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1 Grid Computing (3) (Special Topics in Computer Engineering) Veera Muangsin 13 February 2004.

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1 1 Grid Computing (3) (Special Topics in Computer Engineering) Veera Muangsin 13 February 2004

2 2 Outline High-Performance Computing Grid Computing Grid Applications Grid Architecture Grid Middleware Grid Services

3 3 Before the Grid User Application Site A Site B Network The User is responsible for resolving the complexities of the environment independent sites independent hardware and software independent user ids security policy requiring local connection to the machine.

4 4 First Step to the Grid User Application Site A Site B Network Centralized Scheduler and file staging Metacenter Two or more resources connected in a controlled user environment Constraints common architecture single name space common scheduler A layer of abstraction is added that hides some of the complexities associated with running jobs in a distributed computing environment, however, limitations exist

5 5 Grid Middleware User Application Site A Site B Network Infrastructure Common Middleware -abstracts independent, hardware, software, user ids, into a service layer with defined APIs -comprehensive security, -allows for site autonomy -provides a common infrastructure based on middleware The Grid Today 1 Request info from the grid 1 2 Get response 2 3 Make selection and submit job 3 The underlying infrastructure is abstracted into defined APIs thereby simplifying developer and the user access to resources, however, this layer is not intelligent

6 6 The Near Future Grid Grid Middleware - Infrastructure APIs (service oriented) User Application Intelligent, Customized Middleware Site A Site B Network Infrastructure Customizable Grid Services built on defined Infrastructure APIs automatic selection of resources information products tailored to users accountless processing flexible interface: web based, command line, APIs Resources are accessed via various intelligent services that access infrastructure APIs The result: The Scientist and Application Developer can focus on science and not on systems management

7 7 Layered Grid Architecture (By Analogy to Internet Architecture) Application Fabric “ Controlling things locally ” : Access to, & control of, resources Connectivity “ Talking to things ” : communication (Internet protocols) & security Resource “ Sharing single resources ” : negotiating access, controlling use Collective “ Coordinating multiple resources ” : ubiquitous infrastructure services, app-specific distributed services Internet Transport Application Link Internet Protocol Architecture

8 Grid Components Grid Fabric Networked Resources across Organisations Computers Clusters Data Sources Scientific Instruments Storage Systems Local Resource Managers Operating Systems Queuing Systems TCP/IP & UDP … Libraries & App Kernels … Distributed Resources Coupling Services Comm. Sign on & SecurityInformation … QoS Process Data Access Development Environments and Tools Languages Libraries Debuggers … Web tools Resource BrokersMonitoring Applications and Portals Prob. Solving Env. Scientific … Collaboration Engineering Web enabled Apps Grid Apps. Grid Middleware Grid Tools

9 9 Compute Resource SDK API Access Protocol Checkpoint Repository SDK API C-point Protocol Example: High-Throughput Computing System High Throughput Computing System Dynamic checkpoint, job management, failover, staging Brokering, certificate authorities Access to data, access to computers, access to network performance data Communication, service discovery (DNS), authentication, authorization, delegation Storage systems, schedulers Collective (App) App Collective (Generic) Resource Connect Fabric

10 10 Example: Data Grid Architecture Discipline-Specific Data Grid Application Coherency control, replica selection, task management, virtual data catalog, virtual data code catalog, … Replica catalog, replica management, co-allocation, certificate authorities, metadata catalogs, Access to data, access to computers, access to network performance data, … Communication, service discovery (DNS), authentication, authorization, delegation Storage systems, clusters, networks, network caches, … Collective (App) App Collective (Generic) Resource Connect Fabric

11 11 Globus Toolkit Grid computing middleware –Software between the hardware and high-level services –Basic libraries, services, command-line programs Most common middleware used in grids Integrated with Web Service

12 12 Globus Software Architecture Grid SSH Grid FTP login execute commands copy files get and put files 3rd party copy interactive file management parallel transfers Monitoring and Discovery Service (MDS) information about resources and services LDAP distributed directory service single sign on delegation of credentials authorization Grid Security Infrastructure (GSI) SSL/TLSX.509 Certificates authentication secure communication credentials for users, services, hosts execute remote applications stage executable, stdin, stdout, stderr LSFPBS Globus Resource Allocation Manager (GRAM) fork/exe c job management systems

