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SARA: A processor interconnection performance analysis tool
North-Holland Microprocessingand Microprogramming24 (1988) 197-204
SARA:
197
A PROCESSOR INTERCONNECTION PERFORMANCE ANALYSIS TOOL
Philippe
NAVAUX , P a u l o FERNANDES and M a u r i z i o TAZZA
CPGCC - DI - U n i v e r s i d a d e F e d e r a l do Rio Grade do Sul CP 150i - 90 001 - P o r t o A l e g r e - RS - BRASIL ** CPGII
Av.
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CITPAR
/
CEFET
C~ndido de Abreu,
-
PR
200 -
80 000 -
Curitiba
-
PR -
BRASIL
SARA is an interactive tool to define and anaIMze t h e performance o f processor interconnections. I t s p u r p o s e as a s o f t w a r e package and i t s u s e r i n t e r f a c e c o n c e p t s a r e p r e s e n t e d . A user-friendI5 tool to give graphic results from the topolog5 d e f i n e d b5 t h e u s e r i s p r o p o s e d . A model based on t h e G e n e r a l Net Theor~ (Petri nets) is used t o analsze the interconnection performance. The academic and comercial uses of SARA a r e s u g g e s t e d and t h e s5stem e v o l u t i o n i s d i s c u s s e d . KeMwords: P e r f o r m a n c e e v a l u a t i o n , Q u a n t i t a t i v e a n a l s s i s , Processor interconnections, Parallel architectures Computer n e t w o r k s , P e t r i n e t s models
I
INTRODUCTION
The studM of the behavior of several interacting processors calls for the analssis of possible connections among them, in o r d e r t o choose one t h a t has the best performance for each application. The different kinds of interconnections can be classified according to i t s use such as computer networks, local networks or parallel computer a r c h i t e c t u r e s . Other possible classification of these i n t e r c o n n e c t i o n s is according to its topological s t r u c t u r e such as r i n g i n t e r c o n n e c t i o n s , crossbar switches, etc. SARA, from its p o r t u g u e s e name: "Si~tema de An~lise de Redes e Arquiteturas" (Architectures and N e t w o r k s A n a l s s i s Ssstem) i s a graphic and interactive tool to define and anals~e the performance of processor i n t e r c o n n e c t i o n s [NAV 8 7 ] . SARA d e f i n e s ~n i n t e r a c t i v e e n v i r o n m e n t i n which t h e user establishes a topolog5 according to his/her interests, its specific configuration ( s t r u c t u r a l and phssical ~ s p e c ( s ) and t h e e n v i r o n m e n t i n which i t is expected to be used (behavior ~ s p e c t ~ ) . Examples o f s t r u c t u r a l a s p e c t s a r e t h e number o f e l e m e n t s (processors, memorM modules, etc). Phssical aspects are tgpicall9 time information
[hlb
work was p a r l i a l l y
a s s o c i a t e d t o t h e e l e m e n t s ( l i n e speeds, switches response time, etc). Behavior ~spects refer to resources (elements) using patterns associated to the d e s c r i b e d s t r u c t u r e . Thus, SARA p r o v i d e s relevant quantitative parameters of the ~nterconnection performance through graphical response and numerical representation. These p a r a m e t e r s a r e typicall5 the throughput, the resources utilizitation i n d e x e s and the induced waiting times in the interconnection bottlenecks, SARA uses a method based on the General Net Theor5 ( P e t r i n e t s [PET 7 7 ] , [PET 8 1 ] and [REI 8 5 ] ) to analsze the performance of interconnections. The proposed model objective is a description of the behavior of interconnections t h r o u g h a timed Petri net (timed P/T-nets). Quantitative p ~ r u m e t e r s which are r e l e v a n t to the i n t e r c o n n e c t i o n performance are obtained through the analssis of the correspondent Petri net. Section two explains all the results t h a t can be e x p e c t e d from SARA. In the third section the application scope o f SARA i s p r e s e n t e d t h r o u g h the ~dopted Laxonomy. S e c t i o n f o u r d e s c r i b e s SARA as a software tool defining its u s e r i n t e r f a c e and a n a l y s i s model based on general net theory (Petri nets).
s u p p o r t e d b5 CNPq, CAPES, FINEP and SID -
Inform~tica.
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Finall~ in the conclusion the present s t a t u s and t h e f u t u r e works o f t h e SARA project and SARA s o f t w a r e tool are suggested.
2.
QUANTITATIVE RESULTS
Any performance e v a l u a t i o n method aims at a qualitative judgement. Basically the question is: "Is the i n t e r c o n n e c t i o n good o r n o t ? " . T h i s k i n d of qualitative evaluation cannot be easi]5 performed. Q u a n t i t a t i v e methods are used to evaluate some parameters which are relevant to the s~stem p e r f o r m a n c e [FER 7 8 ] . These p a r a m e t e r s give numerical r e s u l t s which must be p r o p e r l 5 i n t e r p r e t e d by t h e u s e r o£ the e v a l u a t i o n method. In the interconnection modelling phase t h e u s e r g i v e s some r e a l aspects b5 numerical i n f o r m a t i o n which can be p r o c e s s e d . F o r example t h e e x p e c t e d t i m e in which l o c a l and g l o b a l memories are going to be used. Similarly in the analysis phase the user will extract from the numerical results the answers needed. T h i s p r o c e s s i s r e p r e s e n t e d b5 figure I.
USER
INPUT PARAMETERS
- number o f processors;
- reference probability matrix;
OUTPUT PARAMETERS
throughput, indexes o f resources underutilization; - induced waiting times;
MODEL
Figure I
-
SARA g e n e r i c r e p r e s e n t a t i o n
The input parameters can be different for each kind of int. e r c o n n e c t i o n . For example for topologies w i t h shared m e m o r 5 modules t h e r e i s no need f o r message l e n g t h . On t h e o t h e r hand, f o r t h e s e t o p o l o g i e s t h e number of m e m o r 5 modules must be specified. The main o u t p u t p a r a m e t e r is the interconnection t h r o u g h p u t which i s t h e number o f c o n n e c t i o n s performed in one u n i t of time. These c o n n e c t i o n s can be an access between a p r o c e s s o r and a memor5 module or a message exchange between processors. The indexes of resources under-utilization show how much t h e system components a r e being wasted. The ssstem bottlenecks are indicated by means of two aditiona] parameters: the induced w a i t i n g times and a v e r a g e p o p u l a t i o n . THese p a r a m e t e r s indicate how much a single component will w a i l i n a b o t t l e n e c k and how man~ components w i l l be w a i t i n g t h e r e .
3
APPLICATION SCOPE
SARA accepts interconnections defined according to a topological taxonom~ based on the Anderson and Jcnben p r o p o s i t i o n [AND 7 5 ] . T h i s c h o i c e was a d o p t e d because i t s taxonom5 s t i l l represents the best accepted classification. The taxonom5 a d o p t e d ( f i g u r e 2) assumes s o m e s i m p l i f i c a t i o n s like c o n s i d e r i n g onl~ processor-memors~wiLch l e v e l (PMS l e v e l [ S I E 8 2 ] ) . This abstraction level considers onl5 four kinds of elements: processors, memor5 modules, buses and switches~ These simplifications were adopted in the first s t e p s o f SARA p r o j e c t but in the future a more refined analssis is intended t o be used, leading to better results. THe inLerconnection topolog~ wa~ a d o p t e d as t h e p r i n c i p a l criterion t(J c ] a s s i f 5 t h e i n t e r c o n n e c t i o n s . Ring: has a c i r c u l a r architecture as its main feature. This group is divided i n two c l a s s e s : standard ring ~Jnd r i n g with central switch. In the first c l a s s t h e messages a r e directl5 exchanged and i n t h e second c l a s s the me~sage always passes through the central ~witch. Complete: these interconnections have an e x c l u s i v e bus f o r each p a i r of processor. A p r o c e s s o r cannot send messages t o a n o t h e r t h r o u g h an~ other wa~ but t h e d e d i c a t e d bus which c o n n e c t s them.
