Today's wireless sensor networks (WSN) focus on energy-efficiency as the main metric to optimize. However, an increasing number of scenarios where sensor networks are considered for time-critical purposes in application sce- narios like intrusion detection, industrial monitoring, or health care systems demands for an explicit support of per- formance guarantees in WSNs and, thus, in turn for a re- spective mathematical framework. In [1], a sensor network calculus was introduced in order to accommodate a worst- case analysis of WSNs. This sensor network calculus fo- cused on the communication aspect in WSNs, but had not yet a possibility to treat in-network processing in WSNs. In this work, we now incorporate in-network processing fea- tures as they are typical for WSNs by taking into account computational resources on the sensor nodes. Furthermore, we propose a simple, yet effective priority queue manage- ment discipline which achieves a good balance of response times across sensor nodes in the field.