13 13 Globus server system PBS GRAM Server Grid FTP Server Grid SSH Server LSF GRAM Server Grid FTP Server Grid SSH Server Globus server system Globus Deployment Architecture MDS server system MDS GRIS MDS GIIS MDS GRIS Globus client system Clients are programs and libraries GRAM Client Grid FTP Client MDS Client Grid SSH Client UserUser application/tool Web portal

14 14 Globus Toolkit™ A software toolkit addressing key technical problems in the development of Grid enabled tools, services, and applications –Offer a modular “bag of technologies” –Enable incremental development of grid-enabled tools and applications –Implement standard Grid protocols and APIs –Make available under liberal open source license

15 15 General Approach Define Grid protocols & APIs –Protocol-mediated access to remote resources –Integrate and extend existing standards –“On the Grid” = speak “Intergrid” protocols Develop a reference implementation –Open source Globus Toolkit –Client and server SDKs, services, tools, etc. Grid-enable wide variety of tools –Globus Toolkit, FTP, SSH, Condor, SRB, MPI, …

16 16 Four Key Protocols The Globus Toolkit™ centers around four key protocols –Connectivity layer: Security: Grid Security Infrastructure (GSI) –Resource layer: Resource Management: Grid Resource Allocation Management (GRAM) Information Services: Grid Resource Information Protocol (GRIP) Data Transfer: Grid File Transfer Protocol (GridFTP)

17 17 The Globus Toolkit™: Security Services The Globus Project™ Argonne National Laboratory USC Information Sciences Institute

18 18 Why Grid Security is Hard Resources are often located in distinct administrative domains –Each resource has own policies & procedures Set of resources used by a single computation may be large, dynamic, and unpredictable –Not just client/server, requires delegation It must be broadly available & applicable –Standard, well-tested, well-understood protocols; integrated with wide variety of tools

19 19 Grid Security Infrastructure (GSI) Extensions to standard protocols & APIs –Standards: SSL/TLS, X.509 & CA, GSS-API –Extensions for single sign-on and delegation Globus Toolkit reference implementation of GSI –SSLeay/OpenSSL + GSS-API + SSO/delegation –Tools and services to interface to local security Simple ACLs; SSLK5/PKINIT for access to K5, AFS; … –Tools for credential management Login, logout, etc. Smartcards MyProxy: Web portal login and delegation K5cert: Automatic X.509 certificate creation

20 20 Site A (Kerberos) Site B (Unix) Site C (Kerberos) Computer User Single sign-on via “grid-id” & generation of proxy cred. Or: retrieval of proxy cred. from online repository User Proxy Proxy credential Computer Storage system Communication* GSI-enabled FTP server Authorize Map to local id Access file Remote file access request* GSI-enabled GRAM server GSI-enabled GRAM server Remote process creation requests* * With mutual authentication Process Kerberos ticket Restricted proxy Process Restricted proxy Local id Authorize Map to local id Create process Generate credentials Ditto GSI in Action “Create Processes at A and B that Communicate & Access Files at C”

21 21 Review of Public Key Cryptography Asymmetric keys –A private key is used to encrypt data. –A public key can decrypt data encrypted with the private key. An X.509 certificate includes… –Someone’s subject name (user ID) –Their public key –A “signature” from a Certificate Authority (CA) that: Proves that the certificate came from the CA. Vouches for the subject name Vouches for the binding of the public key to the subject

22 22 Public Key Based Authentication User sends certificate over the wire. Other end sends user a challenge string. User encodes the challenge string with private key –Possession of private key means you can authenticate as subject in certificate Public key is used to decode the challenge. –If you can decode it, you know the subject Treat your private key carefully!! –Private key is stored only in well-guarded places, and only in encrypted form

23 23 User Proxies Minimize exposure of user’s private key A temporary, X.509 proxy credential for use by our computations –We call this a user proxy certificate –Allows process to act on behalf of user –User-signed user proxy cert stored in local file –Created via “grid-proxy-init” command Proxy’s private key is not encrypted –Rely on file system security, proxy certificate file must be readable only by the owner

24 24 Delegation Remote creation of a user proxy Results in a new private key and X.509 proxy certificate, signed by the original key Allows remote process to act on behalf of the user Avoids sending passwords or private keys across the network

25 25 GSI Applications Globus Toolkit™ uses GSI for authentication Many Grid tools, directly or indirectly, e.g. –Condor-G, SRB, MPICH-G2, Cactus, GDMP, … Commercial and open source tools, e.g. –ssh, ftp, cvs, OpenLDAP, OpenAFS –SecureCRT (Win32 ssh client) And since we use standard X.509 certificates, they can also be used for –Web access, LDAP server access, etc.