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RING
COMPLETE
BUS
~
? ?
REGULAR ~
STAR
IRREGULAR
NNNNN~ NNNN~ NNNNN
? ?
MULTIPROCESSOR
Regular: in this group the proccssor~ are interconnected through d ~ d l c a t e d and i d e n t i c a l links with their neighbors. Of course t h i s c r i t e r i o n is v a l l d o n l 5 f o r t o p o l o g i e s not c l a s s i f i e d in uther groups. The interconnection pattern identifies the classes of this group. There are several kinds of g~.ometrical forms, and f o r t h i s r e a s o n ~cveral classes. The b e s t known c l a s s e s are composed b5 mesh, cube, tree and hspercube o r g a n i z a t i o n s . Irregular: theoreticall5 an5 o t h e r t s p e o f t o p o l o g y can be c l a s s i f i e d as a irregular nelwork. In t h i s group the proue~sors are l i n k e d t o a network of switching e l e m e n t s which e s t a b l i s h e s a pou~ible path between two of the processors.
4.
SARA'S FUNCTIONAL STRUCTURE
SARA is a software package which implements a tool for performance anal~sis. Its goals as a software package will not be limited to the performance analssis but a l s o include the development of a user-friend]5 interface. These twu i m p o r t a n t f e a t u r e s ,~re d i s c u s s e d i n t h i s section. Section 4 I d e s c r i b e s t h e i n t e r f a c e in a g e n e r i c way. S e c t i o n s q . 2 , 4 . 3 and 4 . 4 d e s c r i b e s the definition e n v i r o n m e n t b5 means o f the definition dialogue, the formalism of modelling and a example of the proposed model. Sections 4.5, 4 . 6 and 4.7 d e s c r i b e s the f o r m a l i s m o f a n a l y s i s , the a n a l s s i s d i a l o g u e and a example of analssis,
0.. { {DD-[3--
Figure 2
-
a d o p t e d taxonom5 4.1
Multiprocessor: this kind of t u p o l o g 5 has g l o b a l memor5 modules which ~re u~ed for exchanging processor me~sages. There have been considered f l v e c l a s s e s in t h i s group: single-bus, m u l t i p o r t memories, m u l t i p l e - b u s , m u l t i s ~ a g e and c r o s s b a r . G l o b a l bus: the princlple of this topulgg3 is a common bus used b5 p r o c e s s o r s t o exchange messages. Notice that single-bus multiprocessors are quite different because i n t h e global bu~ case onl5 the bus, not memor5 moduleo, a r e used t o exchange messages. There are two c l a s s e s i n this group: ~ t a n d a r d g l o b a l bus and g l o b a l bus with central switch. Star: the communication between processor~ is a l w a s s made t h r o u g h the bWl[ching element whlch has buses for a l l the p r o c e s s o r s .
USER INTERFACE
SARA's u s e r i n t e r f a c e must d i a l o g u e with the user o f f e r i n g the following posbible operations: -
interconnection definition (modelling) interconnection analssis (performance evaluation) - l o a d and s t o r e f e a t u r e s ( d a t a base) •- u n - l i n e h e l p (common h e l p ) The t s p l c a l d i a l o g u e c o n s i s t s o f an intercunnection definltion, its unalyuis, followed b5 a repeated redefinitions and new a n a l y s i s u n t i l the bturage of the interconnection. SARA's dialogue has been d e s i g n e d t o g i v e all the posoible sequences of operations through a menu-drlven n a v i g a t i o n . A l l ssstem n a v i g a t i o n i s d r i v e n b5 menu~ In the main menu t h e u s e r can
F Navaux et aL / SARA
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choose one o f
all the operations alread5 Each operation Has its s p e c i f i c menu and a t an5 s t a g e t h e user can go t o a l l o t h e r o p e r a t i o n s . A few obvious restrictions are made to navigation possibilites, which a r e :
mentioned.
a new i n t e r c o n n e c t i o n d e f i n i t i o n begin w i t h i t s c l a s s d e f i n i t i o n ~ -
must
an incompletel5 defined interconneckion, with structural, phssic~l and b e h a v i o r a l a s p e c t s cannot be anal~sed~ -
-- an un-named or non-classified interconnection c a n n o t use t h e l o a d and store features~ Fu manage t h e d i a l o g u e w i t h i n this restrictions t h e r e i s an i n t e r c o n n e c t i o n ~tatu~. This status represents the possibilities to use the s~stem operutions. THe possible v a l u e s to t h e s t a t u s are: draft an un-named and incomplete]5 defined interconnection~ a n a m e d and non-classified interconnection~ -
-
defined draft -- an u n - n a m e d interconnection~ interconnection a named interconnection; -
complete15
and
defined
classified
complete i n t e r c o n n e c t i o n .- a named and c o m p l e t e l 5 d e f i n e d intcrconnection~ -
4.8.
DEFINITION ENVIRONMENT: INTERFACE
This operation begins with the interconnection class definition. A menu analogous t o t h e taxonom5 t r e e (figure 0) i s used t o choose t h e i n t e r c o n n e c t i o n class. After that the interconnection specific characteristics are d e f i n e d in three levels: structural, p h s s i c a l and behavioral aspects. All these aspects are asked b5 ~imple questions in a board. These questions Have or a n u m e r i c a l r e s p o n s e o r a menu o p t i o n s f o r non-numerical aspects. The definition dialogue is complete]5 interactive within the interconnection aspects, such that the user can define the characteristics i n an~ o r d e r . The definition r e f r e s h i s made i n lwo different waSs for a) the i n ~ e r c o n n e c t i o r } c l a s s and t h e s t r u c t u r a l aspects and b) f o r the phssical and behavioral aspects. For the first
i n f u r m u t i o n (a) a g r a p h i c r e p r e s e n t a t i o n (topology> is shown during all the SARA's processes. These processes can also be included in other operations ~uch as i n t e r c o n n e c t i o n analysis. For physical and behavioral (b> a s p e c t s two boards with all the questions and respective answers are shown just like w h e n I H e 9 were asked. Other i n f o r m a t i o n considered of H i g h i m p o r t a n c e is a l w a y s shown on the s~stem screen, as the graphic representation of the topology. THis information is the interconnection name, its c l a s s and its s t a t u s . 4.3
DEFINITION ENVIRONMENT: MODEL
THe e x t e r n a l mode] i s t h e u s e r v i e w uf the i n t e r c o n n e c t i o n . Figure 3 is an IMC [RIC 85] representation of the c>(tcrnu] and i n t e r n a l m o d e l f o r c l a s s e s of interconnections. The i n t e r n a l model i s o b t a i n e d from a mapping o f t h e i n f o r m a t i o n given b5 l.h~ u s e r t o an i n t e r n a l representation uf the interconnection. The mapping between t h e models i s t r a n s p a r e n t t o t h e user. It must be noticed that the ueneric behavior of the interconnection i v n o t d e f i n e d b5 t h e u s e r . Instead, it i s embedded i n t h e i n t e r n a l mode] d u r i n g s~stcm construction. During the external model definition phase the information about the structural, yh~sic~l and behavioral aspects of a g i v e n i n t e r c o n n e c t i o n a r e t r a n s l a t e d and a s s o c i a t e d to the i n t e r n a l description. A f t e r a step o f s e m a n t i c a l v e r i f i c a t i o n , the internal model is read5 to be ar~al~zed THe a n a l s s i s o f t h e internal model allows the computation of the proposed q u a n t i t a t i v e p a r a m e t e r s . In order to describe the analysis method, i t i s n e c e s s a r 5 t o d e s c r i b e some details of the internal model. THe general b e h a v i o r o f a given topolog~ is modeled i n t e r m s of a place-transition net N. Formall~, N = (S,T,F,K,B,Mo)0 w h o r e S0 T and F ( F ~ ( S x T) U (T x S)) are re~pectivel~ the set of places, transitions and the flow relation between e l e m e n t s o f S and T. The v e c t o r K (K:S .-) Nw) a t t a c h e s a c a p a c i t y t o t h e p l a c c ~ of N. THe v e c t o r B ( B : F -> N*> defines a weight a s s o c i a t e d to the arcs of the net and Mo (Mo:S -> N) is the initial marking o f the net. Timed-P/T n e t s a r e used t o t h e i n t e r n a l mode]. A net N ~ (S,T,F,K,B,Mo,Z), where Z a t t a c h e s an u n a v a i l a b i l i t 5 time to ~ome places uf the net. More i n f o r m a t l o n on t h e s e P e t r i n e t s i s found i n [ R I C 8 5 a ] . In SARA, a k i n d o f P e t r i net is a~sociated w i t h each i n t e r c o n n e c t i o n in the a p p l i c a t i o n scope ( f i g u r e 3>. The
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APPLICATIONSCOPE
[
TOKEN-RING INTERCONNECTiON
?,, . oo.
