# A Framework to Model Bursty Electronic Data Interchange Messages for Queueing Systems +
## 3 Results
### Model Non-Batch By Category
#### 3.2.3 Message Interdependence  
Message interdependence is critical when simulating a queueing system. Modelling single message behaviour through a queueing system is less complicated than modelling messages where there is a parent-child relationship, and the relationship may be one too many. The service times of a batch message may not be determined until the last child message arrives and is processed in the queueing system. Using the classification model, we attempted to understand if we could easily identify a parent-child relationship within our dataset. Applying the models from Figure 21, we observe that we were able to determine if a message was dependent on previous messages based on the \"Batch By Split Count\" model and the \"Non-Batch By Split Count\" model.  
Figure 21: Interdependence by classification.  
Figure 20: Tail of data, by hour, ST.  
We now explore the text in Figure 22 to give some context on how we came to this conclusion.  
At a high-level view, a message first arrives in line 2. The message is set to an associated state defined by a map associated with the message as per line 3, and the customer name is associated in line 4 using a Reference ID. The message is then sent for translation in line 5, and the XML for the message is produced in line 6. The message is then completed processing in line 7. A subset of this message is then processed again starting from line 15 and is finished at line 20. This means that this message is split into two messages and is fully complete at line 20.  
In more detail, we took the ID of the message and split the string in two (id1:id2). The first string was the Company ID (id1), and the second string was the Message-ID (id2). Consider the hypothetical example in Figure 22. Using the second part of the ID in the second delimited column (id2), we counted the number of times the message had a string tag of <XML>. We note that the message first enters the system on line 2. It then has an <XML> tag on line 6. We count this as 1 XML document. We then note the message arrives in the system again at line 15, and at line 19, it has another <XML> tag. We count this as 2 XML documents for id2. We iterate through all the log data until the last part of the message comes into the system, and we aggregate the count of <XML> tags.  
It is important to note that if there were 2 <XML> tags, i.e., if we had one on lines 26 and 27, we would only take the first <XML> tag as a count. Although we never saw this behaviour in the wild, we note this in case it happens on other systems.  
Using the signature, we can now determine if a single arrival will send an influx of messages into the queueing system.  
We also seek to understand if there is a dependence between the service times of these independent and non-independent messages. To explore this, we split the messages into messages where the service time exceeds 1 s or 2 s (see Table 17). We chose these values, as they reflect the tail of our data, and it would be useful to know if these messages are more likely to be in the tail.  
We perform a Fisher's exact test on our data to check for independence. Table 18 of the [PERSON]'s exact test indicates that there is no significant association [_p_ < 0.05] between independent and non-independent messages, where the service times exceed 1 or 2 s in duration.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Classification** & **ST \(\leq\) 1 s** & **ST \(>\) 1 s** & **ST \(\leq\) 2 s** & **ST \(>\) 2 s** \\ \hline Independent & 126,585 & 157 & 126,731 & 11 \\ Non-Independent & 884,722 & 2714 & 857,160 & 276 \\ \hline \hline \end{tabular}
\end{table}
Table 17: ST exceeds 1:2 s.  
Figure 22: Log message.