Algorithm and Formal Model of Recovering Network Connectivity in Battlefield Surveillance

Battlefield surveillance requires mission-critical operations and tasks which can effectively be performed using Wireless Sensor and Actor Networks (WSANs). We have used clustering approach for deployment of WSAN to minimize energy consumption and to limit the processing cost. The adverse environment conditions in battlefield may cause a loss of connectivity but there is a need of continuous flow of information in this application. Therefore an algorithm for network recovering is proposed. Firstly, graphical model of the system is presented using graph theory which is then transformed into a formal model by developing formal specification using Vienna Development Method-Specification Language (VDM-SL). Invariants and pre/post-conditions are defined for its validation. The correctness of the formal specification is assured by an analysis through VDM-SL toolbox.


Introduction
In recent years, army has started to take interest to use advance technologies for handling tactical tasks in a battlefield [1][2].In a battlefield, the environment may change rapidly but the soldiers need to be connected continuously to share information with each other and to take action collectively.Wireless Sensor and Actor Networks (WSANs) are used in various military applications as these are autonomous and are able to handle tactical tasks according to the environment [3].Therefore WSANs are used in this work for battlefield surveillance.In our previous work, an abstract model for battlefield surveillance was presented [4] but this work is mainly focused on recovering connectivity of the network in a battlefield.
WSANs consist of sensors and actors where sensors have limited capabilities as compared to actors in terms of power, communication and computation.The topology for clusterbased WSAN in a battlefield is shown in Fig. 1.Graphical way is used to describe the topology as it provides better and easier understanding.Graphical models are effective to represent networks as nodes, e.g., sensors or actors, are represented through vertices and communication between them can be modeled through edges.Most of the existing work on WSANs is based on simulations which have certain limitations.For example, simulations cannot be performed for the whole system and do not have an ability to prove correctness of a system completely.That is why formal methods are used here to minimize the limitations of simulations techniques.Formal methods are mathematical techniques used for developing specification of a system and verifying its properties.In this work, we have used Vienna Development Method-Specification Language (VDM-SL) [5] for specifying proposed algorithm for battlefield termed as Recovering Network Connectivity (RNC).VDM-SL Toolbox [6] is used for proving correctness of the algorithm.Rest of the paper is organized as follow: Section 2 discusses the relevant work in this area.The system model and proposed algorithm are presented in Section 3. Formal specification of the algorithm is described in Section 4. Finally, Section 5 concludes the paper with discussion.

Related Work
A group mobility model for battlefield to simulate behaviors of realistic soldiers and leader in the battlefield is presented in [1].The demand of autonomous sensors in battlefield is increased therefore this leads to the demand of localized and independ-ent energy harvesting capabilities for sensor nodes which are summarized in [7].An application of battlefield based on MANET is reviewed in [8] and compared with the two emerging commercial MANET scenarios, i.e., campus network and urban vehi-cle grid.Robots can provide better surveillance in battlefield in case of war.That is why different projects have been presented in using robots systems [9][10].Many methods are proposed to protect link failure in ad hoc networks as the movement of nodes is unpredictable due to dynamic topology.For example, to pre-dict partition and replication of services on the server nodes, a model is described in [11].Replication of data with dynamic deployment and network partitioning are discussed in [12], which increase overhead of memory and communication band-width.To overcome the limitations of simulations formal methods are used in this work.For various safety and mission critical systems, formal methods have been used [13].The algorithms are proposed for WSANs using Z notation in [14][15][16] and VDM-SL [17].

System Model and Algorithm
WSANs are deployed in pre-planned way in the form clusters.A cluster head exists in every cluster which collects information from the cluster and reports to the base station.If any node is lost from the cluster and network connectivity is lost, it is recovered from the highest degree neighbor.Then base station decides where and when to deploy a new node to replace the lost node.It is assumed that sensors, actors and a cluster head are mobile nodes while base station is assumed as static.It is assumed that every node has at least two and at most four neighbors.
The algorithm for recovering network connectivity is presented in Fig. 2. Sensors, actors and cluster heads are deployed in the form of clusters.Every node in a cluster is assumed to have minimum 2 and maximum four degrees (lines 1-7).Similar assumption is taken for the base stations (lines 8-9).In a cluster, sensors detect mines, enemy and other attacks and transmit information to actors.Actors fire gun, bomb and function as tank and transmit the information to the cluster head.The cluster head transmits the information to the base station (lines 10-18).In the battlefield, the nodes may fail which may result a loss of a path.The failure is detected by identifying the loss of path which implies the loss of connectivity in the network.The path may loss between any two sensors, any two actors or between sensor-actor (lines 19-25).The path may loss between sensor-cluster head, actor-cluster head, any two cluster heads, cluster head and base station or between any two base stations (lines 26-38).Initially, the connectivity is recovered by the neighbor of highest degree and then a new node is deployed to replace the failed node (lines 39-40).

