Analytical Modeling of Wireless Communication Systems

2Hybrid Automata for Transient Delay Analysis

This chapter deals with hybrid automata (HA) [HEN 00] and their application to the study of wireless sensor networks (WSNs). The HA technique allows for a compact, clear description of the behavior of systems with both discrete and continuous components. In addition, it provides a detailed model that considers every possible evolution of the system, taking into account rare events that are difficult to be captured by simulation. Here, HA are used to perform a transient analysis of WNSs and investigate delay in reporting event detection [GRI 11]. In particular, by exploiting the properties of WSNs, it is possible to design an efficient solution algorithm that significantly reduces the complexity of the model and its solution time. The solution technique is supported by a tool, which converts HA into an equivalent discrete time Markov chain (DTMC).

Although being designed for the study of a WSN, the presented methodology has a general validity and can find application in different contexts.

2.1. Event detection in WSNs

Let us consider a WSN for event detection where every point of the monitored area is covered by k sensors. Upon an event occurrence, all the k nodes generate a detection report and try to send it to a central controller. Assume that the central controller detects an event if it receives m positive reports from different sensors (with m ≤ k), within a time interval of t_d seconds since the event occurrence. Note that setting ...