In this paper, to analyze end-to-end timing behavior in heterogeneous processor and network environments accurately, we adopt and modify a heterogeneous selection value on communication contention (HSV CC) algorithm, which can synchronize tasks and messages simultaneously, for stream processing distribution. In order to adapt the concepts of a static algorithm like HSV CC to automotive data stream management system (DSMSs), one must first address three issues: (i) previous task and message schedules might lead to less efficient resource usages in this scenario; (ii) the conventional method to determine the task scheduling order may not be best suited to deal with stream processing graphs, and; (iii) there is a need to be able to schedule tasks with time-varying computational requirements efficiently. To address (i), we propose the heterogeneous value with load balancing and communication contention (HVLB CC) (A) algorithm, which considers load balancing in addition to the parameters considered by the HSV CC algorithm. We propose HVLB CC (B) to address issue (ii). HVLB CC (B) can deal with stream processing task graphs and more various directed acyclic graphs to prevent assigning a higher priority to successor tasks. In addition, to address issue (iii), we propose HVLB CC IC. To schedule tasks more efficiently with various computation times, HVLB CC IC utilizes schedule holes left in processors. These idle time slots can be used for the execution of an optional part to generate more precise data results by applying imprecise computation models. Experimental results demonstrate that the proposed algorithms improve minimum schedule length, accuracy, and load balancing significantly compared to the HSV CC algorithm. In addition, the proposed HVLB CC (B) algorithm can schedule more varied task graphs without reducing performance, and, using imprecise computation models, HVLB CC IC yields higher precision data than HVLB CC without imprecise computation models.