Prof. Dr. Victor KHOROSHEVSKY Corresponding Member of Russian - - PowerPoint PPT Presentation

7/6/2005 7/6/2005 1 1

ARCHITECTURE AND FUNCTIONING OF HIGH-PERFORMANCE DISTRIBUTED RECONFIGURABLE COMPUTER SYSTEMS AND DATA PARALLEL PROCESSING

• Prof. Dr. Victor KHOROSHEVSKY

Corresponding Member of Russian Academy of Sciences

Computer Systems Laboratory Institute of Semiconductor Physics Lavrentiev ave., 13 630090, Novosibirsk, Russia

• Tel. & Fax: +7 (3832) 33 21 71

E-mail: khor@isp.nsc.ru. Computer Center for Parallel Technologies Siberian State University of Telecommunications and Informatics Kirov str., 86 630102, Novosibirsk, Russia

• Tel. & Fax: +7 (3832) 66 38 37

E-mail: khor@neic.nsk.su.

Novosibirsk – RGW – 2005 –27.06 – 06.07.2005

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LECTURE OUTLINE

Russian – German Workshop – 2005

• 1. Conception and Architecture of Reconfigurable Distributed Computer

Systems (DCS)

• 2. Soviet and Russian Reconfigurable DCS

2.1. Architecture Facilities of DCS 2.2. Space-distributed Multicluster Computer System

• 3. Parallel Multiprogramming

3.1. DCS Multiprogram Modes 3.2. Game-theoretical Optimization of Functioning DCS 3.3. Stochastic Programming Optimization of Functioning DCS

• 4. Functioning Effectiveness Analysis of DCS

4.1. DCS Continuous Model 4.2. Robust DCS 4.3. Robustness of DCS 4.4. Parallel Solving Realizability of Tasks

• 5. Conclusion

Novosibirsk, RGW – 2005, 27.06. – 06.07.2005

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COMPUTER ARCHITECTURE DEVELOPMENT

SISD; Computer

SIMD; Array System MIMD; Distributed Programmable Structure Computer System EP – Elementary Processor EM – Elementary Machine Common Control Unit … … … … … … … … Control Memory ALU Processor … … Elementary Processing Units

Data Flow

Memory

Result Flow

. . . . . .

MISD; Pipeline System

n

EPU

11

EP

i

EPU

1

EPU

21

EP

n1

EP

12

EP

22

EP

n2

EP

1n

EP … …

2n

EP

nn

EP … … …

11

EM

21

EM

n1

EM

12

EM

22

EM

n2

EM

1n

EM

2n

EM

nn

EM … …

… … … …

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DISTRIBUTED RECONFIGURABLE COMPUTER SYSTEMS

Распределенные вычислительные системы с программируемой структурой - сочетание архитектурных свойств универсальных и специализированных средств обработки информации. Академик Н.Н. Яненко: “Чем шире класс задач, охватываемой специализированной машиной, тем сложнее ее структура и как наиболее совершенную форму ЭВМ следует рассматривать ЭВМ с перестраиваемой архитектурой”. (Доклад на Конференции по проблеме “ЭВМ. Перспективы и гипотезы”, посвященной дню Советской науки, Новосибирск, СО АН СССР, 17 апреля 1981 г.).

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DISTRIBUTED RECONFIGURABLE COMPUTER SYSTEMS

COMMUNICATION NETWORK

Distributed Computer System (DCS)

• a composition of sets of elementary

processors, local memory, control means and communication network DCS Architecture

• MIMD-architecture
• programmability of intermachine network

structure

• program transform possibility of MIMD

architecture into SIMD and MISD ones

• massively parallelism
• homogeneity, modularity and scalability
• decentralization, distributeness

(of control and data).

