# Dynamic Controllability of Processes without Surprises
## 9 Related Work  
Semi-contingent activities and semi-dynamic controllability have been introduced in our previous work [11], which, to the best of our knowledge, was the first to address them. Here, we extended the work in [11] with an extensive formalization of the sudden termination patterns, a formalization of the sudden start problem, and a mapping of sudden start into sudden termination. The most relevant related work, therefore, is in the areas of (a) formulation of temporal constraints in process models, (b) checking consistency and controllability of time-aware process models, and (c) scheduling and monitoring of process execution. For general overviews of process time management, we refer to [5; 12; 19]. The work in [20] marks a milestone in the representation of temporal aspects in process models, as it presents a formalization of time patterns and their semantics, based on the analysis of recurring temporal constraints in a wide number of real world process models. Nevertheless, despite being a thorough investigation, it did not identify semi-contingent activities and the problems of sudden start and sudden termination. With this work, we established a number of (anti-)patterns of temporal constraints, which may lead to potentially undesirable behaviors during the execution of a process, and which designers should look for in their process models to prevent such behaviors. The focus of this work is on business processes with temporal constraints. Several previous works focused on the verification of deadlines and temporal constraints in business processes, see, e.g., [21; 22; 23; 24]. Similarly to our proposed approach based on STNUs, these approaches are based on network analysis, scheduling, and constraint networks. None of these works, however, addressed the problem of induced sudden termination of tasks. We integrate these verification approaches with the identification of a run-time behavior that can be performed at design time, without the need to develop new formalisms for temporal reasoning. Figure 13: Results of the evaluation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subset** & **Min Time [ms]** & **Max Time [ms]** & **Average Time [ms]** \\ \hline
10N & 78 & 250 & 134 \\
20N & 484 & 1438 & 829 \\
30N & 4177 & 9340 & 6291 \\
40N & 11,865 & 26,558 & 18,936 \\
50N & 29,971 & 5  
More recent works such as [25; 26] combined the temporal aspects of a process definition with other constraining dimensions, e.g., resource availability. Our work, instead, currently focuses on the temporal dimension only. Looking into future research directions, we regard these recent works as interesting starting points for a holistic investigation of the problems of sudden termination and sudden start in processes. Here, we concentrate on verifying process qualities at design time. We recognize that design time is only one stage of the process lifecycle and prior work was indeed conducted around the verification of temporal qualities at run time, e.g., pro-active monitoring of the compliance of process instances to their process model [27; 28; 29]. Nevertheless, to the best of our knowledge, all such approaches to monitoring and compliance checking address the notion of satisfiability rather than dynamic controllability and do not consider the problem of sudden termination. We consider it an interesting research opportunity to extend our current work also to the run time of processes, e.g., exploring the possibility of pro-actively giving warnings about the need to start or end tasks, even if they are not semi-contingent or necessarily require advance notice. A popular technology for gaining insights about process definitions is process mining [30]. Process mining relies on the existence of a large number of cases (process logs) for discovering process definitions and being able to provide scheduling and monitoring information about them. Thus, it is not adequate for new or frequently changing processes, or processes with small number of instances.