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As alluded to previously, network quality has an impact with respect to overall churn. While there have been a variety of ways to estimate those who will churn in a wireless network [1, 2], it is first important to distinguish different reasons why a customer would churn (or leave a certain operator for another), and later identify the reasons that are impacted by SON. For example, the reasons for churn can be classified into the following categories (in line with [3]):
Service cost. Out of the total number of churners, the fraction due to this reason is in the following denoted by cfcost, which can take a value between 0 and 1.
Billing (fraction = cfbilling, between 0 and 1).
Brand image (fraction = cfbrand, between 0 and 1).
Customer service (fraction = cfservice, between 0 and 1).
Service plan options (fraction = cfoptions, between 0 and 1).
Network quality (fraction = cfnetwork = cfn, between 0 and 1).
Mathematically, the following expression must hold:
cfcost + cfbilling + cfbrand + cfservice + cfoptions + cfn = 1 (7.13)
While a churning customer may actually have several reasons to churn, one reason is typically dominant. To obtain a first approximation about the relative importance of the different reasons to churn, satisfaction surveys, such as those by J.D. Power, Nielsen or o thers, can be reviewed. A typical finding in these reports is that network quality is normally the most important metric driving overall customer satisfaction. Indeed, J.D. Power [3] breaks down the drivers of overall satisfaction as shown in Figure 7.17, where it can be seen that network quality has a contribution of 32% to overall customer satisfaction. In this respect, it is assumed that improving network q uality via SON or other approaches will reduce primarily the churn due to network quality issues.
To characterize the benefit of improving network quality from a churn perspective, the first step is to compute the overall percentage of users that are churning due to network quality, denoted by cn, which is obtained by multiplying the total churn rate (denoted by c) with the fraction of churners that are due to network quality (denoted by cfn).
cn = c · cfn (7.14)
There can be several ways to historically estimate cfn, such as surveying customers that churned and asking them to classify the primary reason why they churned, looking at proxies for complaints due to network quality (for example, based on calls into customer care) or relying on external third party surveys measuring network satisfaction. These approaches work well for understanding what happened after the customer has already switched carriers. However, to predict how much the network churn rate (c) can be reduced by improving network quality, a model is required as a function of Key Performance Indicators (KPIs) that can be measured using network statistics. Since the objective here is to formulate a model for ROI purposes, let us consider using a simplistic linear model to estimate the value of cfn as:
cfn = w1 × KPI1 + w2 × KPI2 + … wn × KPIn + b (7.15)
where {wi} denotes the set of weights characterizing the relative importance of each KPI, and b is a constant. As an example, let us assume that that the following three KPIs will be considered to model churn:
Percentage of customers which are unhappy due to coverage.
Percentage of calls that are dropped due to network quality issues.
Percentage of calls that cannot be started due to accessibility issues.
Specifically, how to measure these three KPIs on a given network will vary depending on the network infrastructure vendor and the wireless access technology. For instance in a UMTS system the following definitions can be applied:
KPI = %callswith⎨⎧(RSCP < −100 dBm)or⎜⎝⎛ EcIo < −15 dB⎟⎠⎞⎬⎫ = Outage (7.16)
1 ⎩ ⎭
KPI2 = Drop Call Rate = DCR (7.17)
KPI3 = Call Setup Failure Rate = CSFR (7.18)
If multiple measurements (K) of cfn(i=1 … K) are available, for example from surveys or statistics related to customer care complaints in different geographic areas, then the optimal values for the weights {wi} and constant b in Equation (7.15) can be easily be computed through standard multi-regression techniques1. In matrix form, the least squares solution for the weights can be illustrated as follows:
⎡ cfn(1) ⎤ ⎡KPI1(1) KPI2(1) ⋯KPIn (1) ⎤ ⎡w1⎤ ⎡ ⎤b
⎢ ⋮ ⎥ ⎢ ⋮ ⋮ ⋮ ⎥ ⎢w2⎥ ⎢ ⎥⋮
⎢ ⋮ ⎥ = ⎢ ⋮ ⋮ ⋮ ⎥ ⎢ ⋮ ⎥ + ⎢ ⎥⋮ (7.19)
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣cfn K( )⎦ ⎢⎣KPI1(K) KPI2(K) ⋯KPIn (K)⎥⎦ ⎢⎣wn ⎥⎦ ⎣ ⎦b
Simplifying in matrix form:
%CFN = KPI ×W + B (7.20)
As explained in [4], the least squares solution for the weights can be found by applying the following equation:
W = (KPI T KPI)−1 KPI T%CFN
(7.21)
–
where B can be calculated as the residual error vector.
Let us then assume that the application of SON multiplies each KPI by a factor Gi (typically with Gi ≤1, implying a KPI improvement). In this case, combining (7.14) and (7.15), the overall reduction in the churning rate due to quality (denoted by Dchurn) would be as follows:
n
Δchurn = cnOLD − cnNEW = c⋅(cfnOLD − cfnNEW ) = c⋅∑wi ⋅KPIi ⋅(1−Gi ) (7.22)
i=1
And the annual revenue loss that is avoided due to quality improvement, denoted by R, can be formulated in the following simplistic way:
R = Dchurn · S · ARPU · 12 (7.23)
where S stands for the number of subscribers and the ARPU is measured on a monthly basis.
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