# End-to-End Delay Model for Train Messaging over Public Land Mobile Networks
## 3 Analysis of Experimental Data
In the Q state, a large number of messages could be buffered due to link unavailability even for a relatively long time. In this case, large transmission delays have been experienced leading to the high spikes in the E2E delay as evidenced in Figure 4.  
To better understand the nature of these events, we have correlated the time the messages are sent with the positions of the train along the line. We have observed that these phenomena \begin{table}
\begin{tabular}{|c|c|c|} \hline Network of 1 & t-Time & Medium \\ \hline E2E & 6:43:49.086780 & 6:43:49.262628 \\ \hline E2E & 6:43:49.286770 & 6:43:49.692338 \\ \hline E2E & 6:43:49.486759 & 6:43:49.692350 \\ \hline E2E & 6:43:49.886751 & 6:43:49.892881 \\ \hline E2E & 6:43:49.886788 & 6:43:50.5022226 \\ \hline E2E & 6:43:50.086788 & 6:43:50.322382 \\ \hline E2E & 6:43:50.286759 & 6:43:51.033155 \\ \hline E2E & 6:43:50.86784 & 6:43:51.033147 \\ \hline E2E & 6:43:50.86789 & 6:43:51.034164 \\ \hline E2E & 6:43:50.86790 & 6:43:51.062097 \\ \hline E2E & 6:43:51.066793 & 6:43:51.792375 \\ \hline E2E & 6:43:51.286774 & 6:43:51.831787 \\ \hline E2E & 6:43:51.86673 & 6:43:51.866291 \\ \hline E2E & 6:43:51.866774 & 6:43:51.943009 \\ \hline E2E & 6:43:51.866725 & 6:43:52.022501 \\ \hline E2E & 6:43:52.06722 & 6:43:52.292359 \\ \hline E2E & 6:43:52.286712 & 6:43:52.830270 \\ \hline E2E & 6:43:52.486716 & 6:43:52.631724 \\ \hline E2E & 6:43:52.686769 & 6:43:52.801989 \\ \hline \end{tabular}
\end{table} 
Table 1: Numerical sample of the E2E delay sequence. Figure 4: E2E delay as a function of the message IDs. Each message is 500 bytes long; messages are generated at a constant rate of 5 msg/s i.e., one message every 200 ms.  
can be related to the received power level, the actual serving radio technology and to the (hard) handover/roaming events. In some sporadic cases, very large E2E delays (on the order of about one minute or more) have led to the automatic reset of the measurement equipment. This has caused the loss of several consecutive messages and, obviously, their IDs have not been recorded at the receiver side. These events have been discarded from the data set used to derive the model presented in this paper. Finally, when the channel is in state Q and the generation rate of the messages is relatively high (e.g., 5 msg/s), buffering of messages to be transmitted may occur frequently. This leads to the saw-tooth like behavior made evident in Figure 5.  
The cases in Figures 4 and 5 are for illustrative purposes only of the main phenomena we need to consider for E2E delay modeling. Before concluding this section, we have also observed the presence of sporadic losses of one or more messages indicated in the previous figures with asterisks. From further analysis, we have observed that sporadic losses are un-correlated and can occur randomly regardless of the channel state G or Q. The message loss probability has been evaluated from experimental results and for different message rates. If we exclude events causing the reset of measurement devices and losses due to coverage holes along the line, we have observed the presence of sporadic messages loss due to momentary bad radio link and/or to message forwarding in the core network. Even though the Vodafone network could be based on a Virtual Private Network Point-to-Point (VPN P2P) link, it still may experience random un-bounded delays. This could be one of the possible causes leading to reset of measurement equipment. From extensive data analysis, after excluding (un-wanted and un-predictable) equipment reset events, we have obtained a (sporadic) message loss probability of about \(5\times 10^{-4}\). This value is not surprising. In fact, the service provided by Vodafone was optimized for M2M communications; presumably, it implements high availability and buffering solutions for reducing/avoiding message loss. In general, it is envisaged that the railway operator will request the MNO for reliable and secure message transmission services for the transport of signaling information.