traffic routing in a hybrid analog-digital network

pp. 521-537 521

Traffic routing in a hybrid analog-digital Bernard J A R R Y - L A C O M B E **

Annick V I D A L - M A D J A R **

Guy M A T I G N O N **

network *

Abstract

This paper presents the results of a study carried out at CNET on the gradual digitalization of a large telecommunication network. SATIN computes the traffic routing and the trunk groups in the hierarchical switched networks and minimizes its global cost. An experi- mental network comprising approximately 770 centres, where the percentage of digital switching centres is increased from 0 % up to 100 % is used. The paper points out the most important effects of digitalization and analyzes the grounds for these effects.

Key words : Telecommunication network, Routing, Dimen- sioning, Digitalization, Teletraffic, Optimization, Switched network.

L ' A C H E M I N E M E N T DU TRAFIC D A N S U N R ~ S E A U M I X T E

A N A L O G I Q U E - NUMI~RIQUE

Analyse

Cet article prdsente les rdsultats d'une dtude faite au CNET sur la num~risation progressive d'un grand rdseau de tdldcommunications. Le programme infor- matique SATIN permet de calculer l'acheminement du trafic et les faisceaux dans les rdseaux commutes hidrarchis~s en minimisant son coat global. L'exemple ~tudid est un rdseau de 770 centres environ dont on fait dvoluer le pourcentage de commutateurs temporels de 0 % ?t 100 %. Les auteurs ont cherch~ ?t mettre en ~vidence les effets les plus importants de la numdrisation et ?t en analyser les causes.

Mots d~s : Rb.seau t61b, communication, Acheminement, Dimensionnement, Num~risation, Trlrtrafic, Optimisation, R~seau commutr.

Contents

1. Introduction - purpose of the study.

2. Network and traffic data. 3. Network dimensioning method.

4. Study plan. 5. Global results : the consequences of progressive

digitalization of the switching centres.

6. Specific influence of maximum efficiency and of modularity.

7. Influence of the size increase of the subscribers switching centres.

8. Sensitivity to cost variations.

9. Conclusion.

References (7 ref.).

1. I N T R O D U C T I O N . P U R P O S E OF T H E S T U D Y

Most telephone networks are now undergoing a change both in transmission and switching techno- logies. The rate of this evolution increasing and for example, within the next ten years, the French network will be a lmost wholly built up of t ime division switching centres and digital transmission systems.

The purpose of this study is to get meaningful and quantified results concerning the evolution of the structure of the French t runk network in pace with the gradual introduct ion of digital techniques. In particular, while engineering rules and ne twork sensitivity to var ia t ions of different parameters are well known in an analog network, it remains to ascertain how they will change first with a mixed network and then with an entirely digital network.

* Cet article est une version rrvisre de la communication prgsentre au Colloque << Planification des rrseaux de trlrcommunications >>, Paris, septembre 1980. lane version frangaise est disponible aupr~s des auteurs.

** CNET, Paris-A, ATR, 92131, Issy-les-Moulineaux.

1/17 ANN. TI~L~COMMUN., 36, n ~ 9-I0, 1981

522 B. JARRY-LACOMBE. - TRAFFIC ROUTING IN A HYBRID NETWORK

The computer p rog ram SATIN has already been used to study the French network structure and is also used in a specialized version, for annual network planning. I t has been used here to determine pictures of the network as t ime division switching centres are progressively introduced in order to answer the following questions :

a) What is the influence of digitalization on the switching network structure, especially as far as the evolution of transit capaci ty and new engineering rules for t runk groups are concerned ?

b) What are the consequences on the available switching infrastructure opt ions (type of equipment, op t imum site, etc.) concerning transit centres in particular ?

c) What are the consequences on the available transmission infrastructure options and, in particular, which policy should be adopted for the introduction and extension of digital t ransmission links ? These choices have impor tan t consequences on traffic routing and t runk groups.

d) During the transition phase, how many analog- digital conversion equipments will be necessary ?

e) What will be the consequences on the quality of service, and in part icular on the evolution of the point- to-point loss rate, and the network resistance to traffic overloads and equipment failures ?

After the description of the network and traffic data (item 2), and of the comput ing method (item 3), item 4 will present the study plan.

2. N E T W O R K A N D TRAFFIC DATA

2 .1 . H i e r a r c h i c a l s t ructure o f the F r e n c h n e t w o r k .

The French network has a four level hierarchical structure including two transit levels and two subscriber levels according to Figure 1.

A principal transit zone (PTZ) includes all subscriber centres associated with a given principal transit centre (PTC). Similarly, a secondary transit zone (STZ) includes all subscriber centres associated with a given secondary transit centre (STC).

The hierarchical rules are as follows :

- - each switching centre is connected via at least one trunk group to its higher ranking centre ;

in each pair o f PTC, there is at least one connecting circuit group ;

- - i n certain cases, two different hierarchical transit centres may be used for outgoing and incoming traffic ;

- - in addition to the general inter-STZ hierarchy,

Forecasts for 19g0 o 9 .PTC

60. SIC ~

o

1200 �9 SSC

level 1

level 2

se ~ t ( ~ level 3

Direct high usage trunk, group, t

t level 4

FIG. 1. - - Hierarchical structure of the French network. PTC )Principal Transit Center. STC ~ Secondary Transit Center. ssc Subscriber Switching centre.

LeVelLeve121 f transit network Level 3 : ssc with traffic routing autonomy Level 4 : ssc without traffic routing autonomy

Organisation hidrarchique du rdseau franeais.

an independent hierarchy can exist within the STZS for the intra-STZ transit traffic.

2.2 . Traf f ic rout ing rules .

Traffic routing in the ne twork under study is determined according to the following rules :

- - traffic between the subscriber switching centre (ssc)-I and (ssc)-J will be routed via trunk groups having both ends on the normal hierarchical route between I and J ,

- - at each switching centre, traffic is routed prefe- rentially over the t runk group which terminates closest to the destination centre. This requires that the trunk groups be considered in a certain order according to the routing rules (Fig. 2 ) ;

K1 3 K4

I J

FIG. 2. - - Traffic routing trunk group creation sequence.

ROgle d'acheminement du trafic-ordre d'ouverture.

- - overflow of direct and transverse t runk groups is allowed. The number of overflows should not exceed one and they should take place only on to hierarchical t runk groups as shown in Figure 3 ;

- - lastly, traffic between neighbouring sscs is not allowed to transit th rough the PTCS So that long distance traffic and local traffic are decoupled. There- fore, the normal hierarchical pa th linking 2 sscs is represented in Figure 4.

ANN. T~L~COMMUN., 36, n ~ 9-10, 1981 2/17

B. JARRY-LACOMBE. - TRAFFIC ROUTING IN A HYBRID NETWORK 523

I j

F[o. 3. - - Author ized overflows (example).

D6bordements autoris~s (exemple).

- v

Neicj h bourincj Distant SSC s S $ C s

Fro. 4. - - Difference between neighbour ing and distant sscs.

Distinction entre CAA voisins et CAA distants.

Two sscs are considered as neighbours if they belong to the same eTZ or if they belong to two adjacent STZS from two different PTZS.

Digital t runk groups ending in at least one analog switching node are subjected to the same rules as analog t runk groups.

2.4. The network under study.

The network under study covers half the projected 1990 French t runk network. The other half is represented by its transit centres which concentrate the entire traffic of their zone.

