Medidas para reducir diferencias entre los resultados experimentales y la

Reliable communication is preferred in most communication systems. Moreover, for some systems reliability is of great importance. In wireless communication, achieving reliable broadcast is more challenging than its wired counterpart as the wireless channel is prone to failures such as collision and interference.

In data dissemination, it is important that the new data is delivered to nodes in its entirety and without any bit changes. Since we focus on data dissemination protocols, the problem of reliable broadcast is relevant. We provide a brief survey here although the works assume permanent or Byzantine failures, where a node can fail in arbitrary ways and behave unusually [72].

The work proposed in [67] is one of the earliest work that deal with the broadcast problem in multihop radio networks. The authors propose fault-tolerant broadcast- ing algorithms and give algorithms’ asymptotic bounds on completion time. They assume permanent faulty nodes of unknown locations that do not receive and send messages.

In [65], the author shows that it is possible to obtain a reliable broadcast when- ever the number of Byzantine nodes, nodes which may behave arbitrarily, f, is no more than some value. This f is defined in terms of a communication range r. Moreover, the author shows that it is impossible to obtain reliable broadcast when f is bigger than some threshold value. The work assumes the existence of a pre- fixed time-slotted transmission schedule and everyone follows this schedule to avoid

collisions.

In [20], the authors improve on [65] by making possibility bounds tighter. In particular, it has been shown that it is possible to achieve reliable broadcast when the number of faulty(Byzantine) nodes is strictly less than the threshold value for which in [65] it is shown that it is impossible to achieve reliable broadcast.

In [66], unlike the previous work where there is no address spoofing and collision, the authors relaxed this assumption and showed that reliable broadcast is possible even in the presence of collisions and address spoofing as long as they are bounded and the number of faulty nodes is less than some threshold value.

In [18], the authors address the broadcast problem in the presence of Byzantine faults with faulty nodes having bounded number of messages mf. They show the

possibility of reliable broadcast whenever the number of messages,m, of the correct node is lower bounded by some value defined in terms of mf. They assume the

existence of a prefixed time-slotted schedule, but faulty nodes may not follow the schedule, thereby making collisions.

In [87], the authors propose a protocol which is safe, i.e., correct nodes do not download an incorrect message. The protocol guarantees this property whenever D≥H+ 2, whereDis the shortest distance between two Byzantine nodes andHis a protocol parameter which is assumed to be known by all correct nodes. The paper also discusses the possibility of reliable broadcast in the torus network whenever D ≥ 5 and H = 2. The same authors generalized this result to planar graphs in [88]. In particular, the authors show that for D > Z, where Z is the maximal number of edges per polygon, it is possible to achieve reliable broadcast.

System and Fault Model

In this chapter, we present the models under which our protocols are designed. In particular, we present what network types and faults we assume in our protocols.

3.1

Graphs and Networks

We define a wireless sensor node as a computing device equipped with a wireless interface and associated with a unique identifier. Communication in wireless net- works is typically modelled with a circular communication range centred on the node. With this model, a node is thought as able to exchange data with all devices within its communication range.

A wireless sensor network is a collection of wireless sensor nodes and is modelled as a directed graph G = (V, A), where V is the set of wireless sensor nodes of size

|V|, and Ais a set of arcs or directed links. Each directed link is an ordered pair of distinct nodes (m, n), meaning nodemcan communicate with noden. For a directed

link (m, n), we callnadownstream neighbourofm, andmanupstream neighbour of n. We denote byMdand Mu, the set ofm’s downstream and upstream neighbours,

respectively. We also assume that, for every node m, Md, Mu 6= ∅. Whenever we

say a node n sends a message, we mean n sends the message to its downstream neighbours, and when we saynreceives a message, we meannreceives the message from its upstream neighbours.

The d-hop neighbourhood of a node m, denoted by Md, is a set of nodes such that the length of the shortest path from m to a node in the set is at most d. We say that two nodes m andn can collide at nodep if (m, p),(n, p)∈A1.