Hybrid Cyber Petri net Modelling, Simulation and Analysis of Master-Slave Charging for Wireless Rechargeable Sensor Networks

Wireless charging provides continuous energy for wireless sensor networks. However, it is difficult to replenish enough energy for all sensor nodes with fixed charging alone, and even more unrealistic to charge a large number of nodes within a short time via mobile charging. In order to overcome the above weaknesses, this paper firstly puts forward a Master-Slave Charging mode for the WRSN (Wireless Rechargeable Sensor Network), where fixed charging is the master mode and mobile charging is the slave mode, respectively. However, Master-Slave Charging is a typical hybrid system involving discrete event decision and continuous energy transfer. Therefore, the Hybrid Cyber Petri net system is proposed to build a visual specification with mathematical expression of Master-Slave Charging. Moreover, wireless charging in the WRSN is modeled and evaluated from the perspective of a hybrid system for the first time. Furthermore, a greedy-genetic algorithm is proposed to obtain the deployment of fixed chargers and the path planning of a mobile charger, by maximizing the actual electric quantity of the master charging problem and minimizing the mobile charger’s travelling path of the slave charging problem. Finally, the simulation results confirm and verify the Hybrid Cyber Petri net model for Master-Slave Charging. It is worth noting that the proposed model in this paper is highly adaptable to various charging modes in the WRSN.

Concurrency cannot be observed, asynchronously

The paper is devoted to an analysis of the concurrent features of asynchronous systems. A preliminary step is represented by the introduction of a non-interleaving extension of barbed equivalence. This notion is then exploited in order to prove thatconcurrency cannot be observedthrough asynchronous interactions, i.e., that the interleaving and concurrent versions of a suitable asynchronous weak equivalence actually coincide. The theory is validated on some case studies, related to nominal calculi (π-calculus) and visual specification formalisms (Petri nets). Additionally, we prove that a class of systems which is deemed (output-buffered) asynchronous, according to a characterization that was previously proposed in the literature, falls into our theory.