506 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



of trunking plan, and a method for estimating quantitatively the essential 

 fluctuation parameters at each point in such a system. The present paper 

 has undertaken to shed some light on the former, and to provide an 

 approximate j^et sufficiently accurate method by which the latter can 

 be accomplished. It may be expected then that these studies, as they are 

 developed, will provide the basis for assuring an adequate direct dis- 

 tance dialing service at all times with a minimum investment in intertoll 

 trunk facilities. 



ACKNOWLEDGEMENTS 



The author wishes to acknowledge the technical and mathematical as- 

 sistance of his associates, Mrs. Sallie P. Mead, P. J. Burke, W. J. Hall, 

 and W. S. Hayward, in the preparation of this paper. Dr. Hall provided 

 the material on the convolution of negative binomials leading to Fig. 19. 

 Mr. Hayward extended Kosten's curve E on Fig. 5 to higher losses by a 

 calculating method involving the progressive squaring of a probability 

 matrix. The author's thanks are also due J. Riordan who has summarized | 

 some of the earlier mathematical work of H. Nyquist and E. C. INIolina, 

 as well as his own, in the study of overflow load characteristics; this 

 appears as Appendix I. 



The extensive calculations and chart constructions are principally 

 the work of Miss C. A. Lennon. 



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taining an Idle Trunk, B. S.T.J. , 25, p. 539, Oct., 1946. 



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