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Here are some books or authors I have found useful in better understanding the complex math behind this subject

Some useful documents are:

Erlang/Traffic Engineering References

Telephony Links.
The WWW site has links to many telephony related sites.

Biography of Agner Krarup Erlang.  
This is just for interest, and so we all know where the units Erlang came from

Worked Examples
The Erlang Program Help File includes a number of worked examples. Download the Erlang Installation kit now for free, install the software, then see the Examples Section of the included Help File.
Traffic Modeling Equations Reference. 
This document has all the equations behind the Erlang program software. It is "The document I wished I had when I started writing the software". It replaces about 4 textbooks on this subject - as no texts have all the equations clearly described, with examples. You can download a version of this document now for free, but all the equations are blanked out. If you like what you see, please buy a copy.
Free Trial (PDF format, 146 kB)

Complete PDF file (Read with Acrobat) (132 kB)

$15.00 ea

Shop Online
Use Adobe Acrobat (Free) to view/print these files.

Elements of Queuing Theory With Applications 
By: Thomas Saaty. 
This book has lots of heavy math but covers the equations in detail. It however does not address the issues of how to numerically solve these equations which can become unwieldy very quickly (i.e. numerical overflows, and underflows).
Introduction to Queuing Theory  
By: Robert Cooper. 
Lots of good material regarding queuing theory and equations.
Tables for Traffic Management and Design 
By: Theodor Frankel. 
This book is great - has very clear complete set of equations and tables of solutions. The solutions only go to fairly low traffic values (e.g. Erlang B traffic levels do not go beyond 170).
Newton's Telecom Dictionary
By: Harry Newton, Ray Horak
An essential 'bible' of Telecoms terms.
Traffic Engineering
By: Cisco
This free (public) 'Technical Tip' from Cisco is a good first read if you want to learn the basics. 80% of the text is of general 'erlang' interest. The final bit relates to Voice-over-IP (VOIP) an may be ignored unless that is your interest.


VoIP References

A Cisco document on general Traffic Engineering, with a method of calculating VOIP. It is a good starting point, but does not cover Layer-2, Control, or VAD effects. Also, Frame Relay overhead omits the ‘Flag’ byte required for each frame.
Read It.
A white paper on ATM–AAL2, explaining clearly how the multiplexed voice channels are assembled into frames of ATM cells. The VAD discussion is superficial; applying an optimistic VAD multiplier to the final answer, instead of including the effect in the number of CELLS per FRAME. 
Read It.
A discussion similar to the one above, that also helps explain ATM-AAL2.
Read It.
Voice over IP Fundamentals 
By: Jonathan Davidson, et al. 
Covered topics: The Public Switched Telephone Network (PSTN), signaling specifications (including Bell System, ISDN, and Signaling System 7), the basics of Internet Protocol (IP), modulation and compression of voice, Quality of Service (QoS), H.323, Session Initiation Protocol (SIP), and gateway protocols. Business considerations of Internet telephony are also addressed.
Carrier Grade Voice over IP 
By: Daniel Collins 
Daniel Collins has written a terrific reference for anyone interested in understanding Voice Over IP. From the very start of the book, it is clear that Collins has the ability to address key areas of interest for technical readers, planners, and executives.
Configuring Cisco Voice over IP
By: Syngress Media, et al. 
This is the book that I have been looking for. The first chapter of the book provides a good high level business justification for VoIP in the enterprise and then quickly launches into a background on the technology. Intricate detail on the particulars of H.323, SIP and MGCP. The following configuration chapters also clearly presented the concepts using examples and sample config files. Highly recommended for anyone considering a VoIP deployment. VoIP will be included on the CCIE as well.


Search for books on these subjects

Telephone Traffic Engineering
Queuing theory
Voice Over IP (VoIP)


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Last modified: January 17, 2006