In this paper, to analyze end-to-end timing behavior in heterogeneous processor and network environments accurately, we adopt 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 HSV_CC to automotive data stream management system (DSMSs), one must address three issues: (i) previous task and message schedules might lead to less efficient resource usages; (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.