CENTRAL RESEARCH

Ку

Uo ^{Те: Т Я л1 2}

KFKI-71-19

könyvtara * '

VITATÓ

BUDAPEST

A. Jávor A. Csákány

S O M E ACHIEVEMENTS IN THE INVESTIGATION O F DATA TRANSMISSION NETWORKS BY USIN G A FLEXIBLE SIM ULATIO N SYSTEM

CENTRAL RESEARCH

INSTITUTE FOR

PHYSICS

EFK I-71-19

SOME ACHIEVEMENTS IN THE INVESTIGATION OP DATA TRANSMISSION NETWORKS BY USING A FLEXIBLE SIMULATION SYSTEM

A. Já v o r - A. Csákány

C e n t r a l R ese arch I n s t i t u t e f o r P h y s ic s , B u d ap e st, H ungary E l e c t r o n i c s D epartm ent

R e p r in t o f a n " E s t r a t t o d a g l i a t t i u f f i c i a l i d e l XVIII C o n g resso s c i e n t i f i c o i n t e r n a z i o n a l e p e r 1* e l e t t r o n i c a , m arzo 1971, Roma”

1 / INTRODUCTION

I n v ie w o f t h e c o m p le x ity and th e g r e a t v a r i e t y o f d a ta t r a n s m i s s i o n n etw o rk a / e . g . d a t a b a n k s , tim e —s h a r in g s y s te m s , e t c . / a n d th e s t o c h a s t i c n a t u r e of t h e i r in f o r m a t io n f lo w , i t i s d e s i r a ­ b l e t o u se s im u l a t i o n i n o rd e r t o g e t some in f o r m a t io n i n advance on t h e i r p e r f ormance [1 ] , [ 2 ] . I n t h i s p a p e r we would l i k e t o de­

s c r i b e t h e d e s ig n p h ilo s o p h y o f a s i m u l a ti o n sy stem w h ic h i s a p p l i ­ c a b le t o t h e s e n e tw o rk s g e n e r a l l y an d t o p r e s e n t some r e s u l t s o f i t s a p p l i c a t i o n .

2 / THE STRUCTURE OF THE SIMULATION SYSTEM

C o n s id e r in g t h e wide v a r i e t y o f d a t a n e tw o rk s [3] u sed f o r t e l e p r o c e s s i n g w ith r e g a r d t o t h e to p o lo g y , e le m e n ts in v o lv e d and t a s k s to be s o lv e d , i t seems r e a s o n a b le t o c o n s t r u c t a s i m u la tio n sy ste m on t h e b a s i s o f m odular p ro g ram s e g m e n ts . By l i n k i n g th e s e g ­ m e n ts a s i m u l a t i n g p ro g ra m f o r a p a r t i c u l a r c o n f i g u r a t i o n can be a ss e m b le d . O b v io u sly t h e program h a s t o d e s c r i b e th e c o n f i g u r a t i o n u n d e r i n v e s t i g a t i o n , i . e . th e o u t l a y o f th e w hole n e tw o rk , and i t s e le m e n ts , t h e i r t o p o l o g i c a l l o c a t i o n , and t h e p r o c e d u r e s ta k in g p l a c e i n t h e netw o rk w h ic h a f f e c t t h e in f o r m a t io n flo w i t s e l f /com ­ mands r e g a r d i n g p r i o r i t i e s , q u e u e in g e t c . / . The d e s c r i p t i o n h a s t o b e such t h a t i t p r o v i d e s f o r th e c o n n e c tio n a n d i n t e r a c t i o n o f t h e

component p a r t s . [4]

C o n s i d e r a t i o n s b a se d o n th e n e tw o rk to p o lo g y

The g e n e r a l i z e d o u tla y o f t h e n e tw o rk can be s e e n i n F i g . 1 a . From t h i s i t i s c l e a r t h a t :

a / t h e m u l t i p o i n t d a ta l i n k / o n t h e r i g h t lo w e r p a r t o f t h e f i g u r e / can be s u b s t i t u t e d b y a s in g l e compound t e r m i n a l /m a rk e d w ith d o t t e d l i n e / w ith r e s p e c t t o th e n e tw o rk , assu m in g t h a t t h e " i n n e r l i f e " o f t h i s n e t­

w ork s e c t i o n w i l l be a d d i t i o n a l l y d e s c r ib e d b y sim u la ­ t i o n . T h is r e s u l t s i n a r e d u c t i o n o f th e u n ifo r m co n - f i g o r a t i o n t o be h a n d le d .