The choice of this network results f rom a trade off between a network size which guarantees reliable results and the capabilities of the SATIN program. The French network has a total of 9 PTZS, the sub- network under study includes :

- - 4 PTZS comprising 4 PTCS, 30 STCS and 699 sscs ;

- - the Pards area comprising 1 PTC, 7 STCS (nodal centres by which all t runk traffic f rom the 340 switching centres in Paris has to pass through ;

- - the remainder of the network is composed of 4 PTZS and is represented by its transit centres : 4 PTCS and 24 STCS. The sscs have an average size of about 20 000 subscribers.

2.5. The traffic matrix.

2.3. Engineering rules for trunk groups.

The rules presently used for sizing the analog trunk groups are as follows :

a) trunk groups are used for only one direction and they are dimensioned with a one-circuit modularity ;

b) last choice t runk groups (whether they be transverse or hierarchical) should have a maximum loss of 1 ~o (grade of service constraint) and a maximum efficiency o f 0.7 ;

c) overflowing t runk groups have a maximum efficiency of 0.8 ;

d) minimum size is 8 circuits for overflowing trunk groups and 12 circuits for non-overflowing trunk groups.

As regards digital t runk groups connecting digital switching centres, the rules a), c) and d) used for the study become :

a') use of a 30 circuit modulari ty except for direct high usage t runk groups which are dimensioned with a 15 circuit modulari ty to obtain a quasi-bidirectional capability (without mixing traffic flows) resulting in a good eCM system rate ;

c ') no efficiency limitation for overflowing trunk groups ;

d ') the minimum size is then 30 circuits.

This is a point-to-point matrix, obtained by pro- jecting a national matrix to the year 1990. Traffic directed to and coming f rom the exterior o f the considered sub-network has been concentrated on the external STCS. This concentrat ion has been carried out so that the impact of this traffic port ion on the transit network is only slightly modified.

The total traffic of the matrix is 262 000 E (Erlang), of which 217 000 E are the outgoing traffic f rom the sscs. Table I and Figure 5 show the structure of this

%A' ee" 199,s% (1) l ooJ 1 9 7 % I 7 n . , ,

6Oiao (z) 0 3E 6E 12E Elementary

point - to - point traffic size

FIG. 5. - - Dis t r ibut ions o f s sc ou tgoing traffic (1) % n u m b e r o f point - to-point traffics. (2) % volume.

Courbe de rdpartition du trafic et du f lux au ddpart des c ~ .

traffic according to the magnitudes of elementary traffic flows.

The values 3, 6 and 12 E used in Table I correspond to the average values of the computed economical threshold for installing various t runk groups.

3/17 ANN. T~L~COt,~CrN., 36, n ~ 9-10, 1981

524 B. J A R R Y - L A C O M B E . - T R A F F I C R O U T I N G I N A H Y B R I D N E T W O R K

TABLE I. - - Detail of the ssc outgoing traffic.

Rdpartition du trafic ddpart des CAA.

Intra-sTz traffic

Intra-PTZ traffic

Inter-PTZ traffic

Traffic to Paris

Total

< 3 E

5% 16%

1770

0%

387o

3 E - 6 E

_ t 6 Z l 4%1

1 2 %

1%

13%

6 E - 1 2 E

8%

3%

1%

2%

14%

> 12E

24 %

3%

1%

7%

35%

Total

43 %

26 %

21%

10%

10o%

�9 3 E is the average value of the threshold for installing analog t runk groups with a min imum size of 8 circuits ;

�9 6 E is the average value of the threshold for installing direct high utilization TDT (time division switching- digital t ransmiss ion- t ime division switching) t runk groups with a min imum size of 15 circui ts ,

�9 12 E is the average value of the threshold for installing transverse TDT trunk groups with a mini- m u m size of 30 circuits.

F r o m these distributions, it is possible to deduce the p ropor t ion of traffic which will be influenced by digitalization i.e., the traffic which would have transited through direct high utilization t runk groups in an analog network but which will transit in a digital ne twork due to the higher t runk group instal- lation threshold. This propor t ion is 12 % of the total traffic (outlined in Table I). We will find this value again when analyzing the detailed results of the study.

3. N E T W O R K D I M E N S I O N I N G M E T H O D

3.1. Criterion to be minimized and resolution principle.

We have used the computer p rog ram SATIN deve- loped by CNET. This p rogram uses a heuristic method to determine the traffic routing and t runk group dimensions to give min imum global network cost and to fulfil the imposed grade of service requirements. The minimized cost is a static investment cost for switching and transmission equipment which can be written :

C = ~ Ct x N, -q- ~ Ck X N~, + L k

Trunk group cos t

Y , r ~ • 2 1 5 TC SSC

Transit s w i t ch i ng C o n s t a n t subscriber cos t s w i t ch i ng cos t

C, = cost o f circuit in t runk group i,

N, : size of t runk group i,

17c = switching cost of one erlang in centre c (transit centres TC or ssc),

Tc = transit traffic in c,

L = the set o f all overflowing trunk groups,

K = the set of all

According to the variables are the Nt tions enables us to course) for the cost

last choice trunk groups.

routing rules, the independent and the following set of equa- obtain an opt imum (local of

function :

~ / L - - O } O, V l ~ L .

I f we write Hi = - = fA(Nz) marginal A

efficiency of t runk group l, where a is the rejected traffic per t runk group and A is the traffic offered to this t runk group, the optimizing equations can be written as (see [1] and [2]) :

{ C t - - H ~ • Cta = 0, V l ~ L } ,

where Ct is the cost of a circuit in trunk group l and C~ is the marginal cost of one erlang overflowing f rom trunk group l in the network.

C t depends on the characteristics of the t runk groups and the transit centres belonging to the normal paths connecting the t runk group l origin to the traffic destinations and on additional traffic to be routed via these elements (Refer to [1] and [2] for the comput ing method of C~).

3.2. Dimensioning trunk groups.

Calculation of C~d and knowledge of the cost C~ allow us to determine the economical value H ~ of H t , and thus the size of the t runk group by solving this equation fAt(N) = H ~ where At is the value of the Poisson offered traffic computed if necessary by the Wilkinson equivalent t runk group method. As an example, if we represent the function fAt(N) on a diagram as in Figure 6, we immediately see how to solve the equations graphically.

ANN. TI~LIECOMMUN., 36, n ~ 9-10, 1981 4/17


1

H Lo . : : : . . ~ I . : ~ ~ ~ N

F~G. 6. - - Trunk groups dimensioning using the curves. Hz = fA~(N).

Courbes H l = fA~(N).

The t r u n k g r o u p is the re fore d i m e n s i o n e d in the fo l lowing w a y :

- - i f H ~ = C d C ~ > 1, t h e t r u n k g r o u p will not be ins ta l led s ince i t is n o t cos t e f f ec t ive ;

- - i f H ~ < 1, the t r u n k g r o u p size N O is de t e rmined by the in te r sec t ion o f the l ine Ht = H ~ a n d the curve I l l = f a t ( N ) ,

�9 i f N ~ < m i n i m u m size, we mus t choose between n o t the t r u n k g roup a n d giving it the m i n i m u m size,

�9 i f N ~ is such t ha t E (N, A) < 1 ~o ( E is the loss ra te given b y the Er lang fo rmula) , the t r u n k g r o u p will be non overf lowing,

�9 o therwise , i t wil l r e m a i n a h igh u t i l iza t ion ove r f lowing t r u n k group .

W e also have to check tha t the t r u n k g r o u p satisfies the m a x i m u m efficiency cons t ra in ts . F o r m o r e detai ls on this heur i s t i c m e t h o d , p lease refer to the b ibl io- g r aphy (see [1] a n d [2]).

sion, t ime d i v i s i o n - t ime divis ion) , there will be two different c i rcu i t cos t s d e p e n d i n g on the type o f t r ans - miss ion : a n a l o g o r digi ta l . The cheapes t s o l u t i o n is chosen. T h e SATIN p r o g r a m can be used w i th c i rcui t l eng th d e t e r m i n e d b y s t ra igh t l ine d i s t ance o r by the sho r t e s t p a t h in the t r ansmis s ion n e t w o r k . In this s tudy , we have used the first o p t i o n .

