BSTJ 10: 4. October 1931: The Interconnection of Telephone Systems - Graded Multiples. (Wilkinson, R.I.)

16 MB·English

The Bell System Technical Journal

October, 1984

‘The Interconnection of Telephone Systems—
Graded Multiples

Eh Sit Siac sta sp nl thm en
cop ane ca mart hs Sy
Soh cache ag pctettina stan es
cc sarin ee ak er aa

Irnonueniox
WT te completion of te thin ema pone iar

rent some Atty edd yan ago was born the problem of Fee
roomieeton. Anda che syste has grow a9 has the demand for a
Universal series. The present compsenity of one enmmunieation

We)

ee

setoork males it ificult to appreciate thst in these early days it was
a rarueatively simple thing r> pravice a direct line fram ench eu
seriber ta every echer abeeiber, a shown inthe seemari ferenn
Section ofthe six telephone stacoaa in Fig. 1. Tw mace achesnes there
is no possililty of theline being hey the only faules a subscriber may
propery fal wit the service frver and above ennamiion trouble)
Ire ths "the ealled party lng” oa aaather line, and "he does si
Jamwers” conditions feyune he peal af che intereornestng system,

"For avery srall nsbar of eubseriben al i love araxiity euch &
selieme srould anal coes serve admirably. As soom a8 che aumber of

satoniters “nc evened, howeray, the number f es, wile
enuala * 2, goes un at a enosmous cate, almost as the square

of the aumber of suisile:s. Since a major cement of che cost is in
ticect vacation with the numberof ives ths plan, even on a modest
seale i quickly prohibited,

‘Nevertheles ia trl universal verve i 0 be furnished it must
not only be posite tor ny aulecrbar to communicate directly with
Eny-other, bac ft niu Le exsily posible. Thin problem was solved

Wy the development the eatial of pl of iaterconnection,

‘Femueateany Somme

We may represent dupliied central ofice exchange system by the
Tine diagram of Pig. 2. "Two sets of 100 subscribers, and 8, may
nate all she apposize set vi the 10 “teunks"" CA line which
Conects an fivivieual subeeder to his central ofice exchange is
fonique in thst it ll ever bw used except when Be i talking. The
Thee Cy howeves, which ase_aravided for estalvahiag eonacetions
Ieee tue telephones iu ane ellce and thove in she other ray well
caer calls originutesl iy 4 lage number of wbeecbe-s, Thereupon
iTioteadily seen tha: ovr teviice line Corr, a4 we all hereafter
Ca i) may easily tain a vexy much higher efcioncy, as measured
bby the percent tie ein uae, the an individual subscriber's Ti
When ce suimcihor is not using a partcular crunk it i available
for uve Uy another, thas we make ene trunk do the work for which
theo mote lies were rewted in the original arrangement of Fi 1.

“To obits this incresed all eaceying capacity per trunke and the
ceunsequent savings dhe o teduetion in the tolal cumber of eeanks,
iV is neeeeary c foreye coe particular advange: we eannot be ab-
solucely sure that these will be aa idle tunle available when cach
Sutoerter desires to plasebia various. Foe tis possible, although
‘ery improbi ile, tut all of the subvervew mighe want €o call ome
another simultsmonrls, and Saving far fewer trunks than subcrer
Sethe: ce many vol bal to get immediate service ‘The

ovo rn acy coils to ve win Se
analyses necessary to determine the thenstial puutubility (or the
proportion af times inthe jong run) chat a particular subverber wl
Find all of group of cranks bey are well Known ;and tables and curves
are available showing for wide ranges of loads aad auabers of tele.
the probly of a particular suberiber nding then all in se?

In Pig 3 fe shown she lad, a, ia average simultaneous calls whit
thesceiclly may be submitted {2 nuevo ty or the average, one
fonehundredth 201), er one cam: lnnmomtih (P= -A00 of al,
the ealls submitted will ind no idle seunk available. By repltting
Fig. 3 tae sein Pig, 4 the averaze lead cased pee ual (eficinicy)
Wwe See Wat a lange group of trunks ie relatively auch atoe elicient
than a emaller ene

