of the 11th European Workshop on Computer Performance Engineering (EPEW)}, volume = {8721 Lecture Notes in Computer Science}, year = {2014}, note = {cited By 0; Conference of 11th European Workshop on Computer Performance Engineering, EPEW 2014 ; Conference Date: 11 September 2014 Through 12 September 2014; Conference Code:107431}, pages = {255-269}, publisher = {Springer Verlag}, address = {Florence, Italy, 11-12 September 2014}, abstract = {

In distributed contexts such as Cloud computing, the reliability and availability of the provided resources and services have to be assured in order to meet user requirements. At the infrastructure level, this specification is translated into tighter ones on the datacenter hosting physical resources. In this paper, starting from a real case study of the IBM BladeCenter, we provide a technique for the quantitative evaluation of datacenter infrastructure availability. The proposed technique allows one to take into account both aging phenomena and multiple operating conditions. In particular, one subsystem of the BladeCenter, the chassis midplane, is studied. Indeed, based on the stochastic characterization of the midplane reliability through statistic measurements, a model dealing with the non-exponential failure time distribution thus obtained is evaluated to demonstrate the suitability and the effectiveness of the proposed technique. {\textcopyright} 2014 Springer International Publishing.

}, keywords = {Aging phenomena, Chassis, Failure-time distribution, Non-Markovian modeling, Operating condition, Physical resources, Quantitative evaluation, Reliability and availability, Stochastic models, Stochastic systems, User requirements}, isbn = {9783319108841}, issn = {03029743}, doi = {10.1007/978-3-319-10885-8_18}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84906969232\&partnerID=40\&md5=6840d4a28b6ed80a602f4db06c10343b}, author = {Salvatore Distefano and Francesco Longo and Marco Scarpa and Kishor S. Trivedi} } @article {Ghosh201457, title = {Scalable analytics for IaaS cloud availability}, journal = {IEEE Transactions on Cloud Computing - IEEE Computer Society}, volume = {2}, number = {1}, year = {2014}, note = {cited By 5}, pages = {57-70}, publisher = {Institute of Electrical and Electronics Engineers Inc.}, abstract = {

In a large Infrastructure-as-a-Service (IaaS) cloud, component failures are quite common. Such failures may lead to occasional system downtime and eventual violation of Service Level Agreements (SLAs) on the cloud service availability. The availability analysis of the underlying infrastructure is useful to the service provider to design a system capable of providing a defined SLA, as well as to evaluate the capabilities of an existing one. This paper presents a scalable, stochastic model-driven approach to quantify the availability of a large-scale IaaS cloud, where failures are typically dealt with through migration of physical machines among three pools: hot (running), warm (turned on, but not ready), and cold (turned off). Since monolithic models do not scale for large systems, we use an interacting Markov chain based approach to demonstrate the reduction in the complexity of analysis and the solution time. The three pools are modeled by interacting sub-models. Dependencies among them are resolved using fixed-point iteration, for which existence of a solution is proved. The analytic-numeric solutions obtained from the proposed approach and from the monolithic model are compared. We show that the errors introduced by interacting sub-models are insignificant and that our approach can handle very large size IaaS clouds. The simulative solution is also considered for the proposed model, and solution time of the methods are compared. {\textcopyright} 2014 IEEE.

}, keywords = {Availability, availability analysis, cloud computing, Downtime, Existence of a solutions, Infrastructure as a service (IaaS), Iterative methods, Lakes, Maintenance, Markov processes, Model driven approach, Numeric solutions, Service level agreement (SLAs), simulation, Stochastic models, Stochastic reward nets, Stochastic systems}, issn = {21687161}, doi = {10.1109/TCC.2014.2310737}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84906976356\&partnerID=40\&md5=a63dc67c92ef7620c8a3b33aca08348b}, author = {Rahul Ghosh and Francesco Longo and Flavio Frattini and Stefano Russo and Kishor S. Trivedi} } @article {Ghosh2014667, title = {Stochastic model driven capacity planning for an infrastructure-as-a-service cloud}, journal = {IEEE Transactions on Services Computing - IEEE Computer Society}, volume = {7}, number = {4}, year = {2014}, note = {cited By 1}, pages = {667-680}, publisher = {Institute of Electrical and Electronics Engineers}, abstract = {