I
INTERCONNECTiON ?EXT. MOC
I
1
are
obtained
.....
scope i n t e r n a l
b~
studsing the interconnection net structure it is e m b e d d e d in SARA During the user session the initial marking and the utilization Limes (Me,Z) w i l l be p r o v i d e d . A f t e r t h e interna] model i s c o m p l e t e d , i t can be anal~ed the computation the performance parameters.
reluvant a s p e c t s o f t h e behaviour Once the (S,T,F,K,B) is o b t a i n e d , for
?
~INT. MOO.
I
Figure 3 - application neLs
CROSS -BAR INTERCONNECTION
STAR
?,..oo.
I representation
Z(u-SMRY) time u n i t s the shared memor5 is released (occurrence of transition a r l d the processor starts a new c~cle.
trl)
we
of
u_LMRY ) ]]
some i n t e r c o n n e c t i o n c l a s s e s a probubi]it5 reference matrix must be defined Lo a n a l ~ z e d i f f e r e n t behaviors example model memor5 contention). Thls matrix describes the probabilit~ of reference between all processors and from it the pattern probabilities can be e x t r a c t e d . Several behavior patterns can be modelled several nets, so e a c h net is evaluated a n d its r e s u l t s w e i g h t e d .
(fo~
~
W_SMRY) PROC ]'S )/J" Y ]'~rt et
to
SMRY<
I.hrouuh
DEFINITION E N V I R O N M E N T :
)
ts4 }"x
For
4.4.
II
(o)
EXAMPLE
The net o f f i g u r e 4a r e p r e s e n t s t h e schema of the internal model for specific interconnection (crossbar).
a )
of
The initial marking p l a c e s PROC and SMRY models t h e number o f p r o c e s s o r s and shared memories i n the topologs, respecLivel5 Places u-LMRY and u-SMRY model the utilization of t h e resources with using time Z(u-LMRY) and Z ( u - S M R Y ) . The l o c a l memories a r e not r e p r e s e n t e d , the~ are exclusive resources each processor. P l a c e w-SMRY i s interpreted as a waiting p l a c e for p r o c e s s o r s with the request for a especific shared memor~ module denied. The infinite initial marking p l a c e we represents an infinite number of accesses requesting to e n t e r t h e s ~ s t e m .
of
~(u-LMRY)=Xz I ~)
~PROC
SMRY~
!
I~
PROC
SMRY~ /_SMRY)=yz
of
D5 o c u r r e n c e of transition tsl a processor e n t e r s in a l o c a l processing mode After Z(u-LMRY) time units, lhrough the occurrence of tl the processor tries to a c c e s s a specific shared m e m o r 5 module SMRYi, where i:=l,~ ..... Mo(SMRY). B5 o c u r r e n c e o f i s 2 shared is utilized. After
the
memor~
(b)
F i g u r e 4 a) b) c)
(c
Generic d e s c r i p t i o n o f crossbar interconnections Number o f p r o c e s s o r s and s h a r e d memor5 modules L o c a l and g l o b a l p r o c e s s i n g times
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4.5.
ANALYSIS ENVIRONMENT: FLOW EOUATIONS
The i n t e r n a l model composed b5 the structure of the net, initial marking, utilizatiun times and probabilit~ reference matrix is read~ for the analssis. The flow equations were developed in [TAZ 85] and the~ are briefIM described. More i n f o r m a t i o n in e n g l i s h can be found i n [TAZ 8 7 ] . The basic period Po(N) of the r e s o u r c e s i n a net i s d e f i n e d as t h e sum of the utilization times between the component a l l o c a t i o n and r e l e a s e . Given Ni components, we have: Po(Ni) For
=
(ui)
S
(eq-i>
the c r o s s b a r case: Po(N-PROC)
= Z(u-LMRY) + Z(u-SMRY)
Po(N-SMRY)
= Z(u-SMRY)
The throughput component is: Do(Ni>
of
an
isolated
Mo(ri) ........ Po(Ni)
The throughput i s g i v e n bs: D(N)
Do(Ni)
= min
of
the
(eq-2)
ssstem as a w h o l e
(Do(Ni)
(eq.-3)
From equation-3 the other performance parameters o f i n t e r e s t are developed: Resource U(Ni): U(Ni)
Induced bsstem:
Ni
under-utilization
= I
D(N) ....... Do(Ni)
wait
Zw(wi)
Mo(ri) = ....... D(N)
Mean v a l u e o f o f the net: M(s) 4.6.
time at
(eq-4)
w-places
Po(Ni>
t h e marking at
= D(N).Z(s)
index
in
the
(eq-5)
a place
s
(eq-6>
ANALYSIS ENVIRONMENT: INTERFACE
If there i s no i n t e r n a l model in Petri nets for the defined interconnection, the analssis operation begins with a translation of the user definition of interconnection to this internal representation. On t h e other h~nd, if t h e r e i ~ a l r e a d 5 an internal model, t h e a n a l s s i s i t s e l f begins.
The n u m e r i c a l o u t p u t o f t h e method suggests a numerical output to the unal~sis, i . e , the i n t e r c o n n e c t i o n i s m o d e l l e d and t h e r e s u l t s a r e g i v e n just l i k e the~ are c a l c u l a t e d . This o p t i o n i s commonl5 used f o r p e r f o r m a n c e e v a l u a t i o n methods in which a single case evaluation took a considerable time. However in our method a single case evaluation is quite quick, i f t h e model has a l r e a d 5 been f o u n d . The a p p l i c a t i o n of the model is fast enough to be a p p l i e d several t i m e s , p r o d u c i n g not one numerical v a l u e but a c u r v e describing an output parameter behavior according to an i n p u t p a r a m e t e r variation. A g r a p h i c c u r v e shows t h e results i n a g e n e r i c was, showing t h e i n f l u e n c e of un input parameter on the output parameters, The modelling assumptions, t h e i m p l e m e n t a t i o n and o t h e r c o n s t r a i n t s are reasons to reduce the model Precision. N u m e r i c a l r e s u l t s cannot be a c c e p t e d as e x a c t p r e d i c t i o n s , but as an aproximation to reality. The was in which an o u t p u t p a r a m e t e r changes for some c o n f i g u r a t i o n s gives much more information than simple numerical results The main goal of the analssis operation dialogue is to define these input and o u t p u t p a r a m e t e r s o r t h e a x i s of the curve. The input and output parameters will be shown on the hori.contal and vertical axis respectivelD.