Formal Specification
The proposed algorithm is transformed into formal specification using VDM-SL which is used as it is effective to specify the specification at detailed level.In the specification, various notations of VDM-SL are used, for example, sets, composite objects, numeric and quote types.
The specification consists of static and dynamic models.The static model includes definitions of composite objects.
Invariants are defined on composite objects to define the correct behavior.The dynamic model includes the definitions of state and operations.Invariants are defined on the state and pre/post conditions are defined on the operations for the correct execution.
In the model, four types of nodes are assumed, i.e., sensors, actors, gateways and base stations.The common fields among them are described in the Node object.The field nidt describes that every node has a unique identifier.The npwr represents the power set of the node.The field mobility is used to define mobility status of a node whether static or mobile.The npos is used because every node is deployed on a certain position.The field c_status shows the connectivity status of a node in the network.The variable battleinfo records whether the information is transmitted or received.In the definition of cluster head, crnode shows that a cluster head is assumed as a node.The field cmonitor represents that a cluster head monitors sensors and actors.The cc_ngbr shows the set of connected neighbor nodes.Invariants: (1) A communication link exists between any two sensors and actors in a cluster.(2) Sensor and actor are connected through a communication link.(3) A cluster head is connected with a sensor and an actor.(4) Every node in a cluster has minimum two and maximum four neighbors which show that there is no leaf node.A cluster is connected with a base station to disseminate the information.A base station is assumed as a node which is a set of nodes, and used to perform actions.The path may loss between a sensor and an actor which exhibits that either sensor or the actor is lost.(3) There may be two actors such that the path may loss between them.(4) The communication between an actor and a cluster head may loss due to loss of connectivity.(5) The path to communicate a cluster head with a base station may loss which shows that either the cluster head or the base station failed.(6) There may be two base stations which may loss from the network.(7) The network nodes are updated by removing the lost node.(8) The connectivity of sensor, actor, cluster head or base station may loss if they have no neighbor.(9) Communication links are updated by removing the lost link.The lost of connectivity is recovered as there is a need for continuous operation which is defined as RecoverNConnectivity.In this operation, recovered node and new node are returned while the lost connectivity and lost node are taken as input.is the body text with indent.This is the body text with indent.This is the body text with indent.This is the body text with indent.This is the body text with indent.This is the body text with indent.This is the body text with indent.This is the body text with indent.This is the body text with indent.
(i) This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.(ii) This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.(iii) This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.This is a list, note the hanging indent.

Conclusion
For battlefield surveillance, WSAN is used to provide better handling of complex tasks.This requires continuous connectivity of the network but harsh environment conditions in battlefield may cause a loss of connectivity.Therefore, a recovery algorithm using clustering approach is presented in this work.The clustering approach is used for increasing energy efficiency and minimizing processing cost.Graph theory is used for topological representation for its effectiveness of modeling networks.Formal methods are observed for correctness addressing limitations of simulations techniques.VDM-SL Toolbox is used for analyzing, validating and verifying the formal specification.
The syntactic and semantic correctness of the specification is ensured through syntax and type checkers of the toolbox.For providing assistance at the implementation level the equivalent C++ code is produced through C++ code generator.The pretty printer generated the specification which is useful for documentation.To identify run-time errors dynamic checking is used.The integrity examiner is used to visualize the formal specification in terms of predicates which are evaluated as true.
cngbrs : set of Node;Connectivity between the nodes is defined through communication links.Any two nodes connected by a link can communicate with each other.A node does not have connectivity with itself which represents that the network does not have a loop.
If the sensor node is lost then it is recovered by the highest degree neighbor.(2) The recovered sensor node must have neighbors greater than the minimum limit.(3) A new sensor is deployed with the passage of time.