# Graph-Driven Exploration of Issue Handling Schemes in Software Projects
## 5 Experimental Results and Analysis
### Profiles of Issue Handling Paths
#### 5.2.3 Path Timing Features  
The time parameters of the IHM states provide only local perspectives on the issue processing phases, while the total issue handling time for the whole project presents general statistics (Section 4.1). More detailed insights regarding handling time require tracing it in relation to IHM paths. The processing time view from the state perspective is presented in Section 5.1. The timing parameters for paths differ, and they result from the aggregation of correlated issues. Typically, most issues are handled by some dominant paths. This is illustrated in Section 5.2 (Tables 4 and 5). In the MongoDB project, maximal issue handling times ranged from 57 to 826 days (often several hundreds), referring to some individual issues and showing some accidentally. The Q2 and Q3 ranges were 1-11 days and 3.4-40 days, respectively. However, the time parameters of the last path in Table 5 (124 issues) differ significantly (several hundred for Q2 and Q3). In fact, these issues were opened after a long period for further processing. Restricting timing features to the dominant paths is not satisfactory due to the high diversity of paths and many paths covering a low number of issues (typical for many projects--see Section 5.2). Hence, we introduced the path timing profiles defined by three values:  
\[TP_{i}=\{\Delta_{i},\,n_{i},\,i_{i}\},\,\Delta_{i},\,=a_{i}-b_{i} \tag{9}\]  
where \(\Delta_{i}\) denotes the range (in days) of the investigated time profile TP (e.g., Q2, Q3, max), while \(n_{i}\) and \(i_{i}\) denote the number of paths and issue coverage (%) related to the i-th parameter range. The index i runs subsequent time ranges in increasing order. Such profiles are mostly interesting for the dominant paths (with high issue coverage)--they provide some insights regarding the effectiveness of typical issue processing sequences. As an illustration, we present TP profiles (Q2, Q3 quartiles) for the commercial project P1 (period 2017-2021) considering 26 dominant paths:  
\[TP(Q2)_{1}=\{\text{4--9, 13, 72\%}\},\,TP(Q2)_{2}=\{\text{10--18, 9, 20\%}\},\,TP(Q2)_{3}=\{\text{35--58, 5, 8\%}\}\]  
\[TP(Q3)_{1}=\{\text{13--30, 11, 66\%}\},\,TP(Q3)_{2}=\{\text{35--58, 9, 22\%}\},\,TP(Q3)_{3}=\{\text{79--94, 5, 8\%}\}\]  
The maximal path handling time range was 100-881, with dominant values of 375-881 (minimal value of 39, with 66 related to 2 paths covering 3% of issues). This proves that in the considered project, most issues are handled in up to 30 days (single Scrum sprint). In case of open source projects, issue handling times are usually higher, e.g., for the Groovy project, we received the following time profiles (related to 26 dominating paths):  
\[TP(Q2)_{1}=\{\text{20--43, 10, 35\%}\},\,TP(Q2)_{2}=\{\text{50--128, 7, 61\%}\},\,TP(Q2)_{3}=\{\text{144--356, 6, 4\%}\}\]  
\[TP(Q3)_{1}=\{\text{42--150, 8, 42\%}\},\,TP(Q3)_{2}=\{\text{208--457, 6, 55\%}\},\,TP(Q3)_{3}=\{\text{500--661, 6, 3\%}\}\]  
Nevertheless, we identified some anomalies (Q2 = 2210, Q3 = 2369 days) for a path covering 19 issues. The maximal values for most paths ranged between 1722 and 4225 days, while for 12 paths, the maximal value was between 500 and 1500 (5% issues), while it was 147 and 57 days for two paths. Better results, as compared with Groovy, were obtained for the MongoDB project (8405 bug issues):  
\[TP(Q2)_{1}=\{\text{1--5, 57, 19, 58\%}\},\,TP(Q2)_{2}=\{\text{5--14, 114, 57, 63\%}\},\,TP(Q2)_{3}=\{\text{15--30, 139, 5, 37\%}\}\]  
\[TP(Q3)_{1}=\{\text{1--6, 70, 9, 92\%}\},\,TP(Q3)_{2}=\{\text{7--14, 59, 14, 77\%}\},\,TP(Q3)_{3}=\{\text{14--30, 132, 46, 19\%}\}\]  
The maximal handling times for some paths reached up to three years. For a significant percentage of issues (70.88%), Q3 was below 30 days. Nevertheless, for some paths covering a few issues, a high handling times appeared. Similarly, good results were observed in the Arrow project: a Q3 below 30 days for 66.99% of bug issues (a Q2 below 30 days covered 83.56% of issues).