The chosen i n p u t p a r a m e t e r s can be almost a l l t h e p a r a m e t e r s asked in the definition phase. For some c l a s s e s not a l l can be used s i n c e i n some cases some behavioral a s p e c t s c a n n o t be chosen to be the horizontal axis. The output parameters can be freel~ chosen. For som~ c a s e s , depending on the chosen horizontal axis the curve cannot be drawn continuosls. I f t h e chosen i n p u t parameter cannot be continuosl5 incremented the curve p o i n t s w i l l be f a r from each o t h e r . For e x a m p l e , if the horizontal axis is the number of l, r o c e s s o r s o n l ~ d i s c r e t e v a l u e s can be evaluated. Even if numerical results have minor importance when compared to graphic curves, t h e 9 can s t i l l be shown through a c u r s o r mechanism. The c u r s o r implementation is activated just after the drawing o f the curve. A s i n g l e p o i n t cursor can run o v e r t h e curve showing numericalls, for all input parameter v a l u e s which o u t p u t v a l u e was o b t a i n e d .
P. Navaux et aL / S A R A
47.
ANALYSIS ENVIRONMENT: EXAMPLE
3.
Flow e q u a t i o n s d e v e l o p e d i n s e c t i o n 4.5 are a p p l i e d t o o b t a i n quantitative ~,uralncturs for t h r e e s i m i l a r cases of crossbar interconnections. More i n f o r m a t i o n about c r o s s b a r quantitative a n a l y s i s a p p l i e d i s found i n [TAZ B 7 a ] .
rlumber -
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Throughput a n a l y s i s c r o s s b a r case
A processor i n t e r connect ion p e r f o r m a n c e a n a l y s i s t o o l based on P e t r i nL'tS performance evaluation has been described. The g e n e r i c SARA's working s c h e m a i s s h o w n on f i g u r e 6.
SARA i s a t o o l which can be used For both comercial and academic purposes I t s academic use w i l l help the research of interconnections behavior, aiding the design of machine archileclures. A f u r t h e r use i s t r a i n i n g o f studenks in the a n a l y s i s o f d i f f e r e n t lopulo~ies. For c o m e r c i a l use i t will facilitate evaluation of existing Interconnections in order to study expansion priorities and reviewing of topologies a i m i n g at p e r f o r m a n c e g a i n . It can also be used to evaluate alternatives
The c u r v e s on f i g u r e 5 d e s c r i b e t h e throughput behavior according to the local processing time variation for the three cases above.
o
CONCLUSIONS
SARA's main g o a l was t o d e s i g n a user-friendly tool for performance analysis. Even the choice of which output parameters will be a v a i l a b l e t o o k that into account. The a d o p t e d output parameters were chosen t o f u l f i l l this g o a l and Lo make p o s s i b l e t h e c o m p a r i s o n w i t h r e s u l t s from o t h e r methods.
Con f i g u r a l i o n : -
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for
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systems.
THe p r o p o s e d a n a l y s i s w o r k s i n the PMS l e v e l e v a l u a t i n g t h e i n t e r c o n n e c t i o n performance. Future works i n c l u d e the uxpuntion of analysis to other levels. By m o d e l l i n g a l o w e r l e v e l , t h e i n t e r n a l performance of the processors can be estimated t o feed t h e b e h a v i o r aspects which refer to the local processing usage times. In modelling at higher levels t h e r e a r e two a n a l o g o u s o p t i o n s : m o d e l l i n g e i t h e r t h e o p e r a t i n g system o r ~he nelwurk p r o t o c o l . In both options the global processing expected is u>(tracted from the analysis of these higher levels. At the p r e s e n t s t a g e SARA models and evaluates interconnections of m u l t i p r o c e s s o r and s t a r g r o u p s . The r i n g and regular groups are currentl5 modelled and t h e i r a n a l y s i s are being implemented. The software has been developed t o be used i n any MS-DOS/IBMPC-like environments. The p r o t o t y p e has been d e v e l o p e d i n PASCAL l a n g u a g e and a final implementation is about to be completed in C language. The software has graphic packages to work with monocromatic and color (EGA) video controllers. The o t h e r m a c h i n e - d e p e n d e n t packaqes can be e a s i l y made t o t r a n s p o r t SARA t o o t h e r e n v i r o n m e n t s .
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REFERENCES [PET 77] PETRI, C. A. General net theory. I n : PROCEEDINGS OF THE JOINT IBM UNIVERSITY OF NEWCASTLE UPON TYNE. SEMINAR, Newcastle upon Tsne, Sep. 710, i976. Proceedings. Universit~ o f Newcastle upon Tsne, 1977. [PET 81] PETERSON, J. L. P e t r i net theor~ and the m o d e l l i n g o f s~stems. Englewood C l i f f s , P r e n t i c e - H a l l , 198i. [REI 85] REISIG, W. introduction. Berlin, 1985.
INOEX
Petri nets: an Springer-Verlag,
[RIC 85] RICHTER, G. Clocks and t h e i r use f o r t i m e m o d e l l i n g . I n : SERNADAS, A. et alli (eds.>: Information ssstems: Theoretical and formal aspects. North-Holland, Amsterdam, 1985. pp. 4V-66 [RIC 85a] RICHTER, G. Utilization of data access and m a n i p u l a t i o n in conceptual schema definition. Information S~stems, Oxford, 6 (I): 53-71, 1 9 8 i . [TAZ 85] TAZZA, M. Ein n e t z t h e o r e t i s c h e s model] z u r q u a n t i t a t i v e n a n a l y s e yon ssstemen (O-model]). R. Oldenbourg V e r l a g , HUnchen, i 9 8 5 . ( B e t . 149)
1
[TAZ 87] TAZZA, M. Quantitative Analssis of a Resource A l l o c a t i o n Problem: A net Theor~ Based P r o p o s a l . In: Voss, K. et a l l i ( e d s . ) , Advances in Petri Nets. Springer-Verlag, B e r l i n , 1987. pp. 511-532. [TAZ 87a] TAZZA, M. et alli. An~lise quantitativa de interconexBes crossbar. In: CONGRESSO DA SOCIEDADE BRASILEIRA DE COMPUTAC~O, 7., Salvador, Jul 11-17, 1987. Anais. S a l v a d o r , SBC, 1987. p. 241-254. [AND 7 5 ] ANDERSON, G. A. & JENSEN, E. D. Computer interconnection structures: taxonoms, characteristics, and examples. Computing Survess, 7 ( 4 ) : 197-213, Dec i775~ [FER 7 8 ] FERRARI, D. Computer s~stems performance evaluation. Englewood Cliffs, P r e n t i c e - H a l l , 1978. [ S I E 8 2 ] SIEWIOREK, D. et a l l i . structures: p r i n c i p l e s and M c G r a w - H i l l , London, 1982.
Computer examples.
[NAV 87] NAVAUX, Ph. et aIli. SARA: Interface com o u s u ~ r i o e escopo de aplicac~o. In: CONGRESSO NACIONAL DE INFORHATICA, 20, S~o Paulo, Ago. 3JSet. 6 1987. A n a i s . S~o Paulo, SUCESU, 1987.