ELEMENTARY PROCESSOR LOCAL MEMORY CONTROL MEANS

Elementary Machine

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SOVIET AND RUSSIAN PRORAMMABLE STRUCTURE DISTRIBUTED COMPUTER SYSTEMS

DCS History

“Minsk-222” 1965 MICROS 1986 Control DCS 1967 MICROS-2 1992 ASTRA Family 1973 MICROS-T 1994 MINIMAX 1975 MBC-100 1992 – 1995 SUMMA 1977 MBC-1000 1997 - current time MICROS Family Architecture Realizability of MIMD-architecture Program-transformation possibility of MIMD-architecture into SIMD and MISD ones Massively parallelism of data processing and control process Programmability of intermachine network structure Homogeneity, modularity and scalability Decentralization (absence of a unique unit for system) Distributeness (of data and control means), short-range interaction Asynchonism and locality (“point-to-point”) of intermachine and interprocess interactions MBC-15000BM System Number of elementary machines (PowerPC970 2.2 GHz) – 924 Structure – Myrinet Performance (Rpeak, LINPACK) – 5,355 TeraFLOPS

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SPACE-DISTRIBUTED MULTICLUSTER COMPUTER SYSTEM

SibSUTI’s local network Internet, telephone lines Elementary machine Cluster network Clusters of SibSUTI Clusters of Siberian Branch

• f Russian Academy of

Sciences

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РЕКОНФИГУРАТОР СИСТЕМЫ ДИАГНОСТИЧЕСКИЕ СРЕДСТВА

(ДИАГНОСТИЧЕСКИЙ СЕРВЕР, КОНТРОЛЬНЫЕ ТЕСТЫ)

ПОДСИСТЕМА АНАЛИЗА ЭФФЕКТИВНОСТИ ДИСПЕТЧЕР РАСПРЕДЕЛЕННЫХ РЕСУРСОВ

(РАСПРЕДЕЛЕННАЯ ОЧЕРЕДЬ, БАЛАНСИРОВКА НАГРУЗКИ)

СРЕДСТВА МУЛЬТИПРОГРАММИРОВАНИЯ Обработка наборов задач Обслуживание потоков задач

MULTICLUSTER SOFTWARE

СРЕДСТВА МЕЖМАШИННОГО ВЗАИМОДЕЙСТВИЯ

(RLOGIN, RSH, TELNET, SSH)

ОПЕРАЦИОННАЯ СИСТЕМА

(Linux kernel v.2.4.20)

Сетевые протоколы

(PPP, TCP/IP)

ПРИКЛАДНЫЕ ПРОГРАММЫ СРЕДСТВА ПАРАЛЛЕЛЬНОГО ПРОГРАММИРОВАНИЯ

(LAM v.6.5.6, MPICH v.1.2.0, PVM v.1.1.1)

СРЕДСТВА ПАРАЛЛЕЛЬНОГО ПРОГРАММИРОВАНИЯ

(LAM v.6.5.6, MPICH v.1.2.0, PVM v.1.1.1)

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DISTRIBUTED CS MULTIPROGRAM MODES

Software Software Hardware Hardware

Tasks are coming to be solved by DCS

• Single rank

Monoprogram mode Operating System Optimal mixed strategies Multiprogram modes Partition of multiple machines Game-theoretical approach Stochastic programming approach

Servicing stochastic flow

• f tasks

Processing set of tasks

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STOCHASTIC-OPTIMAL FUNCTIONING ORGANIZATION OF DCS Game-theoretical approach

1. Statement of problem. Task stream with a queue. DCS of N Elementary Machines (EM) Task queue of all ranks Solution of a task of rank j requires j EM Operating System (OS) – for distribution tasks between the system machines. 2. Simplest Game Model. Game of two objects: DCS & Operating system i – pure strategy of DCS, it allocates i machines for the task solution j – pure strategy of OS, it assigns the task of rank j for DCS

• payment matrix, .
• payment of OS to DCS, if DCS and OS choose strategy numbers i and j

respectively

• mixed strategy of DCS
• mixed strategy of OS

ij

c C =

{ }

N j i , , 1 , , K ∈

ij

c

{ }

N

p p p p , , ,

1

K =

{ }

N

π π π π , , ,

1

K =

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STOCHASTIC-OPTIMAL FUNCTIONING ORGANIZATION OF DCS Game-theoretical approach (continuation)

3. Optimal mixed strategies Average payment to DCS – if DCS and OS employ mixed strategies and respectively. There are optimal mixed strategies and for DCS and OS so that: Game cost It is proposed to take the following matrix:

• payment for the usage of one EM per unit time

and - penalties per unit time for the idle time of one EM and for j – i = 1

• Theorem. The matrix C has no saddle point if and only if
• 4. Parallel method for game solution is based on a composition of the modified