From an enterprise perspective, one key motivation to transform the traditional IT management into Cloud is the cost reduction of the hosted services. In an Infrastructure-as-a-Service (IaaS) Cloud, virtual machine (VM) instances share the physical machines (PMs) in the provider{\textquoteright}s data center. With large number of PMs, providers can maintain low cost of service downtime at the expense of higher infrastructure and other operational costs (e.g., power consumption and cooling costs). Hence, determining the optimal PM capacity requirements that minimize the overall cost is of interest. In this paper, we show how a cost analysis and optimization framework can be developed using stochastic availability and performance models of an IaaS Cloud. Specifically, we study two cost minimization problems to address the capacity planning in an IaaS Cloud: 1) what is the optimal number of PMs that minimizes the total cost of ownership for a given downtime requirement set by service level agreements? and, 2) is it more economical to use cheaper but less reliable PMs or to use costlier but more reliable PMs for insuring the same availability characteristics? We use simulated annealing, a well-known stochastic search algorithm, to solve these optimization problems. Results from our analysis show that the optimal solutions are found within reasonable time. {\textcopyright} 2013 IEEE.

}, keywords = {Capacity planning, Capacity requirement, Clouds, Cost benefit analysis, Cost reduction, Downtime, Infrastructure as a service (IaaS), Maintenance, Optimization, Optimization framework, Optimization problems, Service Level Agreements, Simulated annealing, Stochastic models, Stochastic search algorithms, Stochastic systems, Total cost of ownership}, issn = {19391374}, doi = {10.1109/TSC.2013.44}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84919717849\&partnerID=40\&md5=34c70f14a9a3f838562335050a628985}, author = {Rahul Ghosh and Francesco Longo and Ruofan Xia and Vijay K. Naik and Kishor S. Trivedi} } @article {Bruneo2013279, title = {Analytical investigation of availability in a vision cloud storage cluster}, journal = {Scalable Computing - SCPE}, volume = {14}, number = {4}, year = {2013}, note = {cited By 2}, pages = {279-290}, abstract = {

The goal of VISION Cloud, a European Commission funded project, is to design a new scalable and flexible storage cloud architecture able to provide data-intensive storage cloud services. The proposed environment employs a distributed file system on top of a set of storage rich nodes composing a cluster. Several clusters constitute a data center, while multiple geographically distributed data centers form a single storage cloud. In this paper, we focus on a single VISION Cloud storage cluster, providing a stochastic reward net model for an investigation of its availability. The proposed model is a first attempt at obtaining a quantification of the availability level of the cloud storage provided by the VISION Cloud architecture. {\textcopyright} 2013 SCPE.

}, keywords = {Analytical investigations, cloud architectures, Data intensive, Digital storage, Distributed data, Distributed file systems, European Commission, Flexible storage, Stochastic models, Stochastic reward nets}, issn = {18951767}, doi = {10.12694/scpe.v14i4.933}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84893439215\&partnerID=40\&md5=cd97e97b8741a1e968a6bf8e20271ff8}, author = {Dario Bruneo and Francesco Longo and David Hadas and Elliot K. Kolodner} } @proceedings {Bruneo201371, title = {Availability Assessment of a Vision Cloud Storage Cluster}, journal = {European Conference on Service-Oriented and Cloud Computing (ESOCC)}, volume = {393 Communications in Computer and Information Science}, year = {2013}, note = {cited By 0; Conference of European Conference on Service-Oriented and Cloud Computing, ESOCC 2013 ; Conference Date: 11 September 2013 Through 13 September 2013; Conference Code:106555}, pages = {71-82}, publisher = {Springer Verlag}, address = {Malaga, Spain, 11-13 September 2013}, abstract = {

VISION Cloud is a European Commission funded project, whose aim is to design and propose a new architecture for a scalable and flexible cloud environment. The VISION Cloud reference architecture considers a single cloud as composed by multiple distributed data centers each of which can be composed by a great number of storage clusters. On top of the storage rich nodes forming each cluster, a distributed file system is built. In this paper, we provide an stochastic reward net model for a storage cluster in the context of the storage cloud environment proposed by the VISION Cloud project. The proposed model represents a first step in the direction of obtaining a quantification of the availability level reached through the use of the VISION Cloud proposed architecture from a user perspective. {\textcopyright} Springer-Verlag Berlin Heidelberg 2013.