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A PROCESSOR INTERCONNECTION PERFORMANCE ANALYSIS TOOL
Philippe
NAVAUX , P a u l o FERNANDES and M a u r i z i o TAZZA
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SARA is an interactive tool to define and anaIMze t h e performance o f processor interconnections. I t s p u r p o s e as a s o f t w a r e package and i t s u s e r i n t e r f a c e c o n c e p t s a r e p r e s e n t e d . A user-friendI5 tool to give graphic results from the topolog5 d e f i n e d b5 t h e u s e r i s p r o p o s e d . A model based on t h e G e n e r a l Net Theor~ (Petri nets) is used t o analsze the interconnection performance. The academic and comercial uses of SARA a r e s u g g e s t e d and t h e s5stem e v o l u t i o n i s d i s c u s s e d . KeMwords: P e r f o r m a n c e e v a l u a t i o n , Q u a n t i t a t i v e a n a l s s i s , Processor interconnections, Parallel architectures Computer n e t w o r k s , P e t r i n e t s models
I
INTRODUCTION
The studM of the behavior of several interacting processors calls for the analssis of possible connections among them, in o r d e r t o choose one t h a t has the best performance for each application. The different kinds of interconnections can be classified according to i t s use such as computer networks, local networks or parallel computer a r c h i t e c t u r e s . Other possible classification of these i n t e r c o n n e c t i o n s is according to its topological s t r u c t u r e such as r i n g i n t e r c o n n e c t i o n s , crossbar switches, etc. SARA, from its p o r t u g u e s e name: "Si~tema de An~lise de Redes e Arquiteturas" (Architectures and N e t w o r k s A n a l s s i s Ssstem) i s a graphic and interactive tool to define and anals~e the performance of processor i n t e r c o n n e c t i o n s [NAV 8 7 ] . SARA d e f i n e s ~n i n t e r a c t i v e e n v i r o n m e n t i n which t h e user establishes a topolog5 according to his/her interests, its specific configuration ( s t r u c t u r a l and phssical ~ s p e c ( s ) and t h e e n v i r o n m e n t i n which i t is expected to be used (behavior ~ s p e c t ~ ) . Examples o f s t r u c t u r a l a s p e c t s a r e t h e number o f e l e m e n t s (processors, memorM modules, etc). Phssical aspects are tgpicall9 time information
[hlb
work was p a r l i a l l y
a s s o c i a t e d t o t h e e l e m e n t s ( l i n e speeds, switches response time, etc). Behavior ~spects refer to resources (elements) using patterns associated to the d e s c r i b e d s t r u c t u r e . Thus, SARA p r o v i d e s relevant quantitative parameters of the ~nterconnection performance through graphical response and numerical representation. These p a r a m e t e r s a r e typicall5 the throughput, the resources utilizitation i n d e x e s and the induced waiting times in the interconnection bottlenecks, SARA uses a method based on the General Net Theor5 ( P e t r i n e t s [PET 7 7 ] , [PET 8 1 ] and [REI 8 5 ] ) to analsze the performance of interconnections. The proposed model objective is a description of the behavior of interconnections t h r o u g h a timed Petri net (timed P/T-nets). Quantitative p ~ r u m e t e r s which are r e l e v a n t to the i n t e r c o n n e c t i o n performance are obtained through the analssis of the correspondent Petri net. Section two explains all the results t h a t can be e x p e c t e d from SARA. In the third section the application scope o f SARA i s p r e s e n t e d t h r o u g h the ~dopted Laxonomy. S e c t i o n f o u r d e s c r i b e s SARA as a software tool defining its u s e r i n t e r f a c e and a n a l y s i s model based on general net theory (Petri nets).
s u p p o r t e d b5 CNPq, CAPES, FINEP and SID -
Inform~tica.
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Finall~ in the conclusion the present s t a t u s and t h e f u t u r e works o f t h e SARA project and SARA s o f t w a r e tool are suggested.
2.
QUANTITATIVE RESULTS
Any performance e v a l u a t i o n method aims at a qualitative judgement. Basically the question is: "Is the i n t e r c o n n e c t i o n good o r n o t ? " . T h i s k i n d of qualitative evaluation cannot be easi]5 performed. Q u a n t i t a t i v e methods are used to evaluate some parameters which are relevant to the s~stem p e r f o r m a n c e [FER 7 8 ] . These p a r a m e t e r s give numerical r e s u l t s which must be p r o p e r l 5 i n t e r p r e t e d by t h e u s e r o£ the e v a l u a t i o n method. In the interconnection modelling phase t h e u s e r g i v e s some r e a l aspects b5 numerical i n f o r m a t i o n which can be p r o c e s s e d . F o r example t h e e x p e c t e d t i m e in which l o c a l and g l o b a l memories are going to be used. Similarly in the analysis phase the user will extract from the numerical results the answers needed. T h i s p r o c e s s i s r e p r e s e n t e d b5 figure I.
USER
INPUT PARAMETERS
- number o f processors;
- reference probability matrix;
OUTPUT PARAMETERS
throughput, indexes o f resources underutilization; - induced waiting times;
MODEL
Figure I
-
SARA g e n e r i c r e p r e s e n t a t i o n
The input parameters can be different for each kind of int. e r c o n n e c t i o n . For example for topologies w i t h shared m e m o r 5 modules t h e r e i s no need f o r message l e n g t h . On t h e o t h e r hand, f o r t h e s e t o p o l o g i e s t h e number of m e m o r 5 modules must be specified. The main o u t p u t p a r a m e t e r is the interconnection t h r o u g h p u t which i s t h e number o f c o n n e c t i o n s performed in one u n i t of time. These c o n n e c t i o n s can be an access between a p r o c e s s o r and a memor5 module or a message exchange between processors. The indexes of resources under-utilization show how much t h e system components a r e being wasted. The ssstem bottlenecks are indicated by means of two aditiona] parameters: the induced w a i t i n g times and a v e r a g e p o p u l a t i o n . THese p a r a m e t e r s indicate how much a single component will w a i l i n a b o t t l e n e c k and how man~ components w i l l be w a i t i n g t h e r e .
3
APPLICATION SCOPE
SARA accepts interconnections defined according to a topological taxonom~ based on the Anderson and Jcnben p r o p o s i t i o n [AND 7 5 ] . T h i s c h o i c e was a d o p t e d because i t s taxonom5 s t i l l represents the best accepted classification. The taxonom5 a d o p t e d ( f i g u r e 2) assumes s o m e s i m p l i f i c a t i o n s like c o n s i d e r i n g onl~ processor-memors~wiLch l e v e l (PMS l e v e l [ S I E 8 2 ] ) . This abstraction level considers onl5 four kinds of elements: processors, memor5 modules, buses and switches~ These simplifications were adopted in the first s t e p s o f SARA p r o j e c t but in the future a more refined analssis is intended t o be used, leading to better results. THe inLerconnection topolog~ wa~ a d o p t e d as t h e p r i n c i p a l criterion t(J c ] a s s i f 5 t h e i n t e r c o n n e c t i o n s . Ring: has a c i r c u l a r architecture as its main feature. This group is divided i n two c l a s s e s : standard ring ~Jnd r i n g with central switch. In the first c l a s s t h e messages a r e directl5 exchanged and i n t h e second c l a s s the me~sage always passes through the central ~witch. Complete: these interconnections have an e x c l u s i v e bus f o r each p a i r of processor. A p r o c e s s o r cannot send messages t o a n o t h e r t h r o u g h an~ other wa~ but t h e d e d i c a t e d bus which c o n n e c t s them.
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RING
COMPLETE
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REGULAR ~
STAR
IRREGULAR
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? ?
MULTIPROCESSOR
Regular: in this group the proccssor~ are interconnected through d ~ d l c a t e d and i d e n t i c a l links with their neighbors. Of course t h i s c r i t e r i o n is v a l l d o n l 5 f o r t o p o l o g i e s not c l a s s i f i e d in uther groups. The interconnection pattern identifies the classes of this group. There are several kinds of g~.ometrical forms, and f o r t h i s r e a s o n ~cveral classes. The b e s t known c l a s s e s are composed b5 mesh, cube, tree and hspercube o r g a n i z a t i o n s . Irregular: theoreticall5 an5 o t h e r t s p e o f t o p o l o g y can be c l a s s i f i e d as a irregular nelwork. In t h i s group the proue~sors are l i n k e d t o a network of switching e l e m e n t s which e s t a b l i s h e s a pou~ible path between two of the processors.
