# A Framework to Model Bursty Electronic Data Interchange Messages for Queueing Systems +
## 4 Discussion
### Modelling  
#### 4.2.1 Parametric Modelling  
**Model By File Size**  
We wanted to understand the range of file sizes within the dataset. This could allow the construction of a test suite based on real data and allow us to understand how the different sizes might impact queue behaviour. This would also facilitate the provisioning of disk space for the queueing system. We were able to fit the head of the data to a uniform distribution, which will support the requirements around disk space. The tail of the data seems to contain specific file sizes, suggesting that KDE fitting or some model based on knowledge of customer behaviour might be useful.  
We considered that if we could identify batch messages via file size, then possibly batch messages would all be large files that are split into smaller pieces. However, we could not determine from the file size whether messages were split. In particular, as the source file size was an optional parameter, we used other fields to determine this.  
**Model Batch By Category**  
We modelled our messages based on the associated \"Category\" on the advice from DevOps; however, we found that the messages identified by the suggested categories could either be single messages or messages that are split into several messages. Further work is required to try and identify the unique features that support this Classification.  
We also investigated fitting a parametric distribution to the message service times when modelling messages matching the \"Batch by Category\". The final model that we selected indicated that the data were close to a log-normal distribution but failed the AD GoF test. We noted from the P-P plot evidence of a significant number of discrete values, suggesting that our data's quantisation may be an issue.  
**Model Batch By Bundle**  
In an alternative approach to understanding batches of messages, we chose to model all messages that were part of a bundle by considering runs of messages where only the last message had a service time greater than 0 s in Section 3.2.1. We felt that this might help merge batches into a single arrival. Again, we partitioned the data by head and tail and observed that the tail of the data was close to a log-normal distribution. The head of the data was not suitable for parametric modelling.  
**Model Batch By Split Count**  
When we analysed the messages by a count of associated XML documents from a queueing perspective, we ascertained that these messages were indeed batch-type messages, even if they were not all batch-type messages from an EDI perspective. We could not get the data to fit a parametric distribution to the partitions of the data we tried. However, some transformations of the head of the data were close to log-normal and Burr distributions.  
**Model Non-Batch By Split Count**  
Here, we considered the messages where the XML count of the documents was one. We were able to fit the tail of the service times to a Burr distribution. The head of the service times may be suitable for modelling by KDE. We also attempted to model the inter-arrival times. If we refer back to our previous paper [11], interestingly, the inter-arrival times showed correlation, and we left modelling these correlations as future work.  
**Model Non-Batch By Category**  
Using the \"Non-Batch By Category\" approach, we could not fit this classification model to a parametric distribution. However, it provided clear evidence of the impact of the quantisation of our dataset on modelling.