26 26 The Globus Toolkit™: Resource Management Services The Globus Project™ Argonne National Laboratory USC Information Sciences Institute

27 27 The Challenge Enabling secure, controlled remote access to heterogeneous computational resources and management of remote computation –Authentication and authorization –Resource discovery & characterization –Reservation and allocation –Computation monitoring and control Addressed by new protocols & services –GRAM protocol as a basic building block –Resource brokering & co-allocation services –GSI for security, MDS for discovery

28 28 Resource Management The Grid Resource Allocation Management (GRAM) protocol and client API allows programs to be started on remote resources, despite local heterogeneity Resource Specification Language (RSL) is used to communicate requirements A layered architecture allows application- specific resource brokers and co-allocators to be defined in terms of GRAM services –Integrated with Condor, PBS, MPICH-G2, …

29 29 GRAM LSFCondorNQE Application RSL Simple ground RSL Information Service Local resource managers RSL specialization Broker Ground RSL Co-allocator Queries & Info Resource Management Architecture

30 30 Globus Toolkit Implementation Gatekeeper –Single point of entry –Authenticates user, maps to local security environment, runs service –In essence, a “secure inetd” Job manager –A gatekeeper service –Layers on top of local resource management system (e.g., PBS, LSF, etc.) –Handles remote interaction with the job

31 31 GRAM Components Grid Security Infrastructure Job Manager GRAM client API calls to request resource allocation and process creation. MDS client API calls to locate resources Query current status of resource Create RSL Library Parse Request Allocate & create processes Process Monitor & control Site boundary ClientMDS: Grid Index Info Server Gatekeeper MDS: Grid Resource Info Server Local Resource Manager MDS client API calls to get resource info GRAM client API state change callbacks

32 32 Job Submission Interfaces Globus Toolkit includes several command line programs for job submission –globus-job-run: Interactive jobs –globus-job-submit: Batch/offline jobs –globusrun: Flexible scripting infrastructure Others are building better interfaces –General purpose Condor-G, PBS, GRD, Hotpage, etc –Application specific ECCE’, Cactus, Web portals

33 33 The Globus Toolkit™: Information Services The Globus Project™ Argonne National Laboratory USC Information Sciences Institute

34 34 Grid Information Services System information is critical to operation of the grid and construction of applications –What resources are available? Resource discovery –What is the “state” of the grid? Resource selection –How to optimize resource use Application configuration and adaptation? We need a general information infrastructure to answer these questions

35 35 Examples of Useful Information Characteristics of a compute resource –IP address, software available, system administrator, networks connected to, OS version, load Characteristics of a network –Bandwidth and latency, protocols, logical topology Characteristics of the Globus infrastructure –Hosts, resource managers

36 36 Grid Information: Facts of Life Information is always old –Time of flight, changing system state –Need to provide quality metrics Distributed state hard to obtain –Complexity of global snapshot Component will fail Scalability and overhead Many different usage scenarios –Heterogeneous policy, different information organizations, etc.

37 37 Grid Information Service Provide access to static and dynamic information regarding system components A basis for configuration and adaptation in heterogeneous, dynamic environments Requirements and characteristics –Uniform, flexible access to information –Scalable, efficient access to dynamic data –Access to multiple information sources –Decentralized maintenance

38 38 The GIS Problem: Many Information Sources, Many Views ? R R R R R ? R R R R R ? R R R R R ? RR VO A VO B VO C

39 39 Information Protocols Grid Resource Registration Protocol –Support information/resource discovery –Designed to support machine/network failure Grid Resource Inquiry Protocol –Query resource description server for information –Query aggregate server for information –LDAP V3.0 in Globus 1.1.3

40 40 GIS Architecture AA Customized Aggregate Directories RRRR Standard Resource Description Services Registration Protocol Users Enquiry Protocol