4.
SARA'S FUNCTIONAL STRUCTURE
SARA is a software package which implements a tool for performance anal~sis. Its goals as a software package will not be limited to the performance analssis but a l s o include the development of a user-friend]5 interface. These twu i m p o r t a n t f e a t u r e s ,~re d i s c u s s e d i n t h i s section. Section 4 I d e s c r i b e s t h e i n t e r f a c e in a g e n e r i c way. S e c t i o n s q . 2 , 4 . 3 and 4 . 4 d e s c r i b e s the definition e n v i r o n m e n t b5 means o f the definition dialogue, the formalism of modelling and a example of the proposed model. Sections 4.5, 4 . 6 and 4.7 d e s c r i b e s the f o r m a l i s m o f a n a l y s i s , the a n a l s s i s d i a l o g u e and a example of analssis,
0.. { {DD-[3--
Figure 2
-
a d o p t e d taxonom5 4.1
Multiprocessor: this kind of t u p o l o g 5 has g l o b a l memor5 modules which ~re u~ed for exchanging processor me~sages. There have been considered f l v e c l a s s e s in t h i s group: single-bus, m u l t i p o r t memories, m u l t i p l e - b u s , m u l t i s ~ a g e and c r o s s b a r . G l o b a l bus: the princlple of this topulgg3 is a common bus used b5 p r o c e s s o r s t o exchange messages. Notice that single-bus multiprocessors are quite different because i n t h e global bu~ case onl5 the bus, not memor5 moduleo, a r e used t o exchange messages. There are two c l a s s e s i n this group: ~ t a n d a r d g l o b a l bus and g l o b a l bus with central switch. Star: the communication between processor~ is a l w a s s made t h r o u g h the bWl[ching element whlch has buses for a l l the p r o c e s s o r s .
USER INTERFACE
SARA's u s e r i n t e r f a c e must d i a l o g u e with the user o f f e r i n g the following posbible operations: -
interconnection definition (modelling) interconnection analssis (performance evaluation) - l o a d and s t o r e f e a t u r e s ( d a t a base) •- u n - l i n e h e l p (common h e l p ) The t s p l c a l d i a l o g u e c o n s i s t s o f an intercunnection definltion, its unalyuis, followed b5 a repeated redefinitions and new a n a l y s i s u n t i l the bturage of the interconnection. SARA's dialogue has been d e s i g n e d t o g i v e all the posoible sequences of operations through a menu-drlven n a v i g a t i o n . A l l ssstem n a v i g a t i o n i s d r i v e n b5 menu~ In the main menu t h e u s e r can
F Navaux et aL / SARA
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choose one o f
all the operations alread5 Each operation Has its s p e c i f i c menu and a t an5 s t a g e t h e user can go t o a l l o t h e r o p e r a t i o n s . A few obvious restrictions are made to navigation possibilites, which a r e :
mentioned.
a new i n t e r c o n n e c t i o n d e f i n i t i o n begin w i t h i t s c l a s s d e f i n i t i o n ~ -
must
an incompletel5 defined interconneckion, with structural, phssic~l and b e h a v i o r a l a s p e c t s cannot be anal~sed~ -
-- an un-named or non-classified interconnection c a n n o t use t h e l o a d and store features~ Fu manage t h e d i a l o g u e w i t h i n this restrictions t h e r e i s an i n t e r c o n n e c t i o n ~tatu~. This status represents the possibilities to use the s~stem operutions. THe possible v a l u e s to t h e s t a t u s are: draft an un-named and incomplete]5 defined interconnection~ a n a m e d and non-classified interconnection~ -
-
defined draft -- an u n - n a m e d interconnection~ interconnection a named interconnection; -
complete15
and
defined
classified
complete i n t e r c o n n e c t i o n .- a named and c o m p l e t e l 5 d e f i n e d intcrconnection~ -
4.8.
DEFINITION ENVIRONMENT: INTERFACE
This operation begins with the interconnection class definition. A menu analogous t o t h e taxonom5 t r e e (figure 0) i s used t o choose t h e i n t e r c o n n e c t i o n class. After that the interconnection specific characteristics are d e f i n e d in three levels: structural, p h s s i c a l and behavioral aspects. All these aspects are asked b5 ~imple questions in a board. These questions Have or a n u m e r i c a l r e s p o n s e o r a menu o p t i o n s f o r non-numerical aspects. The definition dialogue is complete]5 interactive within the interconnection aspects, such that the user can define the characteristics i n an~ o r d e r . The definition r e f r e s h i s made i n lwo different waSs for a) the i n ~ e r c o n n e c t i o r } c l a s s and t h e s t r u c t u r a l aspects and b) f o r the phssical and behavioral aspects. For the first
i n f u r m u t i o n (a) a g r a p h i c r e p r e s e n t a t i o n (topology> is shown during all the SARA's processes. These processes can also be included in other operations ~uch as i n t e r c o n n e c t i o n analysis. For physical and behavioral (b> a s p e c t s two boards with all the questions and respective answers are shown just like w h e n I H e 9 were asked. Other i n f o r m a t i o n considered of H i g h i m p o r t a n c e is a l w a y s shown on the s~stem screen, as the graphic representation of the topology. THis information is the interconnection name, its c l a s s and its s t a t u s . 4.3
DEFINITION ENVIRONMENT: MODEL
THe e x t e r n a l mode] i s t h e u s e r v i e w uf the i n t e r c o n n e c t i o n . Figure 3 is an IMC [RIC 85] representation of the c>(tcrnu] and i n t e r n a l m o d e l f o r c l a s s e s of interconnections. The i n t e r n a l model i s o b t a i n e d from a mapping o f t h e i n f o r m a t i o n given b5 l.h~ u s e r t o an i n t e r n a l representation uf the interconnection. The mapping between t h e models i s t r a n s p a r e n t t o t h e user. It must be noticed that the ueneric behavior of the interconnection i v n o t d e f i n e d b5 t h e u s e r . Instead, it i s embedded i n t h e i n t e r n a l mode] d u r i n g s~stcm construction. During the external model definition phase the information about the structural, yh~sic~l and behavioral aspects of a g i v e n i n t e r c o n n e c t i o n a r e t r a n s l a t e d and a s s o c i a t e d to the i n t e r n a l description. A f t e r a step o f s e m a n t i c a l v e r i f i c a t i o n , the internal model is read5 to be ar~al~zed THe a n a l s s i s o f t h e internal model allows the computation of the proposed q u a n t i t a t i v e p a r a m e t e r s . In order to describe the analysis method, i t i s n e c e s s a r 5 t o d e s c r i b e some details of the internal model. THe general b e h a v i o r o f a given topolog~ is modeled i n t e r m s of a place-transition net N. Formall~, N = (S,T,F,K,B,Mo)0 w h o r e S0 T and F ( F ~ ( S x T) U (T x S)) are re~pectivel~ the set of places, transitions and the flow relation between e l e m e n t s o f S and T. The v e c t o r K (K:S .-) Nw) a t t a c h e s a c a p a c i t y t o t h e p l a c c ~ of N. THe v e c t o r B ( B : F -> N*> defines a weight a s s o c i a t e d to the arcs of the net and Mo (Mo:S -> N) is the initial marking o f the net. Timed-P/T n e t s a r e used t o t h e i n t e r n a l mode]. A net N ~ (S,T,F,K,B,Mo,Z), where Z a t t a c h e s an u n a v a i l a b i l i t 5 time to ~ome places uf the net. More i n f o r m a t l o n on t h e s e P e t r i n e t s i s found i n [ R I C 8 5 a ] . In SARA, a k i n d o f P e t r i net is a~sociated w i t h each i n t e r c o n n e c t i o n in the a p p l i c a t i o n scope ( f i g u r e 3>. The
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P. Navaux et al. / S A R A
APPLICATIONSCOPE
[
TOKEN-RING INTERCONNECTiON
?,, . oo.