}, keywords = {Architecture, Availability assessment, cloud computing, Cloud environments, Distributed file systems, European Commission, Proposed architectures, Reference architecture, Stochastic models, Stochastic reward nets, Stochastic systems, User perspectives}, isbn = {9783642453632}, issn = {18650929}, doi = {10.1007/978-3-642-45364-9_7}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84904676242\&partnerID=40\&md5=d7510b50bf986e126b22270279202382}, author = {Dario Bruneo and Francesco Longo and David Hadas and Hillel Kolodner} } @proceedings {Distefano201377, title = {Investigating mobile crowdsensing application performance}, journal = {Proceedings of the 3rd ACM International Symposium on Design and Analysis of Intelligent Vehicular Networks and Applications (DIVANet), Co-located with the 16th ACM Int. Conf. on Modeling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM)}, year = {2013}, note = {cited By 0; Conference of 3rd ACM Int. Symp. on Design and Analysis of Intelligent Vehicular Networks and Applications, DIVANet 2013, Held in Conjunction with the 16th ACM Int. Conf. on Modeling, Analysis and Simulation of Wireless and Mobile Systems, MSWiM 2013 ; Conference Date: 3 November 2013 Through 8 November 2013; Conference Code:101342}, pages = {77-83}, publisher = {ACM}, address = {Barcelona, Spain, 3-8 November 2013}, abstract = {

Mobile Crowdsensing (MCS) is an emerging distributed paradigm lying at the intersection between the Internet of Things and the volunteer/crowd-based approach. MCS applications are usually deployed on contributing nodes such as smart devices and mobiles, equipped by sensing resources that sample the physical environment and provide the sensed data, once filtered, aggregated and preprocessed, to the MCS application server. The MCS opportunistic approach unlocks new form of pervasive, participatory sensing applications, acquiring interests also in business contexts that call for adequate techniques and tools to drive architects and developers in MCS application design. Aim of this paper is to evaluate the performance of an MCS application though a stochastic model able to stochastically represent the overall MCS environment, thus providing a valid support to MCS application development. The Petri nets formalism is used due to its expressiveness and the capabilities to represent complex, dependent, non-Markovian, phenomena usually characterizing MCS environments. A specific MCS application is then evaluated to demonstrate the effectiveness of the proposed technique on a real case study. {\textcopyright} 2013 ACM.

}, keywords = {Application development, Application performance, Complex networks, crowdsensing, Design, Digital storage, Internet of Things (IOT), Participatory sensing applications, Performance, Petri nets, Physical environments, Stochastic models, Techniques and tools}, isbn = {9781450323581}, doi = {10.1145/2512921.2512931}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84889685098\&partnerID=40\&md5=15df22b992482173437dcd8080bbbc94}, author = {Salvatore Distefano and Francesco Longo and Marco Scarpa} } @article {Ghosh20131216, title = {Modeling and performance analysis of large scale IaaS clouds}, journal = {Future Generation Computer Systems - Elsevier}, volume = {29}, number = {5}, year = {2013}, note = {cited By 10}, pages = {1216-1234}, abstract = {

For Cloud based services to support enterprise class production workloads, Mainframe like predictable performance is essential. However, the scale, complexity, and inherent resource sharing across workloads make the Cloud management for predictable performance difficult. As a first step towards designing Cloud based systems that achieve such performance and realize the service level objectives, we develop a scalable stochastic analytic model for performance quantification of Infrastructure-as-a-Service (IaaS) Cloud. Specifically, we model a class of IaaS Clouds that offer tiered services by configuring physical machines into three pools with different provisioning delay and power consumption characteristics. Performance behaviors in such IaaS Clouds are affected by a large set of parameters, e.g., workload, system characteristics and management policies. Thus, traditional analytic models for such systems tend to be intractable. To overcome this difficulty, we propose a multi-level interacting stochastic sub-models approach where the overall model solution is obtained iteratively over individual sub-model solutions. By comparing with a single-level monolithic model, we show that our approach is scalable, tractable, and yet retains high fidelity. Since the dependencies among the sub-models are resolved via fixed-point iteration, we prove the existence of a solution. Results from our analysis show the impact of workload and system characteristics on two performance measures: mean response delay and job rejection probability. {\textcopyright} 2012 Elsevier B.V. All rights reserved.

