# Graph-Driven Exploration of Issue Handling Schemes in Software Projects
## 5 Experimental Results and Analysis
### Profiles of Issue Handling Paths
#### 5.2.1 Structural Features  
Analysing IHM path structures, we distinguish two taxonomy profiles, namely the path length (PL\({}_{\text{P}}\)) and path state (PS\({}_{\text{P}}\)) profiles, defined as follows:  
\[PL_{P}=[l1\ (c1,\ n1);\ l2\ (c2,\ n2)\ \ldots\ lk\ (ck,\ nk)] \tag{8a}\] \[PS_{P}=\{Pi:S1_{i},\ S2_{i},\ \ldots\ Sm_{i}\ |\ c_{Pi},\ 0\leq i\leq r\} \tag{8b}\]  
where \(l1,\ l2,\ \ldots,\ lk,\ c1,\ c2,\ \ldots,\ ck\), and \(n1,\ n2,\ \ldots,\ nk\) denote the path lengths (the number of consecutive states) in increasing order, the summarized issue flow of these paths, and the number of different paths of the specified length, respectively. PS\({}_{\text{P}}\) is the set of all paths P\({}_{i}\) composed of state sequences \(S1_{i},\ \ldots\ Sm_{i}\) and \(c_{Pi}\) is the issue flow (coverage) of the i-th path. It is reasonable to list the paths in decreasing order of relevant flow coverage. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**State** & **Us** & **Ns** & **Q2** & **Q3** \\ \hline NES (Needs scheduling) & 12,644 & 14,725 & 0.2 & 4.9 \\ NEM (Needs Merging) & 1728 & 1765 & 0.1 & 0.7 \\ INV (Invalid) & 1678 & 2430 & 1.1 & 9 \\ IPR (In progres) & 8489 & 9702 & 0.2 & 2.8 \\ OPE (Opened) & 11,325 & 13,573 & 1.1 & 23.4 \\ ICR (in Code Review) & 8767 & 9316 & 1.9 & 5.8 \\ NED (Needs verification) & 12,400 & 12,466 & \textless{}1 h & \textless{}1 h \\ C (Closed) & 11,811 & 12,575 & 1 & 7.3 \\ NET (Needs Triage) & 88 & 90 & 0.2 & 2.8 \\ WFU (Wait for user input) & 437 & 723 & 1.9 & 17.9 \\ BAC (Backlog) & 2034 & 2124 & 17.1 & 70.2 \\ BLO (Blocked) & 298 & 332 & 7.1 & 28.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: State time profiles for the MongoDB project. Issue flow (coverage) can be specified explicitly as the number of handled issues or the percentage of all covered issues. In simplified profiles, issue flow (\(c_{i}\), \(cp_{i}\)) can be skipped. Other aggregated profiles can also be derived, e.g., considering path groups covering specified ranges of handled issues. These ranges can be specified in absolute or relative scales. In compact profiles, we can use ranges of state lengths. Deriving path profiles, we can also consider issue restrictions, R (issue types (bugs or new functionality), issue priority, issue reporting time, range of covered issues, etc.) or path classes (discussed in Section 5.3). Similarly, we can use generalized states equivalent to some individual ones, e.g., _Resolved_* corresponding to resolved states with diverse individual suffixes (e.g., fixed, rejected, or duplicated). As an illustration, we present a sample of \(\mathrm{PL}_{\mathrm{P}}\) and \(\mathrm{PS}_{\mathrm{P}}\) profiles for some projects. In the commercial Scrum project P1, the ITS repository comprised 2378 issues (related to the year 2022), including 1555 bugs (1434 closed and 121 open) and 823 other cases (425 paths). The distribution of the last group was as follows: _User story_--274 (209 closed); _Task_--342 (282 closed); and _New Feature_--234 (134 closed). The derived \(\mathrm{PL}_{\mathrm{P}}\) profile was as follows:  
\(\mathrm{PL}_{\mathrm{P}}\)_(P1) = 23(4;4)--0.17%; 21(4;3)--0.17%; 20(5;5)--0.21%; 19(9;9)--0.38%; 18(8;8)--0.34%; 17(13;13)--0.55%; 16(12;12)--0.5%; 15(18;15)--0.76%; 14(17;17)--0.71%; 13(33;24)--1.39%; 12(16;14)--0.67%; 11(53;37)--2.23%; 10(49;27)--2.06%; 9(138;45)--5.8%; 8(82;35)--3.45%; 7(160;43)--6.73%; 6(341;27)--14.34%; 5(750;29)--31.54%; 4(164;16)--6.9%; 3(214;20)--0.0%; 2(148;8)--6.22%; 1(140;2)--5.89%;  
Limiting HUM to bug issues (restriction, R), we obtained 1555 issues which were handled in 332 unique paths with the following distribution: (12-23)--8.54%; (8-11)--16.01%; (6-7)--14.02%; (5)--41.29%; (1-4)--20.13%. In the brackets here, we give the range of path lengths followed by the relevant issue coverage percentage. Similarly, we can explore the impact of other issue features on path profiles. Issues with the highest priority (32 closed) were handled within 16 unique paths with the following distribution: (7-20)--21.86%; (5-6)--40.62%; (2-3)--37.5%.