2

Ъ / th e w hole re d u c e d n e tw o rk can h e b u i l t fr o m b a s ic n e t ­ work m odules shown i n F ig . l b .

с / any n e tw o rk c o n s i t s o f th e f o l l o w i n g f o u r e le m e n ts : - d a t a t r a n s m i s s i o n c h a n n e ls ,

- t o p o l o g i c a l node f a c i l i t i e s , - d a t a t e r m i n a l s ,

- p r o c e d u r e s /c o m m u n ic a tio n s o f t w a r e / .

M odular s e g m e n ta tio n o f th e s i m u l a t i o n sy ste m

I n o r d e r t o g e t a f l e x i b l e s y ste m which e n a b l e s u s t o sim u la ­ t e v a r i o u s c o n f i g u r a t i o n s , i t s e le m e n ts a r e d e s c r i b e d b y s e p a r a t e sub­

r o u t i n e f u n c t i o n s . The in d e p e n d e n t v a r i a b l e s o f t h e s e f u n c t io n s a r e o b ta in e d a s th e c o rre s p o n d in g o u tp u t v a l u e s from t h e s u b r o u tin e s o f th e t o p o l o g i c a l l y n e ig h b o u r in g e le m e n ts , a n d v ic e v e r s a . The communi­

c a t i o n n etw o rk s o f tw a r e s u b r o u tin e i s i n a s p e c ia l p o .s i t i o n , s i n c e i n th e s i m u l a t i o n sy stem i t h a s d i r e c t com m unication w ith e v e r y e le m e n t.

The p seu d o tim e o f t h e p r o c e s s i s an i n p u t v a r i a b l e t o th e e le m e n t s u b r o u t i n e s . The s u b r o u tin e s h a v e to p r o v i d e f o r c h e c k p o in ts a t which th e w hole program c an c o l l e c t t h e in f o r m a t i o n r e q u i r e d f o r e v a l u a t i n g th e r e s u l t s o f t h e s i m u l a t i o n . The d e te r m in a tio n o f t h e i n t e r a c t i n g v a r i a b l e s i n a p a r t i c u l a r c a s e i s v e ry s im p le , i n a c c o rd a n c e w i t h s ta te m e n t b / .

U sin g a n a d d i t i o n a l p ro g ram seg m en t w hich i s b ased on t h e e v a l u a t i o n s , i t i s e a s y t o a l t e r p a r t i c u l a r e le m e n ts o r t h e i r g iv e n p a r a m e t e r s , and b y r e p e t i t i o n o f t h i s p r o c e s s we may s y n th e s iz e t h e optimum s o l u t i o n w ith r e s p e c t t o p r e s c r i b e d a s p e c t s .

The o v e r a l l o u tla y o f t h e s i m u l a t i n g p ro g ram can be s e e n i n F i g . 2 , w h ile t h e flo w d ia g ra m f o r t h e o u tp u t f u n c t i o n - g e n e r a t i n g p a r t a t t h e r e c e i v i n g end o f a sy n c h ro n o u s d e c is io n f e e d b a c k - ty p e d a t a t r a n s m i s s i o n c h an n e l i s shown i n T i g . 3 . The b l o c k e r r o r d i s t r i ­ b u t i o n i n th e c h a n n e l i s assú m ed t o f o l l o w th e P o i s s o n d i s t r i b u t i o n la w .

