Return on Investment (roi) for Multi-Technology son juan Ramiro, Mark Austin and Khalid Hamied

7.3.4. Characterizing the Traffic Profile

7.3.4.1. Traffic Distributions

The traffic profile is an important piece of information for ROI calculation. When calculating the ROI of Self-Planning functionalities, two types of traffic (voice over UMTS Release 99, denoted by R99, and data over High Speed Downlink Packet Access, denoted by HSDPA) will be considered and, for each one of them, two main properties need to be carefully taken into consideration: (i) temporal evolution of the average traffic per sector during the busy hour; and (ii) distribution of the traffic per sector across the network during the busy hour.
The first one is a key input to the process, which is typically obtained through traffic forecasts, taking the operator’s business plan into account. The second one is needed to model the fact that networks are not uniformly loaded. When analyzing the distribution of the traffic per sector in the busy hour, results from real networks have shown that it can be represented by means of a Gamma function in which the standard deviation is roughly proportional to the average (although the factor relating both magnitudes will change from network to network). The Gamma distribution reads as follows:
f x( ) = xk⁻1 exp(−xθ_k ) (7.2)
Γ( )k θ
From 9 to 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Traffic (Erlangs)
From 14 to 15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Traffic (Erlangs)
Figure 7.7 Distribution of the traffic per sector at two moments of the day: (top) from 9 to 10; (bottom) from 14 to 15.
where G is the Gamma function and the parameters q and k can be derived from the desired mean and standard deviation by means of the following equations:
θ= Var x( ) (7.3)
E x( )
k = E x( ) (7.4) θ
Figure 7.7 depicts the distribution of the traffic per sector, measured in a commercial network for two different periods of one hour, together with the way in which the Gamma function models such distribution, taking the average and standard deviation of the traffic per sector as an input.

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00
Mean (traffic)
Figure 7.8 Average versus standard deviation of the traffic per sector.
Figure 7.8 correlates the average and the standard deviation of the measured traffic per s ector for different periods of one hour within one day, showing that the standard deviation grows with the average in a roughly proportional way (dictated by q).