W e use 5 cos t f o r m u l a s ca l led SAS/SDS, SAT/SDT and TDT which a r e s u m m a r i z e d in T a b l e I I a n d F igure 7.

SAS

SAT

TAT

A S Sc -- ( 2 ) ~ ( 2 ) --oS

O : : ,T S - ~-~-~ (2) (2)

SDS

SDT

(2)(2)0) (I) (I) (2)(2) 13)

FIG. 7. - - Cost formulas.

S : space division switching technique T : time division switching technique A : analog transmission technique D : digital transmission technique o : input/output point. [] 12 analog channel terminals. 17] : analog/digital conversion (30 channel terminals) (1) 90 ~ of equipment in use (2) 80 % of equipment in use (3) 100 ~ of equipment in use

Formules de co~t utilisdes.

3.3.2. Trunk group modularity.

The c a l c u l a t i o n o f the cos t C u enables us to select the t r a n s m i s s i o n t e c h n i q u e a n d we can n o w d e t e r m i n e the va lue o f the t r u n k g r o u p d ime ns ion ing m o d u l a r i t y , as shown in the t ab l e I I .

3 . 3 . T a k i n g d i g i t a l i z a t i o n i n t o a c c o u n t in t h e c a l c u -

l a t i o n m e t h o d .

The di f ference be tween an ana log a n d a digi ta l t echn ique has an inf luence on the fo l lowing po in t s :

- - ca l cu l a t i on o f the C u circui t costs,

- - m o d u l a r i t y o f t r u n k g roups M u ,

- - m a x i m u m efficiency o f t r u n k g roups e u .

These th ree e lements d e p e n d on the type o f switching centres l o c a t e d a t b o t h ends o f the c i rcui t a n d on the length L u o f c i rcu i t ij which de te rmines the type o f the t r ansmiss ion , T u .

3.3.1. Calculation of the cost C i j .

Circui t cos t s have the fo l lowing fo rm :

C u = t r a n s m i s s i o n cos t + i n p u t / o u t p u t cos t at bo th ends.

F o r each p a i r o f swi tch ing nodes , cha rac te r i zed by the i r swi t ch ing t echn ique at b o t h ends (space d i v i s i o n - s p a c e d iv is ion , space d i v i s i o n - t ime divi-

TABLE II

Analog transmission Digital transmission

s-s M = 1 or 12 circuits 31 = 1 or 30 circuits S-T M = 1 or 12 circuits M = 1 or 30 circuits

M = 30 circuits and 15 circuits T-T M = I or 12 circuits for direct high utilization trunk

groups (15 in each direction)

In this s tudy , we have selected the usua l va lues o f one c i rcu i t in eve ry case except in the TDT case where the m o d u l a r i t y is 30 ( and 15 in each d i r e c t i o n for d i rec t h igh u t i l i z a t i o n t r u n k groups) .

N u m b e r o f m o d u l e s p e r t r u n k g r o u p .

W e a re f aced wi th a t heo re t i ca l p r o b l e m for de te r - min ing the leas t cos t o p t i m u m ne twork .

A s imple a n d eas i ly i m p l e m e n t e d s o l u t i o n cons i s t s in se t t ing a t h r e s h o l d 8 a n d c h o o s i n g b e t w e e n t w o consecu t ive n u m b e r s o f m o d u l e s ( M a n d M + 1) a c c o r d i n g to the r e l a t ive va lues o f the of fe red t raff ic A a n d the m a x i m u m l imi t efficiency ~ m a x (F ig . 8).

5/17 ANN. TI~LI~COMMUN,, 36, n ~ 9-10, 1981


A / I/max ~_~ number of circuits

FIG. 8. - - Dimensioning a modular trunk group using a fixed threshold.

a) M is selected such that M ~< A/~qrnax < M q- 1. b) The trunk group size is :

I M i fA[~ <~ M q- 8 M q- 1 otherwise

Calcul d'un faisceau modulaire : utilisation d'un seuil d'ouverture fixd.

HO C~

C o ~ G i v e n traffic A 1; ~) ~ 25 60 ~'Number of circuits

O N~

FIG. 9. - - Dimensioning a modular trunk group using a variable threshold.

The trunk group size is :

t M if ~1 ~< ~2 M-t- 1 if 81 > 82

Calcul d'un faisceau modulaire : utilisation d" un seuil variable.

A better solution consists in using a variable threshold ~ depending on the traffic A and also on the cost ratios (Fig. 9).

This heuristic process can be easily adapted to the method already used in SATIN and results in a lower cost than when using the first so lu t ion ; however, convergence is not certain. Slight oscillations have been noted on the results af ter several iterations on small scale test networks.

However , this feature has not been observed between successive i terations in the present study.

3.3.3. Maximum efficiency of the trunk groups.

As already ment ioned for engineering rules, the imposed m a x i m u m efficiency of an overflowing t runk group depends on the types of the switching centres at both ends :

T runk g roup s-s : 0.8.

Trunk group s-r : 0.8.

T runk group T-T : 1.0.

For hierarchical t runk groups, the purpose of the l imitation on efficiency is to ensure an excess of circuits capable of absorb ing addi t ional traffic without a deterioration in the overall grade of service. This

limitation is independent o f the types of switching centres. Its value is 0.7.

4. STUDY PLAN

4.1. Main parameters studied.

This study basically measures the effects of four parameters which are the principal new elements brought by digitalization :

a) drop of transit switching costs in time division switching centres and of digital transmission costs ;

b) modular i ty of links between time division switching centres built up with 30 channel groups (PCM systems). As long as cost-efficient channel mixers are unavailable, t ransmission and switching will still be directly integrated using 30 channel modular i ty t runk groups ;

c) the efficiency (or mean occupancy) of the incoming circuits of t ime division switching centres is not limited as in the case of analog switching centres. The present limit o f 0.8 used in France for overflowing t runk groups will therefore be cancelled. On the other hand, the l imitat ion of efficiency for last choice t runk groups will be maintained to pre- serve the quality of service in case of traffic overload ;

d) the introduction of t ime division subscribers switching centres ssc raises their average size justifying the creation of more direct high utilization groups and tending to lower the transit rate. The same trend results f rom the increasing average subscriber traffic.

The first three parameters tend to increase transit traffic while the last one has an opposite effect. I t is therefore desirable to isolate the various effects for their investigation.

4.2. Study plan.

We have used the following study plan :

- - a global approach to the effects which tend to increase the transit capacity. To do this, the number and the capacity of subscribers switching centres have been fixed and their type has been gradually changed to study the transit ion f rom an all-analog network to an all-digital ne twork ;

- - a detailed approach of the effects due to the modular i ty of digital t runk groups and the suppression of max imum efficiency constraints as regards digital t runk groups overflowing ;

- - consequences of ssc capaci ty evolution ;

- - sens i t iv i ty of results to switching and transmission costs.

ANN. T~L~COMMUN., 36, n ~ 9-10, 1981 6/17

B. JARRY-LACOMBE. -- TRAFFIC ROUTING IN A HYBRID NETWORK 527

5. G L O B A L RESULTS : T H E C O N S E Q U E N C E S

OF P R O G R E S S I V E D I G I T A L I Z A T I O N OF T H E S W I T C H I N G CENTRES

In this section, we study the global influence of those parameters which are modified during the digitalization process. The number of switching centres remains constant, the rate of digitalization goes f rom an all-analog network (-r = 0 %) to an all- digital network ( , = 100 7o).

