US1528920A - Trunking system - Google Patents

Description

March l0, l925.

R. M. FOSTER TRUNKING SYSTEM Filed Feb.

26, 1921 2 Sheets-Sheet l 3mm/Lto@ dll/Favier March l0- 1925.

R. M. FOSTER TRUNKING SYSTEM Filed Feb. 26, 1921 2 Sheets-Sheet 2 www /-Mwe EFM@ Patented Mar. 10, 1925.

nonnina fx. rosafm, or ianoom-.Ymmiw YoRxg-.fnssmNonaonMnmcAn:TnLnnHoNE:

AND .TEDEGBAPH COMPANY,A A JCORPORALTIN NEWl` YORK-.J

TRUNKING SYS'TliEllLlSJ.y

Application niearetrnary 26,1921. seriamv: 445056.

T allmiuhmn` t may concer/nz' Be it known that LR'oNALD ITKOSTER, y,

residing at Brooklyn, in the' county of Kings and State of New"York, have inventedcerl tain 'Improvements .ini TrunkingfSystems,

or" which thefollov'vingnisal specification."

"This invention relates to signalingcircuits and more particularlyjto methods'and means for trunking between different subi 1.0 scribers'in a telephone/exchange orbetween subscribers in differentexchanges.y

He'retofore in" providing Y trunking arrangements for handling the. traic origi-l nated by.v subscribers lines,-V particularly where" the connections were established' `by means of switching machinery,` two' general inethodshave been proposed. O'ne method involved `providing'a suflicient rnumberl of trunks'to handle all ofthe trallic originated" method 'is' subject'tof the disadvantage, however, tlrat while. economic' inthe ImatterV of switching arrangements: or machinery itil is prodigal intheuse ofk trunks, since the total number of trunksf'requir'ed 'to handlethe traffic lfrom .all of' the subscribersis greater v.than .would be thecase in the irst method' referred' to above, du'e to the" factthat` the ratio of'ftrunks .td subscribers "varies inversel7 .witl'i'th number'of subscribers having access to the trunks.

It is one. of the'principal objects orV the presentlinvention `to provide a scheme for multipling trunks such thatV thense of switches having a small `number of switching points will be permitted without requiring a large ratio 'of "thetotal num-ber of ftrunks to the' total" number' of's'ubscribers;

yThe above object, as well'ias other objects "by thes'ubscribers lines' involved" and es-` number of selectin@- points corresponding to kthenumber'ol'trun is 'necessary to handle'the traffic.

"in the group.

The first ofA these methods-possessesthe The other methodv consists in-'divid ing the subscribers lines into groupsjand" providing trunks for each group sufficient in number to handle the trafiic' originating advairtage'that the number of trunksk neces-k large probability of a Acall beinglostfdue serious disadvantage, however, that each subscriber must have l available a switching arrangement having a number of switching to all of the trunksfbeing busy will be a minimum. `The method is subject to the'A 4o `vterminal's suliicient to 4connect with 'each Cand allof the trunks,iand where ythetraffi'c is so large as' to require a :great number; of trunks 1 hating in each gro-up willbe"Within"tthe'capacity limits of a relatively small and inexpensive switching arrangement; that is, a switching arrangement: having acomparay, more Yfullr .a earinof hereinafter i are kactablishin-g conneotionsfbetween the calling 5 Pp l" subscribers lines and the `trunks through' a switcliingi arrangement equipped with a complished 'byi the use ofawhat Sis herein termed a random slip,a multiple. Tlienature of'this multiple will `now be clear .from

the followingdescription ofthe invention, y

wheny read in connection with theac'companying drawing, Figure' l fof which" 1s a 1schematic diagram of Ia soc'alled straight multiple, Figs. 2 and 3y inclusive, of which are `schematic diagramsof a trunking system vin which" the multiples are"slipped upc-n a purely random' basis; while Fig.V 4

is a schematic diagram lof a modification in which.'` the slipping4 of `y the multiple is worked' out in 'accordance with' a Adefinite law which closely approximates theu conditionsinvo'lv'ed in a perfect ran-domslip."