41 41 Metacomputing Directory Service Use LDAP as Inquiry Access information in a distributed directory –Directory represented by collection of LDAP servers –Each server optimized for particular function Directory can be updated by: –Information providers and tools –Applications (i.e., users) –Backend tools which generate info on demand Information dynamically available to tools and applications

42 42 Two Classes Of MDS Servers Grid Resource Information Service (GRIS) –Supplies information about a specific resource –Configurable to support multiple information providers –LDAP as inquiry protocol Grid Index Information Service (GIIS) –Supplies collection of information which was gathered from multiple GRIS servers –Supports efficient queries against information which is spread across multiple GRIS server –LDAP as inquiry protocol

43 43 Grid Resource Information Service Server which runs on each resource –Given the resource DNS name, you can find the GRIS server (well known port = 2135) Provides resource specific information –Much of this information may be dynamic Load, process information, storage information, etc. GRIS gathers this information on demand “White pages” lookup of resource information –Ex: How much memory does machine have? “Yellow pages” lookup of resource options –Ex: Which queues on machine allows large jobs?

44 44 Grid Index Information Service GIIS describes a class of servers –Gathers information from multiple GRIS servers –Each GIIS is optimized for particular queries Ex1: Which Alliance machines are >16 process SGIs? Ex2: Which Alliance storage servers have >100Mbps bandwidth to host X? –Akin to web search engines Organization GIIS –The Globus Toolkit ships with one GIIS –Caches GRIS info with long update frequency Useful for queries across an organization that rely on relatively static information (Ex1 above) Can be merged into GRIS

45 45 Logical MDS Deployment ISI GRISes GIIS Grads Gusto

46 46 Example: Discovering CPU Load Retrieve CPU load fields of compute resources % grid-info-search -L “(objectclass=GlobusComputeResource)” \ dn cpuload1 cpuload5 cpuload15 dn:, ou=MCS, o=Argonne National Laboratory, o=Globus, c=US cpuload1: 0.48 cpuload5: 0.20 cpuload15: 0.03 dn:, ou=MCS, o=Argonne National Laboratory, o=Globus, c=US cpuload1: 3.11 cpuload5: 2.64 cpuload15: 2.57

47 47 The Globus Toolkit™: Data Management Services The Globus Project™ Argonne National Laboratory USC Information Sciences Institute

48 48 Data Intensive Issues Include … Harness [potentially large numbers of] data, storage, network resources located in distinct administrative domains Respect local and global policies governing what can be used for what Schedule resources efficiently, again subject to local and global constraints Achieve high performance, with respect to both speed and reliability Catalog software and virtual data

49 49 Desired Data Grid Functionality High-speed, reliable access to remote data Automated discovery of “best” copy of data Manage replication to improve performance Co-schedule compute, storage, network “Transparency” wrt delivered performance Enforce access control on data Allow representation of “global” resource allocation policies

50 50 A Model Architecture for Data Grids Metadata Catalog Replica Catalog Tape Library Disk Cache Attribute Specification Logical Collection and Logical File Name Disk ArrayDisk Cache Application Replica Selection Multiple Locations NWS Selected Replica GridFTP Control Channel Performance Information & Predictions Replica Location 1Replica Location 2Replica Location 3 MDS GridFTP Data Channel

51 51 Globus Toolkit Components Two major Data Grid components: 1. Data Transport and Access lCommon protocol lSecure, efficient, flexible, extensible data movement lFamily of tools supporting this protocol 2. Replica Management Architecture lSimple scheme for managing: lmultiple copies of files lcollections of files

52 52 Access/Transport Protocol Requirements Suite of communication libraries and related tools that support –GSI, Kerberos security –Third-party transfers –Parameter set/negotiate –Partial file access –Reliability/restart –Large file support –Data channel reuse All based on a standard, widely deployed protocol –Integrated instrumentation –Loggin/audit trail –Parallel transfers –Striping (cf DPSS) –Policy-based access control –Server-side computation –Proxies (firewall, load bal)

53 53 And The Protocol Is … GridFTP Why FTP? –Ubiquity enables interoperation with many commodity tools –Already supports many desired features, easily extended to support others –Well understood and supported We use the term GridFTP to refer to –Transfer protocol which meets requirements –Family of tools which implement the protocol Note GridFTP > FTP Note that despite name, GridFTP is not restricted to file transfer!