The results of the study cover :

- - the network cost,

- - t h e transit capacity,

- - the number of transmission equipments,

- - the t runk groups and the mesh rate,

- - traffic routing,

- - lost traffic and resistance to overload.

5 .1 . C o s t s .

We consider the criterion of network cost as a first evaluation of its structure.

The results obtained here depend on the per-unit costs of individual components . The relative compo- nent costs may vary with time. We study the sensitivity of the results to cost variat ions in i tem 8.

The cost data used in this study, given under the fo rm of the ratios analog cost/digital cost are :

- - for switching costs : abou t 3 ,

- - for transmission costs : about 5.8 for fixed costs abou t 0.25 for per km costs.

Figure 10 shows the evolution of the total cost

COST

7O

50

38

'100= Total cost of analog network

" ~ 5 0 transit COSt

' t 3 4

transmission cost .'ILL" .-_

' " 5 0 " " ' 1 0 0 ~ o

FIG. 10. - - Cost evolution with digitalization rate.

Evolution des coats en fonction du taux de numdrisation.

of the network and of its main factors :

- - t r a n s m i s s i o n cost (including multiplexing and analog-digital conversion) ;

- - transit switching cost ;

- - ssc switching cost.

The network cost is very sensitive to the presence of digital switching centres, and decreases mono to - nously with increasing digitalization rate. The decrease is only due to transit cost.

Transmission cost does not vary much. The fall in total cost ( - - 40 7o) mainly comes f rom the decrease in transit switching costs (in spite o f an increase in the transit rate) as well as in the costs o f ssc incoming and outgoing circuit terminal equipment.

5 .2 . T r a n s i t c a p a c i t y .

Since the only criterion which lowers the transit rate - - the mean size of the sscs - - was not modified, the transit volume will increase with the digitalization rate.

A significant transit capaci ty rate independent f rom the value o f studied traffic can be used. We call it global transit rate (GT). I t is defined in Figure 11.

Figure 12 shows the dependence on v of bo th the transit capacity (TC), split into its two components (total capacity of the PTCS + total capacity of the STCS), and the global transit rate (GT).

Table I I I , which recapitulates the results for the two extreme cases, shows the high transit capacity

[ TC i

SSC ~ NTT

FIG. 11. - - Definition of the global transit rate OT. TC : transit capacity. TT : transiting traffic.

NTr : nontransiting traffic. T : total ssc outgoing traffic. T C T C

G T - - - - T T -{- N T T T

D~finition du taux de transit global.

20o

15000(3

100000.

50000.

@

transit capacity i in erlangs

/ s. ~" s

4 , ~ l ~ " j "

6 2 %

98 %

5 ! r

5o too %

FIG. 12. - - Transit capacity and global transit rate GT as a function of -r.

Capacitd de transit et taux de transit global en fonction de T.

7/17 ANN. T~L~COMMUN., 36, n ~ 9-10, 1981


TABLE III. - - Comparison of transit capacity for "r = 0 and -r = 100 ~.

Comparaison des capacitds de transit pour "r = 0 et 100 ~

-r 0~o 100~o A in E A in Yo

GT

STC capacity PTC capacity Total capacity Ratio PTC capacity

STC capacity

62 % 105 680 E 14 020 E

119 700 E

13%

98 % 165 230 E 51 890 E

217 120 E

31%

+ 59 550 E + 37 870 E + 97 420 E

+ 56% + 27O% q- 81%

variation ( + 81 ~o) when the network changes from an all-analog network to an all-digital network. The PTC/STC ratio also shows that the relative importance of the higher transit level increases with the digitalization rate -r.

5.3. The required transmission equipments.

The transmission equipment considered here consists of :

- - 1 2 channel terminal equipment building up elementary analog transmission g r o u p s ;

- - analog to digital conversion units building up 30 channel t'CM systems from the voice frequency circuits. The other PCM systems are directly built up in the digital switching centres ;

- - transmission systems, represented by their pro- duct km • circuits - - analog or digital - - (A or D) (multiplexing and demultiplexing equipments are represented by an average fixed cost included in the transmission cost).

As we did not introduce the structure of the transmission network in the traffic routing calculation, the results provided by SATIN should be interpreted as being applicable to an idea l transmission network.

�9 Figure 13 shows that the number of 12 channel terminals, which varies with the number of HF circuits,

Number of terminal equipments . , ~ ~ n n e l terminal.s

5o lOO %

FIG. 13. - - Evolution of the number of terminal equipment.

Evolution du nombre d'd.quipements d'extr(mitd.

drops very sharply as digitalization is increased. On the other hand, the number of analog/digital con-

version units has a maximum peak for -r _~ 20 ~o (installations of ST trunk groups being more nume- rous than sos t runk groups suppressions) and then drops down to zero (as does the number of ss and ST trunk groups).

�9 Figure 14 shows the slow decrease of the total number of km • circuits with �9 ( - - 8 ~) , the numbers of A and D km • circuits having a nearly symetrical evolution.

10o 95

0

Number of km x circuits

km x circuits A + D

~ ' ~ ' ~ l n x circuits D

~ . k r ~ x circui,s A

50 IO0 %

FIG. 14. - - Evolution of the number of km • circuits.

Evolution du nombre de k m • circuits.

5.4. Results on the trunk groups.

The drop in the total number of trunk groups with the switching centres digitalization rate is shown in Table IV. The total decrease between the all-analog network and the all-digital network is about - - 60 ~o.

This drop is a result of the increasing proport ion of the number of TT trunk groups which are dimensioned with a 30 circuit modularity (or 15 circuit modularity between 2 sscs) and of the low cost of digital transit centres, which is in the advantage of a concen- tration of traffic on transit trunk groups.

The average size of all t runk groups increases with -r.

Digitalization enhances the relative importance of hierarchical t runk groups compared to the other trunk groups (they represent 7 ~ of all t runk groups in an all-analog network, and 18 ~o in an all-digital network ; their average size is doubled).

From the detailed statistics of SATIN, we have been able to draw the curves showing the mesh rate evolution (ratio between the number of existing trunk

ANN. T~L~COMMUN., 36, n ~ 9-10, 1981 8/17

B. JARRY-LACOMBE. - TRAFFIC ROUTING IN A HYBRID NETWORK

TABLE I V . - - Evolution of the number and size of trunk groups.

Evolution du hombre et de la taille des faisceaux.

5 2 9

-r 0 % 20 % 50 Yo 75 % I00

Total number of trunk-groups 27 551 24 545 20 489 15 942 11 107 % TT 0% 4% 21 ~o 44% 100%

Total number of circuits 580 432 590 980 631 533 669 963 716 850

number 11 299 10 021 8 384 6 731 5 611 ssc-ssc high-

usagetrunk average size 14C 15C 17C 19C 21C groups

average efficiency 0.65 0.65 0.65 0.67 0.66

Transit ( number 14 262 12 536 10 115 7 220 3 503

high-usage t average size 16C 18C 22C 29C 57C

trunk-groups average efficiency 0.65 0.66 0.68 0.71 0.77

Hierarchical [ number 1 990 1 990 1 990 1 990 1 990

trunk 1 average size 98C 108C 135C 167C 199C

groups average efficiency 0.65 0.65 0.63 0.61 0.60

groups and the number o f possible t runk groups) for various t runk g roup categories depending on "r (Fig. 15 and 16). Compar i son o f these results shows which of these categories are mos t sensitive to digitalization.

mesh rate % 100' ST, C- $T,C ,

o 2 0 5 0 75 l o o % v

FIG. 15. - - Intra-PTZ mesh rate evolution (~rz = Pxc's transit zone).