In ordertofunderstand tlieprincipleunderlying a lrandom slip multiple Ictus consider, for. example,v a group "of 100 trunks Ycarrying the' traffic originated by subscribers` lines.` Assume that eachsubscribers line is equipped 'witlia "100 point selector,

thereby" giving each" linev access" to the Yentire trunks. VLet'tlie` order in which v*the trunks are connected to the different selectors be varied as much. as possiblev A perfectly heterogeneous arrangement would be onesuch that when 37 (for'ex'ample)` of the trunks are as likely to be the trunks-actually advantages previously discussed. Let us now calculate for such a promiscuously7 connected multiple the probability that more than 20 terminals (for example) will have to be hunted over by a selector before an idle trunk is obtained. The load to be earried may be adjusted so that the probability comes ont any desired value as. for example .001. It is evident that under these conditions the last 80 terminals ot every group may be disconnected from the trunks without appreciably changing the eiiiciency ot the group of 100 trunks. Consequently each partially wired selector may be replaced by a 20 point switch having access to the same trunks in the same order as the {irst Q0 trunks hunted over by the corresponding 100 point selector. Such an arrangement will involve what is herein termed a random slip multiple and has the obvious advantage that a 20 point switch may be used having access to 20 trunks previously selected at random trom the total number ot trunks without increasing the total number ot trunks required to handle the traiiie from all ot the subscribers.

Considering the saine arrangement trom another view point, assume 5 independent groups ot lines equipped with selectors.` Let `each group ot selectors be wired to a group of 9.0 trunks. The total number oi' trunk required will therefore be 100. li' we bring together these isolated groups oi' selectors and groups ot trunks by a partial interchange ot trunks, or in other words, by arranging matters so that each one ot the 5 groups oi selectors exchanges some ot its trunks 'for some of the trunks assigned to each ol the other 4v groups, we will. have a promiscuously connected multiple ot l00 rtrunks to some 20 of which each selector will have access. .lt this interchanging were done thoroughly the load carried by the total number of -trunks with a given probabilityT :o't' lost calls would be appreciably greater than the load carried by the same number oi: trunks when divided into live isolated groups each ot which is accessible to a 20 point selector.

In order that the advantages inherent in the random slip multiple may be more apparent a mathematical solution oi' the problem involved willnow be given. rThe problem may be stated as itollows:

A group of T trunks handles the tratlic originated by n sub-groiips of lines or switches.

Sub-group ,itl oit lines or switches has access to a specified number t1 ot the T trunks.

Subgroup #2 of ylines or switches has access to a speciiied number t2 ot the T trunks. Some of these t2 trunks are not iiicluded in the l trunks assigned to subgroup #1.

Subgroup :#:3 ot lines or switches has access to a speciiied number t.; ot' the T trunks. Some of these t3 trunks are not included in the t1 trunks assigned to subgroup .tz-"l and some are not included in the f2 trunks assigned to sub-groiip #2. The trunks i. and t2 together may, however, include all the t., trunks.

Sub-group :tt/1i. ot lines or switches has access to a specitied number t ot the T trunks. with either the t1, t2, t. or t-l trunks `but they are all included in the totality oi tl-tetg-l- -l-tu-l trunks.

Thus, no sub-group of lilies or switches has the exclusive use ot a set o't trunks chosen from among the T trunks and on the other hand no two or more. sub-groups use identically the same trunks. Y

lt is not assumed above that numerically tlztgztn: nml-tn although this will probably be the case in practice.

Such a group ot T trunks giving servcc to several over-lapping or inter-linking subgroups ot lines, each of which subgroups makes partial use ot the T trunks`r may be defined as a random slip multiple provided the 'following statement can be niade with reference to it when S ot the T trunks are busy they are as likely to be one speeii'ied set oi" S trunks as another specified set ot S trunks.

ln (.ider to solve this` problem let P. :probability that a subscriber originata call from a sub-group havin?.- access to a i' ot T trunks tails to get an idle truuk.

