# A Next-Generation Core Network Architecture for Mobile Networks
## 11 Measurements
**Analysis 2:** We study users' traffic patterns in order to determine the life cycle of an entity between its creation and its destruction. Given our sample of call records, we found some calls to be extremely short (shorter than ten seconds). One common pattern for these short calls is that two records of a phone number \(A\) show the same start time and duration but with different phone numbers, that is, one towards phone number \(B\) and one towards phone number \(C\). These cases correspond to calls for which the callee (i.e., phone number \(A\)) does not answer the caller (i.e., phone number \(B\)). Instead, the calls are redirected to voicemail (i.e., phone number \(C\)), a service that stores voice messages. In such a case, setting up a VCN is inefficient as no real call happens. This suggests a change in our protocol for VoLTE calls (see Section 5). In particular, instead of deploying a VCN when the SN receives an INVITE, the VCN gets deployed once the SN receives the 200 OK to the INVITE, that is, once the callee has accepted the call. For the rest of the analysis, we remove calls that last less than ten seconds. We measure the duration of a call in minutes. Figure 22a,b show the Empirical Cumulative Distribution Function (ECDF) of the number of calls and call duration over a ten-day period, respectively. Notice that both the number of calls and the call duration are discrete variables; this makes the ECDF look like a step function. The median number of calls per user over ten days is 28, with approximately three calls per user per day. About 90% of the users have less than 130 calls over ten days (i.e., approximately 13 calls/day) which is consistent with the results in [36]. The median of the call duration is two minutes and approximately 90% of the calls are less than ten minutes long. This means that the majority of the calls has a short duration, that is, the lifetime of an entity could be short if based only on the call duration. However, we need also to consider the time between calls since we do not want to destroy an entity just to find out that we have to deploy it again a few seconds later. A _call interval_ is defined as the lag between the time a call terminates and the time the next call is placed, for a given user. As before, we measure the call interval in minutes. Figure 23 shows the box-and-whisker plot of the ratio of calls with different call interval levels per user. The levels are indicated by the labels on the left side of the \(y\)-axis. For example, a level of \((2,5]\) indicates a call interval that goes from above two to five minutes. The levels are evenly partitioned with a step size of five minutes, excluding the last level which represents a call interval longer than 30 min. The first 5-min  
Figure 21: Forecast of one-day traffic from a seasonal ARIMA model fitted on concurrent voice-calls data over six weekdays. level is further broken into two levels to show more details on very short call intervals (i.e., less than two minutes). The labels on the second \(y\)-axis on the right indicate the percentage of outliers for each level (i.e., shown as black dots in the plot). If the time interval between two calls is short, or if the majority of the calls are placed within a certain time interval, it may be inefficient to destroy the entity around that interval. For example, if a user places a call every three minutes, it is inefficient to destroy his VCN at the 2-minute mark as it will have to be deployed again 1 min later. **Recommendation 2:** In Figure 23, a small ratio value on the \(x\)-axis for a given call interval tells us that the percentage of calls per user that have a time between calls as indicated by the interval on the \(y\)-axis is small and, thus, unlikely. From our collected data sample, the median for interval not longer than two minutes is 8%, meaning that half of the users have 8% of the call intervals shorter than or equal to two minutes. The median and third quartile are 4% and 8%, respectively, for the next two call interval levels, i.e., (2, 5) and (5, 10).