Maillage intra-ZTP.

,ooi

50

~mesh rate %

@ TC-STC "., Tc-sTi SSC- PTC

src-ssc , ~"

I ssc - STC,

FIG. 16. - - Inter-PTZ meshing rate evolution.

Maillage inter-zTP.

The essential points to be noted here are :

the mesh rate o f the direct high util ization t runk groups ssc-ssc decreases linearly with -r. I t is very

low in the inter-PTZ case ( 1 % ) and in the intra-eTZ case, it varies f r o m 10 % (al l-analog ne twork) to 4 % (all-digital ne twork) ;

- - t h e SSC-STC and STC-SSC t runk g roups which character ize i ncoming and ou tgo ing transi t traffic have a regular ly decreasing mesh rate. I t m a y also be noted tha t the mesh rate o f the STC-SSC t runk groups is very close to the mesh rate o f the SSC-STC t runk groups in an all-digital ne twork , while in the all- ana log ne twork the fo rmer one is 1.6 t imes larger. There is thus a closer balance between single incoming and ou tgo ing t ransi t rout ings ;

- - t h e intra-PTZ SSC-PTC t runk groups which are used to car ry inter-PTZ traffic present a decreas ing mesh rate as the n u m b e r o f t ime division switching centres increases. This mesh rate then increases, after hav ing passed t h r o u g h a m i n i m u m value correspond ing to -r = 25 %. As a result o f modu la r i ty some SSC-STC (inter-PTZ) t runk groups are no t cons t ruc ted and their traffic is carr ied on the incoming SSC-PTC t runk g r o u p , when the latter is still t oo small, the traffic overflows to the ou tgo ing SSC-I'TC t runk group. Fo r low values o f % the effect o f modula r i ty is greater than the influence o f increasing the offered traffic for the ou tgo ing SSC-PTC t runk groups. Conversely , beyond a cer ta in threshold , the mesh rate increases ;

- - the mesh ra te o f the inter-PTZ PTC-STC t runk groups has an evolu t ion similar to tha t o f the in t ra-vTz SSC-PTC t runk groups . This means tha t it is cheaper to use doub le t ransi t than high uti l ization PTC-SSC t runk groups.

The prev ious remarks on the evolu t ion o f the t runk g roups g r a p h s t ructure illustrate one o f the reasons for the rap id g rowth o f the PXCS. Th e o ther reasons are connec ted to the traffic rout ing evolut ion.

9/17 ANN. TI~L~COMMUN., 36, n ~ 9-10, 1981

530 B. JARRY-LACOMBE. -- TRAFFIC ROUTING IN A HYBRID NETWORK

5 . 5 . T r a f f i c r o u t i n g .

Traffic routing in the network can be analyzed in various ways.

5 . 5 . 1 . A c t u a l r o u t i n g .

This corresponds to the route actually used by the traffic, taking overflow into account. It can be mea- sured via the outgoing transit (OT) rate (see Fig. 17).

Intra- STZ f lows ~neighbouring centers distant centers/ v I i

inter- STZ flows

FIG. 1 9 . - Normal backbone paths for intra-sTz and inter-sTz point-to-point traffic (STZ = STCS transit zone).

Chemins normaux des flux intra-zTs et inter-zTs.

I TC I TT

S s c T - ~ , " ~- NTT

FIG. 17. - - Definition of the outgoing transit rate OT. T : total ssc outgoing. TC : transit capacity, oT : TT/T.

D~finition du taux de transit ddpart.

- - inter-sxz flows, which can transit up to 4 times, and which represent 57 % of the traffic and 96 % of the flows.

Table V and Figure 20 show the first choice routing evolution (all values are given as percentages of the total ssc outgoing traffic).

I n sect ion 5.2, we def ined the g loba l t r ans i t ra te (6T). F r o m this we can d e d u c e the p r o p o r t i o n o f t rans i t traffic (TT) which t r ans i t s a t leas t twice :

Mul t i p l e t r ans i t r a te = MT --~- TC/TT = GT/OT. Va r i a t i ons o f the v a r i o u s ra tes a re r ep resen ted in

F igu re 18.

%

52

1.17

~Tronsit rate 63 %

. _ ~ ~ 1 . 5 5

I I I I I I t I I p - 0 % 50% 100% r

FiG. 18. - - Evolution of the transit rates OT and Mr. (sir : multiple transit).

Evohaion des taux de transit TD et TM.

It may be noted that the transit rate varies almost linearly while the multiple transit rate increases more rapidly with increasing "r. This implies that the total transit capacity increases with "r stronger than the transit rate.

%

37

9

4 �84

1 inter. STZ transit 61 ~

m.1%~'%

%

25 22

11

. . . . m ~ 3 5or T ! : . I | ' I

50 loo% -

FIG. 20. - - Evolution of first choice transit.

Evolution du transit en premier choix.

TABLE V . - - Transit distribution in the all-analog and all-digital networks (% of total ssc outgoing traffic).

R~partition du transit dans les rdseaux entidrement spatial et enti~rement numdrique.

% Intra-sTZ transit % Single inter-sTz transit % Single transit total ~0 Double transit % Transit >I 3 times

Total

0 % lOO% A

4% 11% + 7

3-3 Co 4 -Co 3-TCo

--6 0 --3 0 -C-3-

5 . 5 . 2 . F i r s t c h o i c e t r a f f i c r o u t i n g .

W e m u s t d i s t ingu i sh be tween 2 types o f flows (Fig . 19) :

- - in t ra - sTz f lows (STZ = T r a n s i t Z o n e o f STC), for which the m o s t c o m p l i c a t e d r o u t i n g type is the t r i ang le a n d which r e p r e s e n t 43 % o f the t o t a l out - go ing traffic a n d 4 ~ o f the f lows ;

There fo re i t is to be n o t e d tha t traffic rou t ing var ies c ons ide r a b ly as the n e t w o r k is g radua l ly d ig i ta - l ized. This va r i a t i on in first cho ice r o u t i n g a p p e a r s in the fo l lowing effects :

- - traffic t r ans i t i ng on ly once decreases b y 8 po in t s in spi te o f inc reas ing in t r a - sTz t rans i t ;

- - traffic t r ans i t i ng twice increases by 16 po in t s ;

ANN. T~L~COMMUN., 36, n ~ 9-10, 1981 10/17


- - traffic transiting more than twice increases by 3 points ;

- - the total transit traffic increases by 11 points ;

- - t h e total transit traffic growth comes partly f rom a transfer f rom single to double transit routing and partly f rom an intrinsic growth in multiple transit traffic. The first choice multiple transit grows f rom 9 % to 28 % (while the propor t ion of transit traffic actually transiting several times grows f rom 17 9/0 to 35 ~o due to overflow).

5.5.3. Role of the hierarchical levels in traffic routing.

The analysis of the role of the STCS and PTCS in traffic routing yields Table VI.

The role of the PTCS as first choice transit centre increases. This confirms the results on trunk groups

TABLE VI. - - Distribution of first choice transit according to hierarchical levels�9

Rdpartition du transit en premier choix suivant les niveaux hidrarchiques.

"r

1 transit per STC 1 transit per PTC 2 transits per STC-STC 2 transits per PTC-STC

Total for STC first Total for Frc first

38% I 32% i--6%

lw .

44~o [ 45% I+ 1%

obtained in the previous sections but it does not completely explain the increase in capacity of the STCS and PTCS because of double transit and overflow.

5.5.4. Conclusion.

Traffic routing gets more and more complex as the network is progressively digitalized.