Assume that at the moment the call is made S ot the T trunks are busv. The probability of the existence ot this Lassumed condition is where A is the average load arried bv the group T. i

rllhe probability that the assumed S busy trunks embrace the particular t trunks tio which the subscriber under consideration has access is Therefore, the compound probability that S of. the T trunks are busy and that'these S trunks include the if trunks under consideration is These t.. trunks are not identical;

Therefore l i A S=T 1,

nelg) (g-Srrrn) n :probabilitylnt all-Ttr-unks are busy. l

Now y l v T-i T-t-i gz lgm--mr-m) Therefore, finally, `t y y y KO y y y The preceding equation gives the probability of lost calls in terms of the average ,load carried by the group of trunks, the total number of trunks involved, and the number of trunks/assigned to each group. lVith this equation asa basis Tables I` and II have been prepared to show the saving involved in a random slip multiple as compared with a straight multiple, that is, a multiple in vwhich vthe trunks are divided into independent groups, Vea'eh group accessible to' a switch having a correspondingly' smallnumber of terminal points.

In a system where 20 point sender seleo .tors give ac oessto the senders of an` automatieI switching exchange the saving in senders when the random slip arrangement is used instead of the. straight multiple will be as indicated in Table I. It can be readily seen from the table that with the l random slip arrangement the number` ot senders required to carry a given loadfis considerably smaller than the number ot senders necessary for the same load with.'

the r straight multiple. `For example, it`

` is apparent that if the allowable probability of lost calls is .O01 and the trunks are dividedv into ten groups of 20eaoh the random slip multiple arrangement Vwill require only 137 senders as against 200 senders inquiredy by the straight multiple ar- `rangement for an average load of 89.6, the

expression average load beinghere taken `to mean the average number of connections existing at any onetime for the entire group of trunks The saving just referred to amounts to 31.5%. On the other hand, in auease where but one group is involved and the average load is 8.96, 20 senders will be required in both' eases; and they random .46'

` slip multiple presentano advantages over Y Straight multiple.

the straight multiple, as in this limiting oase the random slip multiplebeeomes a Table II shows the saving in fina-l switches which would result from a random arrangement of trunks to finals 1n a panel sys* tem where the incoming multiple is divided into groups of 24 trunks each. Here also a smaller number of switches can carry the same load as a larger number with the straight multiple or inversely, the same number of `switches in the random arrangement can take care of a larger load than in the straight multiple arrangement. f Table I.

j l Random l btnught multiple. umltipla y l Per cent Average load. y y l Swingin Number lotal Total senders.

0f You s senders senders ,i gl p required. requiredq 1 20 20 .f 04 .2 ll() 34 i 15. 0 3 eo .471 21.7 4 S0 (i0 l 25.0 5 100 T. l 27. 0 l0 200 137 3l. 5 l5 300 199 i 33.7 2O 400 262 .f 34.5 25 500 326 34. S

Tabla II.

Straight multiple.

i J UM Pereentl` Average load. saving in Egg? umher Total Total finals. y i ou s finals finals l gr p required. required.

I i l 1 241 24 o i 2 48 43 10.4 3 72 I eo m. 7 4 as i 7s 18.8 5 120 96 20. 0

rangements involving' the random slip CFI principle may be embodied in various forms. In Figs. 2 and 3 are shown perfect random slips permutations of the numbersl, 2, 3 and 4, the permutations being shown in Fig. l, which illustrates in schematic form the permutations of four trunks taken four at a time in accordance with the first method outlined at the beginning of this specification. In all three figures a group of T24 trunks is shown, together with `a:24 sub-'groups of subscribers lines. Each sub-group is represented by one line equipped with a selector giving the line access to four trunks in the case of Fig. l, three`-trunks in the case of Fig. 2 and two trunks in the case of Fig. 3. In Fig. I and the succeeding figures the arrows may therefore be taken to represent the wipers of the switches,each of which is available to one or more subscribers and each switch having terminal points equal in number to the vertical lines connecting the arc of a circlerepresenting the contact points of the switch-with the horizontal lines representing ythe trunks; The numbers below the arrows representing the wipers of the switch indicate the order in which the switches obtain access to the trunks.

If, in the case of the arrangement of Fig. 1 a determination is made of the probability that more than 3 terminals will have to be hunted over by the selector before an idle trunk is obtained and it be found that this robability is withinthe allowable probaiiility of lost calls, the connection leading to the last trunkkby each switch may be omitted from the switches in Fig. 1, in which case we get the perfect random slip arrangement of Fig. 2, which is based upon permutations of 4 trunks taken 3 at a time.

Similarly, vif it be found that the allowable probability will permit of dispensing with connect-ions to the last two trunks selected by each switch in Fig. 1, we may obtain the perfect random slip multiple illustrated in Fig. 3 which involves permutations of 4 trunks taken two at a time.

