# Scheduling the Exchange of Context Information for Time-Triggered Adaptive Systems
## 5 Results and Discussion
### Experimental Setup and Communication Cost Modeling
with the propagation of context information among end systems (ES) within the network. To accurately compute this cost, we adopted the following approach:  
1. We categorized end systems requiring context information as'recipients'. This categorization is based on Equations (1) and (2). 2. We incorporated a dedicated time slot for the exchange of context information prior to the commencement of task scheduling on the end systems. Following the occurrence of a context event, we established the current time for each affected end system (denoted as \(t_{c_{1}},t_{c_{2}},\ldots,t_{c_{n}}\)). We then reserved time slots following the initiation of a broadcast of context events to all recipient end systems. This process included the assumption of a specified delay, denoted as \(dx_{i}\), which varies based on the path index of each context message, reflecting the network's topology and the data flow paths. The overall communication cost associated with each scheduling decision is given as  
\[\text{Comm\_cost}/\text{Affected\_ES}=\sum_{i=1}^{n}(dx_{i}) \tag{3}\]  
Equation (3) captures the cumulative path delays (\(dx_{i}\)) based on routing decisions made during schedule construction. Other sources of communication latency, such as serialization time or software-induced processing delays, are not explicitly modeled. We assume fixed-size messages and static link characteristics, where serialization is either negligible or embedded within the path delay values used in the model. Moreover, such delays remain constant across all schedules and are not influenced by the optimization variables. As the genetic algorithm ranks individuals by relative makespan, including such constants would not change the selection process and can therefore be safely omitted to simplify the model. The value of (\(d_{x_{i}}\)) in Equation (3) is derived from the platform model using a set of precomputed multicast paths. These paths are generated by solving the k-shortest-path problem between relevant end-system pairs. For each message, the genetic algorithm selects one of these precomputed paths through its path index \(P\) genome. The associated path delay \(d_{x_{i}}\) is calculated as the number of hops (i.e., the total number of links and switches traversed) along the selected path. This value is retrieved from the platform data structure  
Figure 6: Abstract JSON schemas of the application model (**left**) and platform model (**right**), used to define jobs, messages, hardware nodes, and interconnects. during schedule reconstruction and used to compute the message delay contribution in the makespan. The communication cost for periodic context information exchange, denoted as \(C_{\text{c}}\), is mathematically expressed in Equation (4). It is proportional to the ratio of the makespan \(M\) over the sampling frequency \(f_{\text{s}}\), scaled by the context information cost \(C_{\text{ci}}\). The makespan \(M\) represents the total time to complete tasks, while \(f_{\text{s}}\) is the rate of system data collection, and \(C_{\text{ci}}\) covers the resources required to process the sampled data. \[C_{\text{c}}=\left(\frac{M}{f_{\text{s}}}\right)\cdot C_{\text{ci}} \tag{4}\]