}, keywords = {Analytic modeling, Analytical models, Clouds, CTMC, Fixed-point iterations, IaaS, Infrastructure as a service (IaaS), Performance, Provisioning, Stochastic models, Stochastic systems, Submodels}, issn = {0167739X}, doi = {10.1016/j.future.2012.06.005}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-84887062784\&partnerID=40\&md5=5aa7bb3aa9d27ba52b585a03501c8e18}, author = {Rahul Ghosh and Francesco Longo and Vijay K. Naik and Kishor S. Trivedi} } @proceedings {Ghosh2010343, title = {Quantifying resiliency of IaaS cloud}, journal = {Proceedings of the 29th IEEE Symposium on Reliable Distributed Systems (SRDS)}, year = {2010}, note = {cited By 16; Conference of 29th IEEE Symposium on Reliable Distributed Systems, SRDS 2010 ; Conference Date: 31 October 2010 Through 3 November 2010; Conference Code:82914}, pages = {343-347}, publisher = {IEEE Computer Society}, address = {New Delhi, India, 31 October - 3 November 2010}, abstract = {

Cloud based services may experience changes - internal, external, large, small - at any time. Predicting and quantifying the effects on the quality-of-service during and after a change are important in the resiliency assessment of a cloud based service. In this paper, we quantify the resiliency of infrastructure-as-a-service (IaaS) cloud when subject to changes in demand and available capacity. Using a stochastic reward net based model for provisioning and servicing requests in a IaaS cloud, we quantify the resiliency of IaaS cloud w.r.t. two key performance measures - job rejection rate and provisioning response delay. {\textcopyright} 2010 IEEE.

}, keywords = {Available capacity, Infrastructure as a services, Performance measure, Quality of service, Rejection rates, Response delays, Stochastic models, Stochastic reward nets}, isbn = {9780769542508}, issn = {10609857}, doi = {10.1109/SRDS.2010.49}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-78650562592\&partnerID=40\&md5=6542308f50d349fc7456919e658e6840}, author = {Rahul Ghosh and Francesco Longo and Vijay K. Naikz and Kishor S. Trivedi} } @proceedings {Bruneo2010243, title = {VO-level performance analysis of gLite Grids}, journal = {Proceedings of the 19th IEEE Workshop on Enabling Technologies: Infrastructure for Collaborative Enterprises (WETICE)}, year = {2010}, note = {cited By 0; Conference of 19th IEEE International Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises, WETICE 2010 ; Conference Date: 28 June 2010 Through 30 June 2010; Conference Code:81490}, pages = {243-248}, publisher = {IEEE Computer Society}, address = {Larissa, Greece, 28-30 June 2010}, abstract = {

Business oriented grids call for effective Quality of Service strategies able to adapt to different user requirements. Performance analyses and predictions with respect to different load conditions or management policies are essential instruments to define such strategies. In this paper, we present a non-Markovian Stochastic Petri Net model that allows to conduct performance analyses of Grid systems focusing on aspects related to the Virtual Organization as a whole. Different job allocation techniques will be evaluated with respect to both user and provider point-of-views. We will also investigate the influence of different information update policies on the accuracy of the allocation schemes, highlighting the costs/benefits in terms of job waiting time, service availability, and system utilization. {\textcopyright} 2010 IEEE.

}, keywords = {Business-oriented, gLite middleware, Graph theory, Grid computing, Grid systems, Information updates, Job allocation, Load condition, Management policy, middleware, Non-Markovian, Performance analysis, performance measurements, Petri nets, Quality of service, Random access storage, Service availability, Stochastic models, Stochastic Petri Nets, Stochastic systems, System utilization, User requirements, Virtual organization, Waiting-time}, isbn = {9780769540634}, issn = {15244547}, doi = {10.1109/WETICE.2010.45}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-77955917215\&partnerID=40\&md5=5f89b9d07327325a09d78d1af77f0519}, author = {Dario Bruneo and Francesco Longo and Marco Scarpa and Antonio Puliafito} }