3 / INVESTIGATIONS ON THE BUFFER MEMORY OF A CONCENTRATOR TYPE NOBE S tu d y o f th e i n f o r m a t io n flo w i n th e n o d e s o f th e n e tw o rk i s o f p a r t i c u l a r im p o rta n c e . We have i n v e s t i g a t e d t h e d i s t r i b u t i o n o f t h e b u f f e r memory c o n te n ts o f a c o n c e n t r a t o r - t y p e node u s i n g th e b a s i c n e tw o rk m odule o f th e s i m u la tio n sy ste m .

3

The num ber o f In p u t p h a n n e le v a r i e d from 1 t o 8 u s in g e q u a l nom inal t r a n s f e r r a t e s . The c h a n n e ls were assum ed t o b e o p e r a t i n g a c c o rd in g t o th e " d e c i s i o n f e e d b a c k " p r i n c i p l e , a s shown i n F i g . 3 | i . e . t h e y w ere d e s c r i b e d by f i r s t o r d e r M arkov p r o c e s s e s . The e r r o r p r o b a b i l i t i e s i n t h e in p u t c h a n n e ls a s w e l l a s i n t h e o u tp u t c h a n n e l were e q u a l . The s i m u l a t i o n was u n d e rta k e n a t t h r e e v a l u e s o f t h e b lo c k e r r o r p r o b a b i l i t y : 10” ^ , 3 .1 0 “ ^ a n d 1 0 “ ^ .

I n o r d e r t o e n su re e r g o d i c i t y o f t h e p r o c e s s , th e e f f e c t i v e in p u t r a t e t o th e node has t o b e l e s s t h a n th e o u t p u t . A c c o rd in g ly we chose a nom in al t r a n s f e r r a t e i n th e o u t p u t o h a n n e l n+1 tim e s l a r g e r t h a n t h a t i n th e i n p u t , w here n r e p r e s e n t s t h e number o f i n p u t c h a n n e ls . T h is c h o ic e makes i t p o s s i b l e t o g e t some i n f o r m a t i o n on th e d i s t r i b u t i o n o f t h e memory C o n te n ts a s a f u n c t i o n o f th e i n p u t t o o u tp u t t r a n s f e r r a t e r a t i o . F i g . 4- shows th e p r o b a b i l i t y o f memory o v e rflo w /Р щ / a s a f u n c t i o n o f t h e o u tp u t t o in p u t t r a n s f e r r a t e / X / , where M=n h a s b een cho o sen a s t h e u n i t o f b u f f e r c a p a c i t y . As i t i s g e n e r a l l y n e c e s s a r y t o a v o id l o s s o f i n f o r m a t i o n i n t h e case o f o v e r ­ flo w , some o r a l l d f th e in p u t c h a n n e ls h a v e t o be s i l e n c e d f o r some tim e . ThiB means t h a t th e e f f i c i e n c y o f t h e sy stem i s re d u o e d , a n d so a c o r r e l a t i o n o f t h e b u f f e r memory s i z e a n d o v e r a l l System s e f f i ­ c ie n c y c a n be d e r i v e d from th e r e s u l t s o f t h e s i m u l a t i o n . A n o th e r

i n t e r e s t i n g r e s u l t i s shown on F i g . 5 , w h ic h p r e s e n t s th e d i s t r i b u t i o n s o f b u f f e r c o n te n t s f o r sy stem s w i t h one a n d e i g h t i n p u t c h a n n e ls . The q u a s i p e r i o d i c a l f e a t u r e o f t h e c u rv e o b t a i n e d f o r e i g h t in p u t c h a n n e ls i s due t o th e r e l a t i o n o f th e i n p u t and o u t p u t i n f o r m a t i o n q u a n t i t i e s .

