422 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



3. Customers Dialing on Groups with Considerable Delay 431 



3.1. Comparison of Some Formulas for Estimating Customers' NC Service 



on Congested Groups 434 



4. Service Requirements for Direct Distance Dialing by Customers 436 



5. Economics of Toll Alternate Routing 437 



6. New Problems in the Engineering and Administration of Intertoll Groups 

 Resulting from Alternate Routing 441 



7. Load-Service Relationships in Alternate Route Systems 442 



7.1. The "Peaked" Character of Overflow Traffic 443 



7.2. Approximate Description of the Character of Overflow Traffic 446 



7.2.1. A Probability Distribution for Overflow Traffic 452 



7.2.2. A Probability Distribution for Combined Overflow Traffic Loads 457 



7.3. Equivalent Random Theory for Prediction of Amount of Traffic Over- 

 flowing a Single Stage Alternate Route, and Its Character, with Lost 



Calls Cleared 461 



7.3.L Throwdown Comparisons with Equivalent Random Theory on 



Simple Alternate Routing Arrangements with Lost Calls 



Cleared 468 



7.3.2. Comparison of Equivalent Random Theory with Field Results 



on Simple Alternate Routing Arrangements 470 



7.4. Prediction of Traffic Passing Through a Multi-Stage Alternate Route 



Network 475 



7.4.1. Correlation of Loss with Peakedness of Components of Non- 

 Random Offered Traffic 481 



7.5. Expected Loss on First Routed Traffic Offered to Final Route 482 



7.6. Load on Each Trunk, Particularly the Last Trunk, in a Non-Slipped 

 Alternate Route 486 



8. Practical Methods for Alternate Route Engineering 487 



8.1. Determination of Final Group Size with First Routed Traffic Offered 

 Directly to Final Group 490 



8.2. Provision of Trunks Individual to First Routed Traffic to Equalize 

 Service 491 



8.3. Area in Which Significant Savings in Final Route Trunks are Real- 

 ized by Allowing for the Preferred Service Given a First Routed 

 Traffic Parcel 494 



8.4. Character of Traffic Carried on Non-Final Routes 495 



8.5. Solution of a Typical Toll Multi-Alternate Route Trunking Arrange- 

 ment : Bloomsburg, Pa 500 



9. Conclusion 505 



Acknowledgements 506 



References 506 



Abridged Bibliography of Articles on Toll Alternate Routing 507 



Appendix I: Derivation of Moments of Overflow Traffic 507 



Appendix II: Character of Overflow when Non-Random Traffic is Offered 



to a group of Trunks 511 



1. INTRODUCTION 



It has long been the stated aim of the Bell System to make it easily 

 and economically possible for any telephone customer in the United 

 States to reach any other telephone in the world. The principal effort 

 in this direction by the American Telephone and Telegraph Company 

 and its associated operating companies is, of course, confined to inter- 

 connecting the telephones in the United States, and to providing com- 

 munication channels between North America and the other countries of 

 the world. Since the United States is some 1500 miles from north to 

 fSOuth and 3000 miles from east to west, to realize even the aim of fast 