The slip arrangements illustrated in Figs. 2 and 3 are based upon all possible permutations of the numbers involved. Conse-v based on all possible permutations, wherev the total number of trunks T is large. For example, a slip multiple of T:25 trunks, in which" each line is equipped with a z5 point selector would require the lines to be divided. into 25 24X23 22 2I:6,375,600 sub-'groups if every possible. permutation ofy \sub-' roup based on all of ther24 possibleU4 therefore becomes desirable to devisea system in which only a part of all of the possible permutations will be used and in which thezse'lectcd permutations will be so chosen that noparticular set of trunks is more likely to be busy than any other set involving the same number of trunks. In selecting a limited number of the .total possible permutations, `it is preferable to select a minimum amount of overlapping i. e. permutations such-that any trunk having a given number will appear in as few chosenA permutations as possible.

Fig. .4 illustrates a practical form of slip arrangement obtained by following the principles above discussed and in which a very thorough intermixture of theI trunks is-obtained without dividing the lines into an abnormal number of sub-groups. This figure illiistrates what is herein called a binomial slip arrangement as applied to a system, involvingl. trunks .and 5 poi-ntselectorsr In accordance with this arrangement.l the trunks assigned to the first' sub-group of lines to the left,.arethose havingY the binomial numbers l, 2, 4:22,' v8:23', .and 16:24. The numbers of the trunks to be assigned to the other groups are. obtained by writing the numbers from 2 .to 17. as the numbers of the first trunks to be selected by the groups to the right of that having assigned to it the numbers l, 2,4 etc.v Similarly the numbers ofthe second set of trunks to be selected is obtained by writingsuccessive numbers beginningv with '3, while the numbers of the third set are .obtained by writing successive numbers beginning with 5, etc. In Veach instance, whenthe number 17 is reached the-succeeding 'number will be 1. An analysis of. this trunking. arrangement shows that whileit is not a perfect random slip arrangement, it conforms. very 'closely to the requirements` of the random slip multiple.

It will be obvious thatthe'lgeneral principles hereinA disclosed `may beembodiedin many other organizations,widely different from those -illustrated, without departing from the spirit of the invention as defined in Y the? following claims.

`What is-claimed is:

l. A trunking system in which a plurality of trunks are provided for handling vthe calls originating from all-of the subscribers lines involved, the subscribers-lines bel ing divided into sub-groups each having access to a number of trunks lessv than `the total number provided, the .trunks vassigned to theseveral sub-groups being interchanged so that the sub-groupsoverlap .each other, the `numbers of the trunksassignedtofthe firstv sub-group and .the order .of-selection thereof.v being obtained by: assigning to. said trunksv having r.' the' i, binomial num ers l, 2, 4:22 etc.,.and the' numbersof lll) the trunks assigned to the other sub-groupsy and the order of selection thereof being obtained by addingk successive numbers to the numbers assigned to the irstfsub-group.

2. A trunking system in which a plurality of trunks gives service-to several overlapping and 'inter-linked' sub-groups of lines, each sub-group of klines having access to a partvonly of the total number of trunks, the

numbers of the trunks assigned to the first sub-group being obtained by assigning to said sub-group the binomial numbers 1, 2, 4:22 etc., and the` numbers of the trunks assigned to the other sub-groups being obtained by adding successive numbers to the numbers assigned to the first sub-group.

3. A trunking system in which ka plurality of trunksl gives service to several over-lapping and inter-linked sub-groups of lines, each sub-group of lines having yaccess to a part only of the total number of trunks, the

numbers of the trunks assigned to the first sub-group and their order of selection being obtained by assigning to said sub-group the trunks having the binomial numbers 1, 2, 4:22 etc., and the numbers of the trunks assigned to the other sub-groups and their order of selection being determined by as-v signing to the other sub-groups trunks whose numbers are obtained by adding successive numbers to the numbers assigned to the iirst sub-group, whereby When a given number of the total number of trunks are busy, the probability of one set of trunks of the given number being busy Will be substantially the saine as the vprobability that any other set of equal number Will be busy.

In testimony whereof, I have signed my name to this specification this 23rd day of February, 1921.

RONALD M. FOSTER.

msk

Images