Braun-Robinson and simplex methods

∑∑

= =

=

N i N j T j i ij

C p p c π π

for all p,

T

p C v π ≤

*

( ) for all

T

p C v π π ≥

* *

( )T v p Cπ = ⎩ ⎨ ⎧ < − + ≥ − + = , ) ( , ) (

3 2 2 1

j i for c i j jc j i for c j i jc cij

{ }

1 2 3

min , . c c c < p π

*

p

*

π

1

c

2

c

3

c

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STOCHASTIC-OPTIMAL FUNCTIONING ORGANIZATION OF DCS Stochastic programming approach

1. Sample of Problem Statement

• number of Elementary Machines (EM)
• number of terminals (for a task stream)
• number of subsystems of rank , which can be loaded from terminal
• probability distribution density of the variable ,
• service price of the subsystem of rank for the terminal
• cost of formation and maintenance of the subsystem of rank for the terminal
• number of subsystems of rank allocated necessarily for the terminal
• number of subsystems of rank allocated additionally for the terminal

N L

jl

a ( )

jl

p a

jl

d

jl

c

jl

y

jl

x ( ) 1,

jl

p a da

∞

=

∫

{1,2, , }, j N ∈ K {1,2, , }, l L ∈ K

jl

a l l l l l j j j j j

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STOCHASTIC-OPTIMAL FUNCTIONING ORGANIZATION OF DCS Stochastic programming approach (continuation)

Expected gain from employment of the subsystems of rank j from the terminal : Problem: here

• 2. Parallel solution of the problem is based on the dynamic programming technics

( ) ( )( ) ( ) ( )

jl jl

x y jl jl jl jl jl jl jl jl jl jl

r x d c x y d x y a p a da

+

= − + − + −

∫

{ }

1 1

( ) max;

jl

n L jl jl x j l

r x

= =

→

∑∑

1, ; j n = 1, ; l L =

1 1

,

n L jl j l

jx n

= =

≤

∑∑

1 1

,

N L jl j l

n N jy

= =

= −∑∑ 1,

jl

x for j n N = = +

l

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FUNCTIONING ANALYSIS OF DISTRIBUTED CS Continuous Model

• число элементарных машин (ЭМ)

m – число восстанавливающих устройств (ВУ)

λ – интенсивность отказов ЭМ

µ – интенсивность восстановления ЭМ одним ВУ

– интенсивность “отключения” неработоспособных ЭМ – интенсивность “переключения машин реконфигуратором – среднее число ЭМ, учитываемых реконфигуратором

' ν

'' ν – интенсивность “включения”

восстановленных ЭМ

' '' ν ν ν = +

N

i

– число работоспособных ЭМ в момент времени

t =

( , ) i t N

– среднее число работоспособных ЭМ,

0, t ≥

( , 0) i i = N

( , ) i t M

– среднее число занятых ВУ

( , ) i t L ( , ) ( , ) ( , ) i t N i t i t = − − K N L

( , ) i t K Распределенная ВС, N ЭМ

K( K(i,t) N ( N (i,t)

Реконфигуратор

L( L(i,t)

Свободные ВУ

m - m - M(i,t)

Занятые ВУ

M ( M (i,t)

Восстанавливающие устройства, m ВУ

Отказавшие ЭМ Работоспособные ЭМ

''

ν λ

'

ν µ K ( K (i,t) N ( N (i,t)

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VIRTUAL MODEL OF ROBUST DCS

Robust DCS is a program-adjusted collective of elementary machines having the following organization:

• minimal permissible number of serviceable machines is singled out to provide a

required value of total performance; possibility is secured to solve complex problems presented by Adapting Parallel Programs with variable number of their branches failures of any EM (right up to the number or restorations of nonserviceable EM lead only to increasing or decreasing time of realizing the parallel program; Performance (with changing a DCS state or a number of serviceable machines) is determined according to the following law: where: is a coefficient, is a performance of one EM;

• non-decreasing function of and .

