THE INTERCONNECTION OF TELEPHONE SYSTEMS 539 



one of several sets of "individual" trunks called a subgroup, and if 

 none are idle they continue on up to the "common" or "partially 

 common" trunks which are made accessible to all of the switches that 

 appear before the contributing subgroups. The essential characteris- 

 tics of the graded multiple are, then: the trunks hunted over first serve 

 a minimum number of switches while those trunks hunted over last 

 are multipled before more or all of the switches. Provided our pre- 

 liminary anal^^sis is correct, the teamwork obtained between the latter 

 portions of all of the subgroups should result in an increased average 

 per trunk carrying capacity throughout the whole multiple. 



Efficiency of Grade.d Multiples 



Several theories for calculating the grade of service of graded mul- 

 tiples with any given submitted load per subgroup have been advanced. 

 All of these involve certain assumptions or empirical approximations. 



Dr. Fritz Lubberger '" of the Siemens and Halske Manufacturing 

 Company, Berlin, in collaboration with Dr. G. Ruckle, ^ has presented 

 a universal scheme, partly theoretical, partly empirical, for estimating 

 the load carried by any trunk in a split or graded, or a combination of 

 the two, multiples. That remaining load which is not carried then 

 constitutes the overflow (" Verkehrsreste") from which the proportion 

 "lost" may immediately be determined. The nub of Lubberger's 

 method consists in the application of so-called " Zuschlagsfaktors " to 

 correct the submitted load for the loss when splitting, and the gain 

 when grading. This modified load, on the assumption that it has been 

 reduced to the appropriate equivalent load, is then used to enter a 

 chart constructed for a straight multiple. Combined with this pro- 

 cedure is the assumption that the busy hour loads in each subgroup 

 may not occur simultaneously, thus giving a still freer opportunity 

 for a cooperative usage of the common trunks. 



A second plan for estimating the probability of loss of a graded 

 multiple was proposed by the late Dr. M. Merker of Antwerp." He 

 developed a very complicated formula which involves a consideration 

 of the various ways in which a graded multiple might accommodate a 

 given number of calls. 



The British Post Office has made some interesting and valuable 



* F. Lubberger: "Die Wirtschaftlichkeit der Fernsprechanlagen fiir Ortsverkehr." 

 R. Oldenbourg, Munchen und Berlin, 1927. 



^ G. Ruckle und F. Lubberger: "Der Fernsprechverkehr als Massenerscheinung 

 mit starken Schwankungen." Julius Springer, Berlin, 1924. 



" M. Merker: "Some Notes on the Use of the Probability Theory to Determine 

 the Number of Switches in an Automatic Telephone Fxchange." The Post Office 

 Electrical Engineers' Journal, vol. 17, Part \, April, 1924. 