TForexampe, ce alin of = 41 at P =.01 we should provide
single group of $7 Wane, wile we are required to carry the same
total loa over groups of ¢ "16 cub, we ball ne lew ouch groupe
(oF tal of 0 trunks. hae chs dal Ie so ty Deore clearer
Dy considering, say 20 trunks, hot as a consplee group and then a
te split gras ur subgroups of 10 crus, each caying oneal of
he otal load se giccured in ig, S.A tna is eepresented by each
Invrizontat He an the load submitied by che vertical arrow, at
thougi it ware starting a the latin of ee group to hunt forthe fist
fale trunk. We fest obeerve that the propoctian of ells Tost on the

ums aml be leas tan in che complete group
ince en ll chefruias ure ul in eier caso the cll coring in wil
Geadelayed o: los allyalie, 228 erly when elf 20 ants ave oocopicd
in theese che corplete group mil eellsbe lat. On the other baud,

csverage inthe splice

ses ngnce en one Genoene3)
inthe spc yenup cla may be lst when as few 25 10 trunks are bury
provided the areal: te group to which the cals ae the moment are
Feng origivate” ‘Thus dhe sphsing of the group and the eons
Fecuetion of she arise aay preven a call in one subgroup, ni
nding ite 10 use ey, fie eontinuing on ever the reraining

= >
ae

5mm of aspen Ney

tru, one af whieh might have Ten idle, We wweluce thea that,
tikes Wings being equal a given Tea anay he moe economically
farce] over one ieege group hm over 30 Of swore sulle EroU

sumone Taursstss

Cntortunately, “ular abinge” are ecolelyy not cqual, Threw
safer considerate may be poet wt whch ite dennitely tend
‘limit che sambes of trite ta whic: a particular urns may he

1, Tle high cos of writes leaving a ange mumie of nts

2 Theundesrabl lng una whieh oeur in sun: groups egos.

2. The double: connections whioh irene ilseelly wits the Toa
‘ariel

OF thew the St to ze usually the wore instrumensal in regulate
the practical upper limits to the acces of hunt. When onsite
swith the ellceney of che truvkyraps in a system they comprnn
ffeneral, he fundancental dst foreleteraising Ue sppronriate arrange
nent wiichsnay be economically employed ohana given amount
ot tale,

We ae then Fare with the problem of obtaining the masimun
sfieney’ maximum average luo per trmk) with a given hunt o
eves, We have soon that she oltimate eiiency is obeained when
the cocal trunks are atvangel in @ complcee or straight grouping
We have also nated low greatly he eticicney is reduced by splitting
the total franks into distinc individual subgroups. Te may well be
that iy certain eantangensents we shall be able to increase this low
tffciency without icessing the access

Gaaoen Munauete Timor

1h “pot uli na fr lnproving the enc of rl
ing tulin aiing more channels then ng sith cn pal.
SDip not over wan propond in 8 by FLA Ceaye” We may ya
Shnagus heme wring yee al ey sing
2 vey np real

Supp vets 1 unc euoup at ag, 6) each t-
ingat sect Wal egg ico predetsigs probably of
dnc, sur P= Ol. Tin te Sppronate svorage ld arid by
{sil ed ets tor te ran sme
Sry, mca able L* “te ipetan eit to lee hve
Katie tt auakis bury goodly pron thee aC) 318
the rcond erate a toner aor tw nal a dow tothe
la tunis mck ave compen Thy tuo ie oth a
tRing muy ov tnt one hal eae per cn fe ne

The svete apostate malate bach e's
groups ei vk woof hs te averse preset al oe
tits ye itely tak bee condo wld cur
three feta ute lese fa howe oan hen sel
Ith ts, nso li a le a
me pees ae ae

id = fag} = BE,
tvailable, Thetia to aay, we should be tole tu eapitilize the poss
bites of teamwork between she more ighsly leet pain ut the
serous

“This aay be doue by arranging che exo groupe as in Pi, 6°B) 80
thet the erae-conasetio of the last choice trunks provides nope
tunity fer ther moa wae hy he cals from ether subgroup. In this
parveular ease, however, the hunt or eves hat besa increased from
10 o 15 cerminels, If we wish to retain the operation of the system.
on 10-prine switching syniprmnl we aust compress he tink Inte
fone auch frm as cael fn Fig (C3. Ln 30 doing we have very
lige Increased the slit gp efclency ofthe series nt the same
time on neon of thei fewas weal number the ld originally
Iritted nay vot le aequstelyrerwed, lene, «remedy sc a hoe
igs (0) may pethape be devised: tha i the alton a move sub
{groupe of the vessicted avalabilgy trunks, The study of the actual
carving espueities of chews various arrangements is reverved for
Tater point in this paper

Tr gonial, then, we may represent ary su a of ceunking by
tie sulnmacice of Figs, FUL) amd 718). Thaw ate called "simple

foo

ie Md} Sgl inde mie we x bon

118) a nace pgresive graded nil

sealed mmltples” and “progstasive graded mulips,” ceapectively,
ne by varving che aumber aad placemest of the trunks composing
Tange vaviely of arvangenteats indeed may be obsained.