Multiple transit increases. Single transit decreases. But on the whole, total transit ing traffic increases.

A greater volume of traffic will be routed as first choice via the PTCS, which tends to strengthen the higher level of the hierarchy.

5 .6 . E v o l u t i o n o f the po in t - to -po in t lo s s and res i s tance

to over load .

O n e o f the purposes of our study has been to investigate the evolution of the propor t ion of traffic lost in the network and of the capabil i ty of the network to absorb traffic surges. We have plotted curves representing the average point- to-point loss rate as a function of the volume of the point- to-point traffic. We have obtained these results using the MALEPESTE p rog ram which computes the loss for each point-to- point traffic. The p rogram input consists o f a network description (trunk groups and traffic routing matrices) and of a traffic matrix (nominal or under overload).

Results shown in Figure 21 concern the all-space division switching network and the all-time division network. We have studied the behaviour under

FIO. 21. - - Evolution of the point-to-point loss rate.

- - ssc-ssc direct routing as first choice - - - - one transit as first choice . . . . . /> 2 transits as first choice.

Evolution de la perte point-~-point.

1.%!

10%'

2o%!

10.

�9 Anal0g network T : 0 % r r \

1%

" - " X

5"E 10'E-

lO% !

~.--~. traffic to Paris

5 10

/ ~t Itraffir to Paris I I , ~ 10

,

%

Digital network T=IOO%.

fiE ~C/E7

-t with

e t / 120~ overload

5 IO

, ic[o Po. 1 I . ~ - - }with

%

11/17 ANN. T~L[COMMUN., 36, n ~ 9-10, 1981


nominal load as well as two cases with an overload of 20 % and 40 % uniformely distributed on all point- to-point traffic. Each graph consists of three curves corresponding to traffic flows routed first choice via a ssc-ssc high utilization trunk group or transiting once or twice.

From the curves of Figure 21, it may be noted that :

- - f o r nominal traff• the mean point-to-point loss rate is very low for both networks, al though its distribution is very different. In the all digital network, point- to-point traffic flows between 5 and 8 E are carried via ssc-ssc non overflowing 15 circuit groups as long as the loss is lower than 1 % . This explains the peak on the graph, which in fact corresponds to the Erlang loss formula E (15, A) ;

- - the average threshold for installing overflowing ssc-ssc t runk groups differentiates point-to-point traffic flows and their respective losses in the all- analog network. Below 3.2 E in the nominal case (i.e, 4 E for 20 % overload and 5 E for 40 % overload), point- to-point traffic flows transit once or twice : their point-to-point loss rate is notably higher than that of larger point-to-point traffic flows which use an overflowing ssc-ssc high utilization trunk group. Above 3.2 E, there is no longer traffic with first choice transit (except for traffic to Paris which must transit in Paris and therefore behaves in the same way as directly routed traffic streams). However their overflow traffic increases rapidly in case of overload and this has an adverse effect on small point- to-point traffic flows. This explains why their loss rate is so h igh ;

in the digital network, there are two average thresholds for installing the ssc-ssc high utilization trunk groups for small volume point- to-point traffic flows : 5 E to create non overflowing ssc-ssc trunk groups, 8 E to create overflowing ssc-ssc trunk groups. The digital network penalizes only slightly the small point-to-point traffic flows since the hierarchical t runk groups are overdimensioned (they have an integer number of modules greater than or equal to the number of circuits required to ensure a 1 loss and a maximum efficiency of 0.7).

The all digital network handles the small point-to- point traffic flows better than the all analog network : it distributes the loss in a more homogeneous way over all point- to-point traffic flows. This is due to the overdimensioning resulting from the modularity.

- - reduced costs of time division switching and digital transmission,

- - introduction of modularity in dimensioning the digital trunk groups,

- - s u p p r e s s i o n of the limitation on efficiency of overflowing t runk groups.

These three parameters act in the same direction. We have tried to determine the specific influence of each of them.

6.1. Specific influence o f the limitation on the efficiency of overflowing trunk groups (Table VII).

We compare the all-digital network with a modularity of 30 circuits and without any limitation on the efficiency (for overflowing trunk groups) with the same network designed with an efficiency limitation of 0.8. In both cases, the efficiency limit of the last choice trunk groups is 0.7 for quality of service reasons, under overload conditions.

Suppressing the efficiency limit of overflowing trunk groups has the following effects :

- - the total number of t runk groups is 4 % less, which means a lower mesh rate of the n e twork ;

the total number of circuits hardly changes ( - - 1%). However, the number of transverse circuits is 20 % less (their efficiency increases from 0.59 to 0.73) and the number of normal hierarchical circuits is 21% greater ;

transit capacity is greatly increased (q- 17 %) especially at the PTC level. This is due to two pheno- mena : the outgoing SSC-PTC trunk groups carry more traffic (threshold effect on the ssc-ssc and SSC-STC trunk groups) and the hierarchical STC-PTC trunk groups receive a greater volume of overflow traffic ;

u the cost of the network is 8 % less : the km • circuits gain compensates for the transit cost increase.

These observations lead us to the three following conclusions :

- - l a r g e increase in transit capacity (q- 17 % ) ;

- - strengthening of the hierarchical t runk groups whose average capacity is 20 % higher ;

- - efficiency increase of the transverse t runk groups.

6. SPECIFIC INFLUENCE OF M A X I M U M EFFICIENCY

AND OF M O D U L A R I T Y

The previous results stress the conjugated influence of :

6.2. Specific influence of the modularity of the digital trunk groups.

We have compared the all-digital network with a 0.8 efficiency limit and a 30 circuit modularity with the same network without modularity. Results are shown in Table VIII.

Introduction of the 30 channel modularity has a significant effect on the network structure :

ANN. T~L~COMMUN., 36, n ~ 9-10, 1981 12/17


TABLE VII. - - Influence of the maximum efficiency limit of overflowing trunk groups.

Influence du rendement maximal des faisceaux d6bordants.

Digitalization rate lOO% ioo%

Efficiency limit 0.8 1

Modularity M = 30 M = 30

A

Total number of trunk groups 11 610 Total number of circuits 723 225

Transverse 1(i number of= circuits 396 405 trunk average size 41C groups average efficiency 0.59

Hierarchical number of circuits 326 820 trunk average size 166C groups average efficiency 0.63

11 107

716 850 320 100

35C 0.73

396 750

199C 0.60

, -- 4 % �9

1% 20 %

15%

+ 21% + 20%

Capacity of the PTCS Capacity of the STCS

Total capacity

PCM km x circuits

Total cost

24400 E

158600 E 183000 E 88 • 10 e

100

51 900 E

165 200 E

214 500 E

75 • 10 e

92

+ 2 7 5 0 0 E = + 110%

+ 66OOE = + 4 %

+ 34 100E = + 17%

--- 15%

- - 8%

GT

OT

MT

% I st choice transit

% triple transit

85% 62 %

1,37 %

61%

1%

98 %

63 %

1,55 % 61% 3% + 2 points

TABLE VIII. - - Influence of the modularity of the digital trunk groups.

Influence de la modularitd des faisceaux numdriques.