The m a th e m a tic a l d e s c r i p t i o n o f t h e p r o c e s s a l t e r i n g t h e b u f f e r c o n t e n t s i s g iv e n i n t h e a p p e n d ix . [5]

- 4 ^-

APPENDIX

MATHEMATICAL DESCRIPTION OP THE PROCESS IN THE BUFFER MEMORY The s t a t e d ia g ra m o f t h e sy stem i s shown i n F ig * IA, w here s t a t e s a d e s ig n a te t h e memory c o n t e n t i n d i c a t e d i n t h e i r in d e x e s a n d t h e p v a l u e s d e s ig n a te t h e c o rr e s p o n d in g t r a n s i t i o n p r o b a b i l i t i e s . D e s ig n a tin g t h e p r o b a b i l i t i e s o f t h e s t a t e s b y P , i t h o l d s t h a t

Pi

n+1 k ik p -k

о

pi+ k

f o r i = О

w here <

-n i n case i > n and

к = О i f О < i < n

О

po = n+1

l p

Pk

k = l P- k K n

I Pk

k=o

w i l l h o ld

n+1

w here J p t * 1 k = -n

A s i m p l i f i e d model i s shown i n P i g . 2A. Р о г t h i s c a se i t can be shown t h a t

p± - ( l - rJr1

. P+1

w here R = ---— an d R < 1 P-1

P o r a P o is s o n b lo c k e r r o r d i s t r i b u t i o n an d a f i r s t o r d e r Markov p r o c e s s d e s c r i b i n g t h e d e c i s i o n f e e d b a c k system

P+1 = Pxi1 - PJ)

P-1 = py ( L - px )

and

-

5

•where p x and py r e p r e s e n t th e b lo c k in p u t a n d o u tp u t p r o b a b i l i t i e s , r e s p e c tiv e ly * . U sin g t h i s model a n d c o r r e c t i n g i n p u t t o o u tp u t r a t e b y th e f a c t o r n/n+1 , t h e a p p ro x im a tio n te n d s t o im prove w i t h d e c r e a s i n g i and n , s in c e th e num ber o f n e g l e c t e d s t a t e s d e c r e a s e s w i t h them* The c a l c u l a t e d r e s u l t s i n th e i= 0 p o i n t s and f o r t h e d i s t r i b u t i o n f o r n = l were i n good ag re em e n t w ith t h e r e s u l t s o f t h e s i m u l a t i o n .

i

)

REFERENCES:

[1] J . P . D a r to is

On a t r a f f i c s im u la tio n p ro b le m o f t h e s w itc h in g n etw o rk f o r a common c o n t r o l e x h a n g e .

Comm, e t E l e c tr o n iq u e N o .3 0 , p p . 36-45» J u l y , 1 9 7 0 . [2] L .E .N . D e lb ro u c k

A s i m u la tio n p ro g ram f o r a common c o n t r o l group “i n a * te le p h o n e ech an g e*

Gen. M eeting o f th e Eng. I n s t , o f C an ad a, 1 0 -1 2 . S ep . 1969» V an co u v er.

[3] D.H. Hamsher

Com m unication sy ste m m o d e lin g . C om m unication System E ng. Handbook, M cG raw -H ill, 1 9 6 7 .

[4] T .H . Lee - G .E . Adams - W.H. G aines

T e c h n iq u es f o r d e v e lo p in g p h y s i c a l p r o c e s s m o d e ls . Com puter p r o c e s s c o n t r o l , Jo h n W iley , 1968.

t5] E .F . Beckenbach

Modern m a th e m a tic s f o r t h e e n g in e e r . M cG raw -H ill, 1 9 6 1 .

(

>

J

P i g . 2

DATA PROCESSING CENTRE TOPOLOGICAL NODES /CONCEN­

TRATORS AND /OR DIFFUSORS/

DATA TERMINALS

DATA TRANSMISSION CHANNELS

H: error status function of the channel

p : block error rate

*

Fig. 3

P+n P-/n+l/.

F i g . 4

P r o b a b i l i t y

Memory contents

F i g 5

. g f O

K ia d ja a K ö z p o n ti F i z i k a i K u ta tó I n t é z e t F e l e l ő s k ia d ó : P á l L énárd ig a z g a tó

Fel e l ős s z e r k e s z tő : S ándory M ihály

a KFKI E le k tr o n ik u s Tudományos T anácsának eln ö k e Szakm ai l e k t o r : Vajda F e re n c

N y e lv i l e k t o r : Timothy W ilk in so n

Példónyszám : 160 T örzsszám : 71-5574

K é s z ü lt a KFKI s o k s z o r o s ító üzem éhen, B udapest