Short note: Telephone traffic engineering

Telephone traffic engineering is the study and design of switching and transmission resources (trunks, switch paths, registers, processors) so that a network gives an acceptable grade of service at minimum cost. It uses probability and queuing theory to relate traffic load, number of servers and service quality.

Basic quantities

• Traffic intensity (Erlang): average number of simultaneously busy servers, $A = C\,h/T$ (C calls of mean holding time h in period T). 1 E = one circuit busy continuously. 1 E = 36 CCS (hundred call-seconds per hour).
• Holding time (h): mean duration a server is occupied per call; usually taken as exponential.
• Busy hour: the continuous 60-min period of the day with the highest traffic; networks are dimensioned for it. Busy hour calling rate and day-to-busy-hour ratio are used to forecast it.
• Grade of Service (GoS): probability that a call is lost (loss system) or delayed beyond a time (delay system), e.g. GoS = 0.01 means 1 call in 100 lost in the busy hour.

Types of systems

Traffic assumptions

1. Pure chance traffic: Poisson call arrivals (large number of independent sources).
2. Exponential holding times.
3. Statistical equilibrium: traffic does not change during the period.
4. Full availability: any free server can be used.

Main formulas

• Erlang B: $B = \dfrac{A^N/N!}{\sum_{k=0}^{N} A^k/k!}$ – probability of loss with N trunks.
• Erlang C: probability of delay in an N-server delay system; mean delay $= P_D\,h/(N-A)$.
• Engset: loss with a finite number of sources (PBX).

Uses

• Dimensioning number of trunks between exchanges and of switching stages.
• Choosing between direct and tandem routes (overflow and alternate routing).
• Planning call centres, cellular channels per cell, and buffers in data networks.
• Measuring and forecasting load for network growth.

Example: with A = 5 E offered and GoS 0.01, the Erlang B table gives N = 11 trunks.

Traffic engineering therefore balances cost (fewer circuits) against service (low blocking or delay).