# A Framework to Model Bursty Electronic Data Interchange Messages for Queueing Systems +
## 3 Results
### Model Batch By Category  
#### Service Time Modelling  
When simulating service and inter-arrival times, it is important to know if the queue will ingest a message as a single message or as a batch of messages. This is because a batch arrival would be a clear type of interdependence between messages that would be relevant for queue modelling. DevOps informed us that certain messages (\"Flat Translation\" or \"Batch Translation\") should be considered batch messages based on their \"Category\" attribute. These messages should be split into smaller files and sent into the system as a batch. All other messages should be considered non-batch type messages. When we inspected the data, we found evidence that the messages for flat translation and batch translation were both single messages and batch-type messages. Based on these initial comments from DevOps, we went ahead and modelled the service times of these messages.  
Before attempting to model the service times of the dataset, we analysed measures of dispersion. From Table 9, we note that of the total batch messages, half of the messages were removed when we removed messages of zero duration. We also observe that these data are heavy-tailed with a skewness greater than 20 and high kurtosis. There is a 0.10 s difference in the 95 th percentile between the service times of both batch messages and batch messages where zeros are removed. Messages greater than zero seconds in service times are likely to take less than 0.26 s to process.  
Figure 8: File size histogram.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Statistic** & **DF** & **a** & \(p\)**-Value** \\ \hline \(18\) & 19 & 0 & \(0.05\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: File size, head, Chi-square uniform distribution test.  
To further understand our results, in Figure 10, we compare the data after a square root transform to the modelled log-normal distribution. The Q-Q plot shows that the data tail off at the start of the quantile line. We observe from the P-P plot that while the data appear continuous on the right-hand side of the plot, there are many discrete values on the lower probabilities.  
If we partition these data into a head and tail, we find clear evidence of discrete values in the P-P plot shown in Figure 11. From these values, we were able to draw four discrete Gaussian distributions. These four Gaussian distributions result from KDE estimation applied to the discrete data and are not a feature of our data but a feature of the underlying system in the way that the mantissa is set on the message timestamp. We expect our data to be continuous, and this figure and data are not a true representation. We discuss this further in Section 4.4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test** & **Transformation Sqrt** & **Transformation Cube Root** \\ \hline Burr & 362 & 362 \\ Log-normal & 281 & 281 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Batch by category AD result.  
Figure 10: Batch by category, log-normal, ST.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Service** & & & & & & & & & \\
**Duration** & **Total** & **Min** & **Mean** & **Max** & **95 th** & **99 th** & **Percentile** & **Var** & **Skewness** & **Kurtosis** \\
**Second** & & & & & & & & & & \\ \hline Batch & 126,742 & 0 & 0.03 & 14.04 & 0.16 & 0.44 & 0.01 & 26.17 & 2716 \\ Batch zero & 65,878 & 0.001 & 0.05 & 14.04 & 0.26 & 0.61 & 0.01 & 20.84 & 1658 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Service times, batch by category statistics.  
Figure 9: Batch by category, classification model.