I
INTERCONNECTiON ?EXT. MOC
I
1
are
obtained
.....
scope i n t e r n a l
b~
studsing the interconnection net structure it is e m b e d d e d in SARA During the user session the initial marking and the utilization Limes (Me,Z) w i l l be p r o v i d e d . A f t e r t h e interna] model i s c o m p l e t e d , i t can be anal~ed the computation the performance parameters.
reluvant a s p e c t s o f t h e behaviour Once the (S,T,F,K,B) is o b t a i n e d , for
?
~INT. MOO.
I
Figure 3 - application neLs
CROSS -BAR INTERCONNECTION
STAR
?,..oo.
I representation
Z(u-SMRY) time u n i t s the shared memor5 is released (occurrence of transition a r l d the processor starts a new c~cle.
trl)
we
of
u_LMRY ) ]]
some i n t e r c o n n e c t i o n c l a s s e s a probubi]it5 reference matrix must be defined Lo a n a l ~ z e d i f f e r e n t behaviors example model memor5 contention). Thls matrix describes the probabilit~ of reference between all processors and from it the pattern probabilities can be e x t r a c t e d . Several behavior patterns can be modelled several nets, so e a c h net is evaluated a n d its r e s u l t s w e i g h t e d .
(fo~
~
W_SMRY) PROC ]'S )/J" Y ]'~rt et
to
SMRY<
I.hrouuh
DEFINITION E N V I R O N M E N T :
)
ts4 }"x
For
4.4.
II
(o)
EXAMPLE
The net o f f i g u r e 4a r e p r e s e n t s t h e schema of the internal model for specific interconnection (crossbar).
a )
of
The initial marking p l a c e s PROC and SMRY models t h e number o f p r o c e s s o r s and shared memories i n the topologs, respecLivel5 Places u-LMRY and u-SMRY model the utilization of t h e resources with using time Z(u-LMRY) and Z ( u - S M R Y ) . The l o c a l memories a r e not r e p r e s e n t e d , the~ are exclusive resources each processor. P l a c e w-SMRY i s interpreted as a waiting p l a c e for p r o c e s s o r s with the request for a especific shared memor~ module denied. The infinite initial marking p l a c e we represents an infinite number of accesses requesting to e n t e r t h e s ~ s t e m .
of
~(u-LMRY)=Xz I ~)
~PROC
SMRY~
!
I~
PROC
SMRY~ /_SMRY)=yz
of
D5 o c u r r e n c e of transition tsl a processor e n t e r s in a l o c a l processing mode After Z(u-LMRY) time units, lhrough the occurrence of tl the processor tries to a c c e s s a specific shared m e m o r 5 module SMRYi, where i:=l,~ ..... Mo(SMRY). B5 o c u r r e n c e o f i s 2 shared is utilized. After
the
memor~
(b)
F i g u r e 4 a) b) c)
(c
Generic d e s c r i p t i o n o f crossbar interconnections Number o f p r o c e s s o r s and s h a r e d memor5 modules L o c a l and g l o b a l p r o c e s s i n g times
F Navaux et al. / SARA
202
4.5.
ANALYSIS ENVIRONMENT: FLOW EOUATIONS
The i n t e r n a l model composed b5 the structure of the net, initial marking, utilizatiun times and probabilit~ reference matrix is read~ for the analssis. The flow equations were developed in [TAZ 85] and the~ are briefIM described. More i n f o r m a t i o n in e n g l i s h can be found i n [TAZ 8 7 ] . The basic period Po(N) of the r e s o u r c e s i n a net i s d e f i n e d as t h e sum of the utilization times between the component a l l o c a t i o n and r e l e a s e . Given Ni components, we have: Po(Ni) For
=
(ui)
S
(eq-i>
the c r o s s b a r case: Po(N-PROC)
= Z(u-LMRY) + Z(u-SMRY)
Po(N-SMRY)
= Z(u-SMRY)
The throughput component is: Do(Ni>
of
an
isolated
Mo(ri) ........ Po(Ni)
The throughput i s g i v e n bs: D(N)
Do(Ni)
= min
of
the
(eq-2)
ssstem as a w h o l e
(Do(Ni)
(eq.-3)
From equation-3 the other performance parameters o f i n t e r e s t are developed: Resource U(Ni): U(Ni)
Induced bsstem:
Ni
under-utilization
= I
D(N) ....... Do(Ni)
wait
Zw(wi)
Mo(ri) = ....... D(N)
Mean v a l u e o f o f the net: M(s) 4.6.
time at
(eq-4)
w-places
Po(Ni>
t h e marking at
= D(N).Z(s)
index
in
the
(eq-5)
a place
s
(eq-6>
ANALYSIS ENVIRONMENT: INTERFACE
If there i s no i n t e r n a l model in Petri nets for the defined interconnection, the analssis operation begins with a translation of the user definition of interconnection to this internal representation. On t h e other h~nd, if t h e r e i ~ a l r e a d 5 an internal model, t h e a n a l s s i s i t s e l f begins.
The n u m e r i c a l o u t p u t o f t h e method suggests a numerical output to the unal~sis, i . e , the i n t e r c o n n e c t i o n i s m o d e l l e d and t h e r e s u l t s a r e g i v e n just l i k e the~ are c a l c u l a t e d . This o p t i o n i s commonl5 used f o r p e r f o r m a n c e e v a l u a t i o n methods in which a single case evaluation took a considerable time. However in our method a single case evaluation is quite quick, i f t h e model has a l r e a d 5 been f o u n d . The a p p l i c a t i o n of the model is fast enough to be a p p l i e d several t i m e s , p r o d u c i n g not one numerical v a l u e but a c u r v e describing an output parameter behavior according to an i n p u t p a r a m e t e r variation. A g r a p h i c c u r v e shows t h e results i n a g e n e r i c was, showing t h e i n f l u e n c e of un input parameter on the output parameters, The modelling assumptions, t h e i m p l e m e n t a t i o n and o t h e r c o n s t r a i n t s are reasons to reduce the model Precision. N u m e r i c a l r e s u l t s cannot be a c c e p t e d as e x a c t p r e d i c t i o n s , but as an aproximation to reality. The was in which an o u t p u t p a r a m e t e r changes for some c o n f i g u r a t i o n s gives much more information than simple numerical results The main goal of the analssis operation dialogue is to define these input and o u t p u t p a r a m e t e r s o r t h e a x i s of the curve. The input and output parameters will be shown on the hori.contal and vertical axis respectivelD.
The chosen i n p u t p a r a m e t e r s can be almost a l l t h e p a r a m e t e r s asked in the definition phase. For some c l a s s e s not a l l can be used s i n c e i n some cases some behavioral a s p e c t s c a n n o t be chosen to be the horizontal axis. The output parameters can be freel~ chosen. For som~ c a s e s , depending on the chosen horizontal axis the curve cannot be drawn continuosls. I f t h e chosen i n p u t parameter cannot be continuosl5 incremented the curve p o i n t s w i l l be f a r from each o t h e r . For e x a m p l e , if the horizontal axis is the number of l, r o c e s s o r s o n l ~ d i s c r e t e v a l u e s can be evaluated. Even if numerical results have minor importance when compared to graphic curves, t h e 9 can s t i l l be shown through a c u r s o r mechanism. The c u r s o r implementation is activated just after the drawing o f the curve. A s i n g l e p o i n t cursor can run o v e r t h e curve showing numericalls, for all input parameter v a l u e s which o u t p u t v a l u e was o b t a i n e d .
