466 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



2 or 3. A load of a erlangs is submitted to each subgroup, a having the 

 values 1, 2, 3, 4 or 5. What grade of service will be given? 



Solution: The load overflowing each subgroup, when a = 1 for example, 

 has the characteristics a = 0.0625 and y = 0.0790. Then A' = 2a = 0.125 

 and V — 2v = 0.158. Reading on Fig. 26 gives the Ecjuivalent Random 

 values oi A = 1.04 erlangs, S = 2.55 trunks. Reading on Fig. 12.1 with 

 C + *S = 3.55 when C = 1, and A = 1.04, we find a' = 0.0350 and 

 oi' liflx + a-^ = 0.0175. We construct Table II in which loss values pre- 

 dicted by the Equivalent Random (ER) Theory are given in columns 

 (3), (5) and (7). For comparison, the corresponding exact values given 

 by Neovius* are sho\vn in columns (2), (4) and (6). (Less exact loss 



s 



(OR X) 



(a) 



ta,v 



(b) 



fa'.v 



ta,v 



(c) 

 fa'.V 



|A fa, f; 



la, faafaa 134*35* J 



Fig. 24 — Various high usage trunk group arrangements producing the same 

 total overflow a, v. 



figures were given previously by Conny Palm^°. The agreement is seen 

 to be excellent for engineering needs for all values in the table. 



Example 2: Suppose in Fig. 24(b) the random offered loads and paths 

 are as given in Table III; we desire the proportion of overflow and the 

 overflow load characteristics from an alternate route of 5 trunks. 



Solution: The individual overflows ai , vi ; a^ , v-i ; and as , Vz are read 

 from Figs. 12 and 13 and recorded in columns (4) and (5) of the table. 

 The a and v columns are totalled to obtain the sum-overflow average A' 

 and variance V . The Equivalent Random load A which, if submitted to 

 S trunks would produce overflow A', V , is found from Fig. 26. Finally, 

 with A submitted io S -\- C trunks the characteristics a' and y', of the 

 load overflowing the C trunks are found. The numerical values obtained 



* Artificial Traffic Trials Using Digital Computers, a paper presented by G. 

 Neovius at the First International Congress on the Application of the Theory of 

 Probability on Telephone Engineering and Administration, Copenhagen, June, 

 1955. 



