Sensor networks play a central role in the Internet of things, which attracts lots of attentions recently. Mathematical models are of much help to explore intricate scheduling on the sensor node or interactions between different sensor nodes. Although many existing approaches have shown that the sensor network behaves like a hybrid system, where discrete character and continuous character exist together, few of them have attempted to consider two characters together. In this paper, we propose a novel quantitative modeling framework based on Fluid Stochastic Petri nets (FSPNs), and provide comprehensive theoretical analysis to a typical sensor network example. Our modeling framework, which combines advantages of both Stochastic Petri Nets (SPNs) and Hybrid Functional Petri Nets (HFPNs), reflects the hybrid nature of sensor networks, and at the same time eases the problem of state space explosion. The modeling mechanism proposed in this paper constructs sensor network models that are comprised of both stochastic processes and fluid flow approximation technique. From the evaluation, it's shown that the new method performs well.

In process mining research, process discovery techniques can produce or rebuild models with the information from logs. There are already algorithms supporting control-flow perspective mining which focus on the order of events and provide understanding workflow paths. But few of them take time perspective and path selection probabilities into consideration, which are important in performance evaluating, delay prediction, decision making, as well as process redesigning and optimizing. This paper provides a novel algorithm which determines the information of time perspective and selection probabilities from a log and integrates them with the control-flow perspective. By applying this algorithm, a stochastic Petri net is provided which is useful in performance analyzing and process optimizing.