54 54 GridFTP: Basic Approach FTP protocol is defined by several IETF RFCs Start with most commonly used subset –Standard FTP: get/put etc., 3 rd -party transfer Implement standard but often unused features –GSS binding, extended directory listing, simple restart Extend in various ways, while preserving interoperability with existing servers –Striped/parallel data channels, partial file, automatic & manual TCP buffer setting, progress monitoring, extended restart

55 55 Replica Management Maintain a mapping between logical names for files and collections and one or more physical locations Important for many applications –Example: CERN HLT data Multiple petabytes of data per year Copy of everything at CERN (Tier 0) Subsets at national centers (Tier 1) Smaller regional centers (Tier 2) Individual researchers will have copies

56 56 Replica Catalog Structure: A Climate Modeling Example Logical File Parent Logical File Jan 1998 Logical Collection C02 measurements 1998 Replica Catalog Location Location Logical File Feb 1998 Size: Filename: Jan 1998 Filename: Feb 1998 … Filename: Mar 1998 Filename: Jun 1998 Filename: Oct 1998 Protocol: gsiftp UrlConstructor: gsi nfs/v6/climate Filename: Jan 1998 … Filename: Dec 1998 Protocol: ftp UrlConstructor: pub/pcmdi Logical Collection C02 measurements 1999

57 57 Replica Catalog Services as Building Blocks: Examples Combine with information service to build replica selection services –E.g. “find best replica” using performance info from NWS and MDS –Use of LDAP as common protocol for info and replica services makes this easier Combine with application managers to build data distribution services –E.g., build new replicas in response to frequent accesses

58 58 Replica Catalog Directions Many data grid applications do not require tight consistency semantics –At any given time, you may not be able to discover all copies –When a new copy is made, it may not be immediately recognized as available Allows for much more scalable design –Distributed catalogs: local catalogs which maintain their own LFN -> PFN mapping –Soft-state updates as basis for building various configurations of global catalogs

59 59 Virtual Data in Action Data request may l Access local data l Compute locally l Compute remotely l Access remote data Scheduling subject to local & global policies Local autonomy

60 60 Evolution of Grid Technologies Initial exploration ( ; Globus 1.0) –Extensive appln experiments; core protocols Data Grids (1999-??; Globus 2.0+) –Large-scale data management and analysis Open Grid Services Architecture (2001-??, Globus 3.0) –Integration w/ Web services, hosting environments, resource virtualization –Databases, higher-level services Radically scalable systems (2003-??) –Sensors, wireless, ubiquitous computing

61 61 Grids and Open Standards Increased functionality, standardization Time Custom solutions Open Grid Services Arch GGF: OGSI, … (+ OASIS, W3C) Multiple implementations, including Globus Toolkit Web services Globus Toolkit Defacto standards GGF: GridFTP, GSI X.509, LDAP, FTP, … App-specific Services

62 62 “Web Services” Increasingly popular standards-based framework for accessing network applications –W3C standardization; Microsoft, IBM, Sun, others WSDL: Web Services Description Language –Interface Definition Language for Web services SOAP: Simple Object Access Protocol –XML-based RPC protocol; common WSDL target WS-Inspection –Conventions for locating service descriptions UDDI: Universal Desc., Discovery, & Integration –Directory for Web services

63 63 The Need to Support Transient Service Instances “Web services” address discovery & invocation of persistent services –Interface to persistent state of entire enterprise In Grids, must also support transient service instances, created/destroyed dynamically –Interfaces to the states of distributed activities –E.g. workflow, video conf., dist. data analysis Significant implications for how services are managed, named, discovered, and used –In fact, much of our work is concerned with the management of service instances

64 64 Open Grid Services Architecture Service orientation to virtualize resources From Web services: –Standard interface definition mechanisms: multiple protocol bindings, multiple implementations, local/remote transparency Building on Globus Toolkit: –Grid service: semantics for service interactions –Management of transient instances (& state) –Factory, Registry, Discovery, other services –Reliable and secure transport Multiple hosting targets: J2EE,.NET, “C”, …

65 65 Open Grid Services Architecture Open Grid Services Infrastructure OGSA services: registry, authorization, monitoring, data access, management, etc., etc. Transport Protocol Hosting Environment Host. Env. & Protocol Bindings OGSA schemas More specialized & domain-specific services Other schemas Web Services Priorities: l Data access and integration l Security l SLA negotiation l Manageability l Monitoring l …