Digitalization rate 100% 100% A

Modularity M = 1 M = 30

Maximum efficiency limit 0.8 0.8 [ Total number of trunk groups 21 508 11 610 - - 46 %

Total number of circuits 592 199 353 732

18C

0.69 238 467

120C

0.65

Transverse 1 (i number of circuits trunk average size groups average efficiency

723 225

396405 41C

0.59 326 820

166C

0.63

Hierarchical 1(i number of: circuits trunk average sine groups average efficiency

+ 22% + 12%

+ 130%

+ 37% + 37%

PTC capacity STC capacity

Total capacity km • circuits

km • PCM systems

Total cost

18443 E

124840 E

143 283 E 75.5 • 106 km • c 3.5 • 10 6 km • PCM

100

24 422 E 158 607 E

183 029 E 88.4 • 106 k m • c

3 • l0 s km • PCM

95

+ 5 9 7 9 E = + 32% + 3 3 767E = + 2 7 %

+ 3 9 7 4 6 E = + 2 8 %

+ 17%

- - 5 % GT

OT

MT

1st choice transit

Inter-sTz single transit Inter-sTz double transit

69 % 56% 1.23 %

53 % 33 % 14%

85 % 62%

1.37 %

61% 25 % 24%

+ 6 points

+ 8 points

- - 8 points + 10 points

13/17 ANN. T~LgCOMMUN., 36, n ~ 9-10, 1981

4

534 B. J A R R Y - L A C O M B E . -- T R A F F I C R O U T I N G I N A H Y B R I D N E T W O R K

- - mesh rate is m u c h lower as there are only half as m a n y transverse t runk g roups bu t their average size is 2.3 times g r e a t e r ;

- - hierarchical t runk g roups have a greater capacity ( + 37 ~o) ;

- - average efficiency o f all t runk groups is lower ;

- - t r a n s i t capaci ty increases by 28 ~o in abou t the same p ropo r t i on for PTCS and STCS ;

- - actual traffic rou t ing (OT and MT) shows that the transit traffic increases as the multiple transit rate does ;

- - first choice transi t ra te is global ly higher, but traffic rout ing changes significantly since the propor t ion o f inter-sTz traffic which transits twice as first choice becomes pract ical ly equal to tha t which transits once o n l y ;

- - the modu la r ne twork is less expensive than the other , due to the low PCM filling rate observed when M = 1 (70 ~ average filling rate).

The main consequences o f the modulari ty of the digital t runk g roups are :

- - for the t runk g roups : lower mesh rate, s tronger hierarchical s tructure, lower efficiency which could be compensa ted for by suppressing the efficiency limit ;

- - greater transit capac i ty (28 ~o) ;

- - s i g n i f i c a n t change in traffic routing.

6.3. Simultaneous effect o f effieiency and modularity.

Simultaneous analysis o f Tables VI I and V I I I shows that the ne twork has evolved in the fol lowing way :

M Modular i ty : 1 - - - ~ 30,

E maximum efficiency limit : 0.8 > l,

M = influence o f modu la r i ty variat ion,

E = influence o f m a x i m u m efficiency limit.

Table IX shows tha t mos t effects are cumulat ive :

(a) lower mesh rate,

(b) stronger hierarchical t r unk groups whose average size increases :

M E 120 circuits > 166 circuits > 199 circuits,

and whose efficiency progressively decreases : M E

0.65 �9 0.63 �9 0.60,

(c) larger transit capaci ty (40 000 E due to modularity and 34 000 E t h rough suppression of the efficiency limit). Fur the rmore , suppression of the efficiency limit mainly acts on the PTCS, while modular i ty mainly acts on the STCS;

(d) lower total cost : M E

100 �9 95 -- ~- 87,

(e) modif icat ion o f traffic rout ing leading to more

TABLE IX. - - Synthesis of influence of modularity and of maximum efficiency limit.

Influences combindes de la modularitd et de rendement maximal. M E

Digitalization rate

Modularity Maximum efficiency limit

1oo%

0.8

100%

30 0.8

Total number of trunk groups Total number of circuits

21 508 592 199

11 610 723 225

lOO%

30 I 1

II 107 716 850

Transverse number of circuits trunk b average size groups average efficiency

Hierarchical trunk groups

number of circuits average size average efficiency

353 732 18C 0.69

238 467 120C 0.65

396405 41C 0.59

326 820 166C 0.63

320 100 35C 0.73

396 750 199C 0.60

PTC capacity STC capacity Total capacity km • circuits Total cost

18443 E 124 840 E 143 283 E 75.5 • 10 e

100

24 422 E 158 607 E 183 029 E

88.4 • 10 e 95

51900 E 165 200 E 214 500 E 75 x 106

87 GT

OT

MT

1st choice transit Inter-sTz single transit Inter-sTz double transit

69 56% 1.23 53 % 33 % 14 ~o

85 62 % 1.37 61% 25 % 24 %

98 63 %

1.55

61% 22 % 25 %

ANN. T~LI~COMMUN., 36, n ~ 9-10, 1981 14/17

B. J A R R Y - L A C O M B E . - T R A F F I C R O U T I N G I N A H Y B R I D N E T W O R K 5 3 5

transits and a more complicated traffic routing : M E

OT 56 % >- 62 9/0 > 63 %, M E

MT 1.23 > 1.37 > 1.55,

( f ) the efficiency o f the overf lowing t r u n k groups

decreases wi th m o d u l a r i t y a n d increases wi th the

suppress ion o f the efficiency l imi t :

M E 0.69 > 0.59 �9 0.73,

On the whole, modulari ty and suppression of the efficiency limit have an equal importance.

7. I N F L U E N C E O F T H E S I Z E I N C R E A S E

O F T H E S U B S C R I B E R S S W I T C H I N G C E N T R E S

(ssc)

We have seen that increasing the average size of the sscs as the network becomes digital is the only parameter which would lower the transit capacity. We have tried to measure its influence by comparing two all-digital networks. The total traffic in both networks is the same but the number of subscribers switching centres are different. The results appear in Table X.

The average size o f the sscs is 29 % larger while

their number is 23 % less. This has many consequences :

- - the mesh rate of the network is higher in spite of the smaller number of direct high usage t runk groups. For example, as regards the direct high utilization trunk groups, the mesh rate grows from :

6189 5611 - - 0.75 % to - - 1 .2%.

906 x 905 699 x 698

W e no t e the same effect fo r t r ansve r se t r u n k g roups

whose average size a l so increases .

- - T h e t r ans i t c a p a c i t y is 7 % less, b u t the capac i ty

o f PTCS increases. T h e d i r ec t c i rcui ts c a r r y m o r e

traffic (3 800 E) so t h a t a c e r t a i n a m o u n t o f t r ansverse

t r u n k g roups to STCS d o n o t have enough offered

traffic to be crea ted . Th is t raff ic is t hen d i rec ted t o w a r d s

the PTCS.

- - T r a f f i c r ou t i ng b e c o m e s s o m e w h a t s imple r :

less t r ans i t a n d less m u l t i p l e t rans i t .

- - F ina l ly , the n e t w o r k is less expens ive due b o t h

to the r e d u c t i o n o f the t r a n s i t c a p a c i t y a n d the n u m b e r

o f k m x c i rcui ts ( - - 8 %).

A s a conclusion, we can say t h a t the 29 % increase

o f the average size o f the sscs , c o m i n g wi th the d ig i ta -

l i za t ion o f the s tud i ed n e t w o r k , has a pa r t l y o p p o s i t e

effect to t ha t o f the a l r e a d y m e n t i o n e d p h e n o m e n a ,

t h o u g h wi th a lower a m p l i t u d e . I t con t r i bu t e s to a

r e d u c t i o n in n e t w o r k cos t (here we d o no t t ake the

d i s t r i b u t i o n n e t w o r k in to accoun t ) .

TABLE X. - - Influence of the ssc size.

Influence de la taille des CAA.