P. Navaux et aL / S A R A
47.
ANALYSIS ENVIRONMENT: EXAMPLE
3.
Flow e q u a t i o n s d e v e l o p e d i n s e c t i o n 4.5 are a p p l i e d t o o b t a i n quantitative ~,uralncturs for t h r e e s i m i l a r cases of crossbar interconnections. More i n f o r m a t i o n about c r o s s b a r quantitative a n a l y s i s a p p l i e d i s found i n [TAZ B 7 a ] .
rlumber -
Of
processors
M o ( P R O C )
:
3
-
number o f s h a r e d memor5 modules Mo(SMRY): 3
-
global processing time Z(u-SMRY): I z
-
-
l o c a l p r o c e s s i n g time -- Z(u-LMRY): v a r i a b l e reference case
probability
Ease
matrix:
l:
p(PROCi, p(PROCi,
SMRYj> = 0 . 9 SMRY3) = 0 . 0 5
i i
= j) ~ j)
(i (i
= j) ~ j)
~:
p(PROCi, p(PROCi, case 3: p(PROCi,
SMRYj) SMRYj)
= 0.7 = 0.13
SMRYj)
= 0.33
LTHROUGHPUT
2.C
~.0
'o',z' "o15
~.0
2.0
3.0
._~
LOCAL PROCESSING TIME
Figure 5 -
Throughput a n a l y s i s c r o s s b a r case
A processor i n t e r connect ion p e r f o r m a n c e a n a l y s i s t o o l based on P e t r i nL'tS performance evaluation has been described. The g e n e r i c SARA's working s c h e m a i s s h o w n on f i g u r e 6.
SARA i s a t o o l which can be used For both comercial and academic purposes I t s academic use w i l l help the research of interconnections behavior, aiding the design of machine archileclures. A f u r t h e r use i s t r a i n i n g o f studenks in the a n a l y s i s o f d i f f e r e n t lopulo~ies. For c o m e r c i a l use i t will facilitate evaluation of existing Interconnections in order to study expansion priorities and reviewing of topologies a i m i n g at p e r f o r m a n c e g a i n . It can also be used to evaluate alternatives
The c u r v e s on f i g u r e 5 d e s c r i b e t h e throughput behavior according to the local processing time variation for the three cases above.
o
CONCLUSIONS
SARA's main g o a l was t o d e s i g n a user-friendly tool for performance analysis. Even the choice of which output parameters will be a v a i l a b l e t o o k that into account. The a d o p t e d output parameters were chosen t o f u l f i l l this g o a l and Lo make p o s s i b l e t h e c o m p a r i s o n w i t h r e s u l t s from o t h e r methods.
Con f i g u r a l i o n : -
for
a
203
for
new
systems.
THe p r o p o s e d a n a l y s i s w o r k s i n the PMS l e v e l e v a l u a t i n g t h e i n t e r c o n n e c t i o n performance. Future works i n c l u d e the uxpuntion of analysis to other levels. By m o d e l l i n g a l o w e r l e v e l , t h e i n t e r n a l performance of the processors can be estimated t o feed t h e b e h a v i o r aspects which refer to the local processing usage times. In modelling at higher levels t h e r e a r e two a n a l o g o u s o p t i o n s : m o d e l l i n g e i t h e r t h e o p e r a t i n g system o r ~he nelwurk p r o t o c o l . In both options the global processing expected is u>(tracted from the analysis of these higher levels. At the p r e s e n t s t a g e SARA models and evaluates interconnections of m u l t i p r o c e s s o r and s t a r g r o u p s . The r i n g and regular groups are currentl5 modelled and t h e i r a n a l y s i s are being implemented. The software has been developed t o be used i n any MS-DOS/IBMPC-like environments. The p r o t o t y p e has been d e v e l o p e d i n PASCAL l a n g u a g e and a final implementation is about to be completed in C language. The software has graphic packages to work with monocromatic and color (EGA) video controllers. The o t h e r m a c h i n e - d e p e n d e n t packaqes can be e a s i l y made t o t r a n s p o r t SARA t o o t h e r e n v i r o n m e n t s .
204
Po Navaux et aL / SARA
CROSS-BAR
~
E
X
T
MOO.
.
I
(~INT.MOO.
II
11
I
PERFORMANCE RESULTS I
THROUGHPUT
IIPREOEFINED I
BASED ON USER DEFINITIONS
USER VIEW
~M
PRoc, O
~
I I I
)Wo INOUCEOWAITING
1"
3
)W-MEM
r
ANALITIC MODEL
t~MEM
PRO(; 2
SUBU~LIZATION
t3
PROC 3 []
Figure 6 -
SARA s working schema
REFERENCES [PET 77] PETRI, C. A. General net theory. I n : PROCEEDINGS OF THE JOINT IBM UNIVERSITY OF NEWCASTLE UPON TYNE. SEMINAR, Newcastle upon Tsne, Sep. 710, i976. Proceedings. Universit~ o f Newcastle upon Tsne, 1977. [PET 81] PETERSON, J. L. P e t r i net theor~ and the m o d e l l i n g o f s~stems. Englewood C l i f f s , P r e n t i c e - H a l l , 198i. [REI 85] REISIG, W. introduction. Berlin, 1985.
INOEX
Petri nets: an Springer-Verlag,
[RIC 85] RICHTER, G. Clocks and t h e i r use f o r t i m e m o d e l l i n g . I n : SERNADAS, A. et alli (eds.>: Information ssstems: Theoretical and formal aspects. North-Holland, Amsterdam, 1985. pp. 4V-66 [RIC 85a] RICHTER, G. Utilization of data access and m a n i p u l a t i o n in conceptual schema definition. Information S~stems, Oxford, 6 (I): 53-71, 1 9 8 i . [TAZ 85] TAZZA, M. Ein n e t z t h e o r e t i s c h e s model] z u r q u a n t i t a t i v e n a n a l y s e yon ssstemen (O-model]). R. Oldenbourg V e r l a g , HUnchen, i 9 8 5 . ( B e t . 149)
1
[TAZ 87] TAZZA, M. Quantitative Analssis of a Resource A l l o c a t i o n Problem: A net Theor~ Based P r o p o s a l . In: Voss, K. et a l l i ( e d s . ) , Advances in Petri Nets. Springer-Verlag, B e r l i n , 1987. pp. 511-532. [TAZ 87a] TAZZA, M. et alli. An~lise quantitativa de interconexBes crossbar. In: CONGRESSO DA SOCIEDADE BRASILEIRA DE COMPUTAC~O, 7., Salvador, Jul 11-17, 1987. Anais. S a l v a d o r , SBC, 1987. p. 241-254. [AND 7 5 ] ANDERSON, G. A. & JENSEN, E. D. Computer interconnection structures: taxonoms, characteristics, and examples. Computing Survess, 7 ( 4 ) : 197-213, Dec i775~ [FER 7 8 ] FERRARI, D. Computer s~stems performance evaluation. Englewood Cliffs, P r e n t i c e - H a l l , 1978. [ S I E 8 2 ] SIEWIOREK, D. et a l l i . structures: p r i n c i p l e s and M c G r a w - H i l l , London, 1982.
Computer examples.
[NAV 87] NAVAUX, Ph. et aIli. SARA: Interface com o u s u ~ r i o e escopo de aplicac~o. In: CONGRESSO NACIONAL DE INFORHATICA, 20, S~o Paulo, Ago. 3JSet. 6 1987. A n a i s . S~o Paulo, SUCESU, 1987.