runt trom fe "bottom" of the group ower puricular
vot af sever sets of inven” tr elle alr, aad if
‘rune ace idle they cortirse on up € the “eommon" o~ “cartaly
‘comion” trunks wien are mede aceatihe so allo the switches that
sppeer before the eosteibutig subgroups. ‘The esental charaecere~
tics che graded multiple are, chen: the trunks huneed over fst serve
4 minimum numberof switches while those trunks hunted over last
fe mulsipled before more or all of the switches. Provided our pre=
‘mnary anaties commect, the teamivark obtained between ae liter
srtions of sl ef the eubgrowps sould seaalt in on inesesed average
ver irk rying expat shroghnt she hole multiple

Epricscy of Graven Metatens

Several cheories for calculating the grade of service of graced mul-
tiples with eny given submitted loa por sugoup have been aulvancod.
All of these involve cerain awumplions or eanpirieal apyaenionlie

Dr, brie Labberger® of she Siemens and Halske Manufacturing
Company, erlin, in solaboration wita Dr, G, Rekha presented
a nnivene! scheme, patie theoretieal, pathy empitial for extmating
The lad carrot by ny run a aplt or graded, or a commbination of
le (vo, multiples That remaining load which isnot eased chen
canattaten the everon ("Verkeheste) Kom whieh te prepoction
Tea" my immedintely be determined, The ub cf Lubherger’s
ree consists the appleation of so-called "Zuschlagsfakizws” to
Corre the animicred Ind for the ee when epliting, andthe gain
‘olen geting "Thixmaded lead om che aesumption tae ic has been
feduced 10 the appropriate equiva lly is len tno ta eater
diet nnstruct foe straight maltiple. Combined with this pro-
fer te assumtion that the busy hour loads in eaek subseoup
flay not oceur sen taneously, thus giving @ stil freer expartuaity
et a couperaiive wg ol the common ern

‘A scnaat phin for estimating tie srabability of loss of a graded
rultiple na proposed hy the late Dr. ME. Merker of Antwerp.’ He
Aleveloned a very complicated formula which iavnlues @ cnesteration
of the various ways in which a grate! sauliple mighe seoomenestate
orn numer of cals

“Tim Brits Post Dice has made some interesting an) valuable

Ingo fr Ove

oe
cmpivcal investigations ofthe graded multinle pre? ‘These have
Selucled. weceaively or progresively-graced multiples as ell aa
those invalving only a ingle vet of aubgroupe cling into a simple
freup a? enmmon ernie, They conclude that for mune than Wo
Subgrnps the auccesive grew ave aoaicnhet advantageous anal the
highest ecenciee are to begotten when theresa smooth progression
fen indviduvle iw comions.” ‘Phat, the nuenberof trunks in each
sugeoup of individuals, pais, fours, eights and eommone, shold he
‘ery nearly equtl, and in gener "no geading should be used. i ecm
be avoided which the setaal number of revive require to the newt
eae exceeds all the maxizum pooible sumbet.” An Igenm
trailing, for example, should nat be wel when more chan 90 circuits
Sre required.» These specific date are, of cours, with reference
aly cathe grange of 1O-eantat ewitees.”

inal, a very inererig ld of study has been opened wp trang
tie design of o> orci Lulie meckine by Mes. E. A. Elliman
nid RoW, Taser of the Standa-d Telephones and Cables, Leda To
the partite machine cometrueted to group gradings eth all arrange
iments of individuals and comamens pf Ita of 28 could be simu
Totes In the sagle examplor given of atraght eed grade proms
the results swing the lead per une appear to be elsely in aera
nce wth sei expocted vaes. 1a more Hlesible mechanism could
be deve aad tected to inenre concordance wth practice a moat
‘allie catibasion to the tof eral would Ie mae

Th the Mathematica Appeadis [of this paper Mir. E. C, Mobis
sets forth the analytical theory far simple single-stage) symmetrical
riled multiples sw srginated and practiced (with certain modifica
tions to Be mentnel lie) by che Bell System. ‘The present mth
of estimate the probability of los, knowing che errengement of
tunes and the avevoge loed submitted per subgroup, isthe natural
putgrowsh of several praungry fosmulaa each of shiek was chal
Hudied ane! compared. with Iie aetuat conditions to ema it
operat

"The Four governing assurmptions which neal earful serutiny in thee
final formula presente this paper 2

1 The ldeag tie ofall rales azeumed He constant

2. Aveell aot recesving immedize service f heli it waiting for te
sormal holding time por, ane i az availa lua becomes idle it
‘nil ecupy it til thie eso fy coaspleted, This uel cferred
ts ie loge cals held” azsumyption.

16, BDL An Ou lwo te Tracy Aves of Aomatic Teeponse
sae ie Zn en ce a Fey
ecient ae Sr f ‘Keil Shake Neh for Aweonme Cees