Published in IET Communications Received on 22nd March 2011 Revised on 9th February 2012 doi: 10.1049/iet-com.2011.0246 ISSN 1751-8628 Modelling and symmetry reduction of a target-tracking protocol using wireless sensor networks S. Bhatti 1 S. Memon 2 I.A. Jokhio 3 M.A. Memon 4 1 Department of Software Engineering, Mehran University of Engineering and Technology, Jamshoro, Pakistan 2 Department of Computer Systems Engineering, Mehran University of Engineering and Technology, Jamshoro, Pakistan 3 Department of Software Engineering, Mehran University of Engineering and Technology, Jamshoro, Pakistan 4 Department of Computer Science, Graduate School of Systems and Information Engineering, University of Tsukuba, Japan E-mail: sania.bhatti@faculty.muet.edu.pk Abstract: To achieve precise modelling of real-time systems stochastic behaviours are considered which lead towards probabilistic modelling. Probabilistic modelling has been successfully employed in wide array of application domains including, for example, randomised distributed algorithms, communication, security and power management protocols. This study is an improvement over our previous work, which was based on the probabilistic analysis of a cluster-based fault tolerant target-tracking protocol (FTTT) using only grid-based sensor nodes arrangement. Probabilistic modelling is chosen for the analysis of FTTT protocol to facilitate benefits of symmetry reduction in conjunction with modelling. It is believed that for the first time correctness of the simplified version of a target-tracking protocol is verified by developing its continuous-time Markov chain (CTMC) model using symbolic modelling language. The proposed probabilistic model of a target-tracking wireless sensor networks will help to analyse the phases of FTTT protocol on a limited scale with finite utilisation of time. There are three main contributions of this study; first consideration of synchronised events between the modules, second, random placement of sensor nodes is taken into account in addition to grid-based sensor node arrangement, third one is the reduction in state space size through symmetry reduction technique, which also facilitates to analyse a larger size network. Symmetry reduction on Probabilistic Symbolic Model (PRISM) checker models is performed by PRISM-symm and the generic representatives in PRISM (GRIP) tool. Modelling of FTTT protocol is proved better with the usage of PRISM-symm after comparing the results of PRISM model, PRISM-symm and GRIP. 1 Introduction The fault tolerant target-tracking (FTTT) protocol is introduced in [1]. The cluster-based network arrangement depending on the maintenance of member nodes related data is presented. It adapts a simple methodology of identifying redundant sensor nodes, which actually depends on the deployment of sensor nodes in the field. The redundant target information is avoided to send to the cluster heads, reducing overall traffic going towards the base station (BS). The clustering scheme assists in managing the member nodes of the faulty cluster heads as the fault-tolerant phase of the FTTT protocol. The redundancy reduction ensures the fault tolerance of sensor nodes without incurring extra cost as the final phase of the proposed protocol. In addition, the metrics to measure the usefulness of the proposed solution are mathematically derived. Probabilistic model checking is a powerful technique for exhaustive analysis of a formal model. The initial model checking of FTTT via PRISM is presented in [2] by placing limited number of sensor nodes at specific locations. The continuous-time Markov chain (CTMC) model of FTTT protocol is developed in PRISM and statistics related to cluster formation; redundancy reduction, target-tracking and fault tolerance are detailed. The FTTT protocol is analysed by finding: (i) the expected message transmission, (ii) the number of sensor nodes joining clusters, (iii) the number of overlapping sensor nodes, (iv) the tracking probability, (v) the energy consumption and (vi) the percentage of fault tolerance during the fault-tolerant phase of the FTTT protocol. The probabilistic modelling of FTTT is one of the practicable ways to comprehend the formal verification of the cluster-based wireless sensor network (WSN). The verification of specific probabilistic properties related to the FTTT protocol without considering the remedy of state space explosion problem is demonstrated in [2]. The ad hoc network arrangement, a practical approach is not considered because of the occurrence of state space explosion problem. This paper focuses on the improved model checking of FTTT protocol in which analysis is performed by considering synchronisation between modules and ad hoc network arrangement. Further analysis is performed by incorporating symmetry reduction feature provided with PRISM, as well as via GRIP tool and the results of three techniques are compared. The function of PRISM-symm is to construct symbolic representation for the unreduced IET Commun., pp. 1–7 1 doi: 10.1049/iet-com.2011.0246 & The Institution of Engineering and Technology 2012 www.ietdl.org