66 66 OGSA Service Model System comprises (a typically few) persistent services & (potentially many) transient services All services adhere to specified Grid service interfaces and behaviors –Reliable invocation, lifetime management, discovery, authorization, notification, upgradeability, concurrency, manageability Interfaces for managing Grid service instances –Factory, registry, discovery, lifetime, etc. => Reliable, secure mgmt of distributed state

67 67 The Grid Service A (potentially transient) Web service with specified interfaces & behaviors, including –Creation (Factory) –Global naming (GSH) & references (GSR) –Lifetime management –Registration & Discovery –Authorization –Notification –Concurrency –Manageability

68 68 Use of Web Services (1) A Grid service interface is a WSDL portType A Grid service definition is a WSDL extension (serviceType) containing: –A set of one or more portTypes supported by the service –portType & serviceType compatibility statements, to support upgradability For discovery of compatible services when interfaces are upgraded –Implementation version information

69 69 Use of Web Services (2) A GSR is a WSDL document with extensions: –Extension to service element to reference serviceType –Service element extensions to carry the GSH, and the expiration time of the GSR A GSH is an URL, with the following properties: –Globally unique for all time –http get on GSH + “.wsdl” returns GSR –Can derive GSH to Mapper from it Registry returns WS-Inspection documents

70 70 Distributed Resources Condor pools of workstations tertiary storage clusters national supercomputer facilities scientific instruments Internet optical networks space-based networks Grid Communication Functions Communications Basic Grid Functions... Resource Discovery Scheduling and Access to Computing Uniform Data Access Monitoring and Events security services transport services Operational Support Portals Resource Brokering Fault Management Accounting Data Management: replication and metadata Encapsulation as Web Services Encapsulation for Script Based Services Encapsulation as Java Based Services Web Portal Access to Application and Grid Services Specialized Portal Access (high performance displays, PDAs, etc.)... Services Building Blocks Services Workflow Management Applications Grids: An Emerging, Common Computing and Data Infrastructure for Science and Engineering

71 71 Application Domain Specific Portals Application Domain Independent Portals Grid Common Services: Uniform Access, Security, and Management of Compute, Data, and Instrument Resources MER/CIP STS/SLI Mission Analysis ES Modeling ISS Training Aviation Capacity User Environment Portals Collaboration Portals Domain Specific Web Services – Encapsulated Applications Domain Independent Grid Web Services Visualization Data Processing & Analysis Data Management Collaboration Services MonitoringEvents Workflow Management Programming Services Experiment Management Instrument & Sensor Gateways System Models Flight Simulation Computational Simulation Archive Gateways Zooming Coupling Portals: Services Presented to the Users to Accomplish Tasks Grid Web Services: Grid Functions and Application Functions Packaged for Building Portals Multi-Site Compute, Data, and Instrument Resources Grids: A Common Computing and Data Infrastructure for Science and Engineering

72 72 Grid Protocols and Grid Security Infrastructure Combining Grid and Web Services Clients Application Portals Web Services Grid Services: Collective and Resource Access Resources Compute (many) Storage (many) Communi- cation Instruments (various) GRAM GridFTP Data Replica and Metadata Catalog Grid Monitoring Architecture Grid Information Service Web Browser Grid Web Service Description (WSDL) & Discovery (UDDI) Grid X.509 Certification Authority SRB/ Metadata Catalogue Condor-G CORBA MPI Secure, Reliable Group Comm. Discipline / Application Specific Portals (e.g. SDSC TeleScience) Problem Solving Environments (AVS, SciRun, Cactus) Environment Management (LaunchPad, HotPage) Job Submission / Control File Transfer Data Management Credential Management Monitoring Events Workflow Management other services: visualization interface builders collaboration tools numerical grid generators etc. Apache Tomcat&WebSphere &Cold Fusion=JVM + servlet instantiation + routing CoG Kits implementing Web Services in servelets, servers, etc. Python, Java, etc., JSPs composition frameworks (e.g. XCAT) XML / SOAP over Grid Security Infrastructure Grid Protocols and Grid Security Infrastructure Apache SOAP,.NET, etc. …… http, https. etc. X Windows PDA Grid ssh

73 73 For More Information Globus Project™ – Grid Forum – Book (Morgan Kaufman) –

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