1 , ( ) ( ) ( , ), ( ) ,

k

for k n k A k n k k n for k n ϕ ω ≥ ⎧ Ω = ⋅∆ − ⋅ ∆ − = ⎨ < ⎩

) N n −

{ }

, 1, ..., ; k n n N ∈ +

N

n

n

n

0, k N =

k

ω

k

A

ω

( , ) k ϕ ω

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POTENTIAL ROBUSTNESS OF DISTRIBUTED CS

Функция потенциальной живучести ВС:

( , ) ( , )/ ( , )/ N i t i t N i t N ω = Ω = N

Простейшая ситуация:

, ν → ∞

λ µ ν < ฀

Уравнения: разностное –

( , ) ( , ) ( , ) ( , ) ( ), i t t i t i t t i t t

• t

λ µ + ∆ = − ⋅∆ + ⋅∆ + ∆ N N N M

дифференциальное –

( , ) ( , ) ( , ), ( ,0) d i t i t i t i i dt λ µ = − + = N N M N

Восстановление без очереди:

( , ) , N i t m N m λ µ − ≤ ≤ N ( ) ( ) ( , ) , N i N i t i t e µ λ µ λ µ λ µ λ µ − − − + = + + + N

где

( ) ; ( , ) ( , ) N m i N i t N i t − ≤ ≤ = − M N

Стационарный режим: 1 lim ( , ) ( ) , i t N t µ λ µ ω − = = + Ω = ⋅ → ∞ N N N

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REALIZABILITY OF PARALLEL SOLVING PROBLEMS BY DCS

Функция потенциальной осуществимости параллельного решения задач на ВС

( , ) 1 exp ( , ) ,

t

i t i t d β τ ⎡ ⎤ Φ = − − ⎢ ⎥ ⎣ ⎦

∫N

– среднее время решения задачи на одной работоспособной ЭМ

1 β −

Простейшая ситуация: λ µ ν < ฀ Восстановление без очереди: ( , ) , N i t m N m λ µ ≤ ≤

• N

Переходный режим: ( ) ( ) ( , ) 1 exp 1 , 2 ( ) N i N i t i t t e µ λ µ λ µ β λ µ λ µ ⎧ ⎫ ⎡ ⎤ − − ⎪ ⎪ − + ⎡ ⎤ ⎢ ⎥ Φ = − − ⋅ + − ⎨ ⎬ ⎢ ⎥ + ⎣ ⎦ ⎢ ⎥ + ⎪ ⎪ ⎣ ⎦ ⎩ ⎭ где

( ) N m i N − ≤ ≤

Стационарный режим:

1 ( ) для , ( ) 1 exp 1 для N t N m t m t N m β µ λ µ λ µ β µλ λ µ − ⎧− + ≤ ⎪ Φ = − ⎨ − − > ⎪ ⎩

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CONCLUSION

Multiprogram Functioning DCS

Distributed Computer System – large-scale stochastic

• bject, serving stochastic streams of parallel jobs

Game-theoretical Technique and Stochastic Programming are bases for stochastic-optimal functioning organization of programmable structure DCS Stochastic optimization of functioning distributed computer systems is realized only once for a long time interval Parallel algorithms of game-theoretical and stochastic approaches are realized effectively Simplest effective parallel algorithms are basis for Distributed Operating Systems Non-complex-multiprogramming problems

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CONCLUSION

Effectiveness Analysis of DCS

Robust DCS – special virtual model and continuous model of functioning DCS are the basis for Effectiveness Analysis of Large-Scale Distributed Computer Systems. Derived results describe the behaviour of DCS in the transient regime as well as the stationary one. There are no difficulties for express-analysis of Potential Effectiveness (robustness, realizability of parallel solving problems and technical- economic efficiency) of Distributed CS with arbitrary number of homogeneous elementary machines. In order to choose the hardware redundancy of high-performance DCS and the number of “restoring devices” it is sufficient to use the following formulae:

Non-calculation – consuming nature Simplest technology of analysis

[ ] [ ]

( ) lg , 1 lg 1 N n N m N ≤ − ≤ ≤ ≤

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THANK YOU VERY MUCH

Novosibirsk – RGW – 2005 –27.06 – 06.07.2005 В.Г. Хорошевский Архитектура вычислительных систем

Москва, МГТУ им. Н.Э. Баумана, 2005, 41,7 п.л.