Number of sscs 906 699 23 %

+ 29% Average subscriber capacity 15 500 20000 .r 100 % 100 %

Number of circuits 120 180 120 450 0 %

Direct circuits

Number of trunk groups Average size Average efficiency

Transverse circuits

Number of circuits

Number of trunk groups Average size Average efficiency

Number of hierarchical circuits

6 189 19 circuits

0.63 191 310

3 525 54 circuits

0.77 483 330

5 611 21 circuits

0.66 199 650

3 503 57 circuits

0.77 396 750

- - 9 %

+ 10%

+ 4%

0 %

+ 6%

- - 1 8 %

STC capacity PTC capacity Total capacity Number of krn • circuits GT

OT

b i t

Total cost

185 595 E 47 050 E

232 645 E 79 • 10 a

105% 67 % 1.57

100

165 230 E 51890 E

217 120 E 75 X 10 e

98 %

63 % 1.55

92

~ 2 0 3 6 5 E = - - 1 1 % + 4840E = + 10%

15 525 E 7 % - - 5 %

- - 8 %

15/17 ANN. TI~LI~COMMUN., 36, n ~ 9-10, 1981

536

.

B. JARRY-LACOMBE. -- TRAFFIC ROUTING IN A HYBRID NETWORK

ching one Erlang increases by 50 %, the switching capacity decreases by 5 %.

SENSITIVITY TO COST VARIATIONS

The costs of the various equipment are considered in the optimization process so that they have an influence on the structure of the network. However, these costs are not precisely known and they can change. It is therefore important to measure the sensitivity of the results to variations of these data.

8 . 1 . S e n s i t i v i t y t o s w i t c h i n g c o s t s .

The analog equipments will gradually disappear. We have therefore studied the sensitivity of the all-digital network to digital switching cost by increasing this cost by 50 %. Results appear in the Table XI.

TABLE X I . - - Sensitivity to switching costs.

Sensibilitd aux co~ts de commutation.

Switching cost 100 150 + 50 %

Number of direct high usage trunk groups 5 611 5 748 + 2 %

Number of transverse trunk groups 3 503 3 827 + 9 %

Average size of hierarchical trunk groups 199 C 191 C - - 4%

Transit capacity 217 122 E 205 410 E - - 5 % % First choice transit 60.7 % 60.2 70 - - 0.5 %

This table confirms the fact that increasing the transit cost increases the mesh rate and lowers the transit capacity and the size of the hierarchical t runk groups. However, traffic routing is only slightly modified.

The sensitivity of the network to switching costs variations is relatively low ; when the cost of swit-

8 . 2 . S e n s i t i v i t y t o t r a n s m i s s i o n c o s t s .

The ratio between analog transmission costs and digital transmission costs is very important to determine the critical distance below which a digital transmission is more cost-effective. In all this study, we supposed that a digital transmission system is always set up between two digital switching centres. On this assumption, the variation of the critical distance only concerns the s-s and S-T trunk groups. The choice must be made between SAS and SDS, and SAT and SDT (of w 3.3.). We have carried out the sensitivity test on the mixed network with 50 70 of digital switching centres. As the choice SAS/SDS and SAT/SDT does not alter the modularity or the efficiency limit of the dimensioned trunk groups, we can expect an evolution of analog and digital equipment and not in the network structure.

The results are given in Table XII. The 60 % decrease in km cost for digital trans-

mission has a very strong impact on the selection of the transmission systems to be used. The number of A and D km x circuits shows this clearly. Therefore, the analog terminal equipment which forms the basic 12 channel multiplex (elementary group) disappears almost completely from the network. On the other hand, the number o f A I D conversions is only slightly higher. This demonstrates that it is mainly the SAT trunk groups which are transformed into SDT trunk groups (it suffices to move the conversion unit from one end of the t runk group to the other).

It appears that the structure of the switching network is only slightly sensitive to transmission costs, but that this is the fundamental parameter in deter- mining the rate of converting analog systems to digital systems.

TABLE X I I . - - Sensitivity to transmission costs. Sensibilitd aux co~ts de transmission.

km x PCM cost

Critical I ss distance

~o of digital switching centres

100 base

44 km 128 km

50 %

42

178 km 516 km

5070

- - 5 8 %

PCM trunk groups 70 PCM circuits % Transit capacity Number of km x circuits A (1) Number of km • circuits D (2) Number of 12 channel terminals A (1) Number of A[D conversion equipments (2) % first choice transit

63 % 80%

154 706 E 49 x 106 km 31 x 10 ~km

25 500 12 190 55.2 %

94% 96 %

150 795 E 15 x 106 km 67 x 106 km

4 965 13 523 54.7 %

+ 31 pts + 16 pts - - 3 % - - 7 0 %

+ 116 % - - 80% + 11%

(1) With a filling rate of 0.9 for analog equipment. (2) With a filling rate of 0.8 for digital equipment.

ANN. T~LF-,COMMUN., 36, n ~ 9-10, 1981 16/!7


9. C O N C L U S I O N

This s tudy has demons t ra ted the main characteristics o f the process o f progressive digitalization o f the t runk ne twork (the n u m b e r o f subscriber exchange remaining constant) :

- - 80 70 increase o f transit capacity, with tripled PrC capaci ty,

- - m o d i f i c a t i o n o f the ne twork structure (the average size o f the hierarchical t runk groups is doubled and the n u m b e r o f direct and transverse t runk groups is divided by 3),

- - transit rate grows f r o m 53 % to 63 70 but the internal s t ructure o f traffic rout ing is greatly modified : the first choice multiple transit traffic is three times

larger and the highest level o f the h ierarchy plays a major role,

- - a bet ter capaci ty to handle overload.

The principal causes o f this evolu t ion are the modula r i ty o f digital t runks groups and the r emova l o f the efficiency limit o f overf lowing digital t r u n k groups all equal ly impor tant . A secondary cause is the lower cos t o f the digital equipment .

S tudy o f cost sensitivity shows that the ta rge t all- digital ne twork is relatively unsensit ive to var ia t ions o f switching costs and tha t the process o f t ransmiss ion digital ization can only grow larger.

These results will enable us to e laborate m o r e precise engineering rules for digital networks.

Manuscri t reeu le 15 ddcembre 1980,

acceptd le 31 ddcembre 1981.

R E F E R E N C E S

[1] MAURY (J. P.). Telecommunication network planning. Program ECRIN. Ann. Tdldcommunic., Fr., (mai-juin 1970), 25, n ~ 5-6, pp. 187-196.

[2] MAURY (J. P.), GAUCHERELLE (G.), ROUSSET (G.). Computer determination of an optimum traffic routing strategy in a communication network. Program ECRIN II. Ann. Tdl# communic., Fr., (sept.-oct. 1970), 25, n ~ 9-10, pp. 361-370.

[3] *** Planification des r6seaux. Echo rech., Fr., (avr. 1978), n ~ 92.

[4] ELSNER (W. B.). Dimensioning trunk groups for digital

networks. 9 c Internation. Teletraffic. Cong. Torremolinos, (oct. 1979).

[5] MAZZEI (V.), MIRANDA (G.), PALLOTA (P.). On a full digital long distance network. 9" Internation. Teletraffic. Cong. Torremolinos (oct. 1979).

[6] BIESEL-GUETONNEAU (S.), CAMOIN (B.). Network design taking into account breakdowns and overloads. Ann. T~l~communic., Fr. (1980), 35, n ~ 3-4, pp. 143-149.

[7l Gtr~RINEAU (J. P.), BERBINAU (J.). Network security : application to the Ile de France area. Ann. Tdldcommunic., Ft. (sep.-oct. 1981), 36, n ~ 9-10, pp. 539-548.

17117 ANN. TI~L~COMMUN., 36, n ~ 9-10, 1981

traffic routing in a hybrid analog-digital network

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