Rapid self-organised initiation of ad hoc sensor networks close above the percolation threshold

نویسنده

  • Reinert Korsnes
چکیده

This work shows potentials for rapid self-organisation of sensor networks where nodes collaborate to relay messages to a common data collecting unit (sink node). The study problem is, in the sense of graph theory, to find a shortest path tree spanning a weighted graph. This is a well-studied problem where for example Dijkstra’s algorithm provides a solution for non-negative edge weights. The present contribution shows by simulation examples that simple modifications of known distributed approaches here can provide significant improvements in performance. Phase transition phenomena, which are known to take place in networks close to percolation thresholds, may explain these observations. An initial method, which here serves as reference, assumes the sink node starts organisation of the network (tree) by transmitting a control message advertising its availability for its neighbours. These neighbours then advertise their current cost estimate for routing a message to the sink. A node which in this way receives a message implying an improved route to the sink, advertises its new finding and remembers which neighbouring node the message came from. This activity proceeds until there are no more improvements to advertise to neighbours. The result is a tree network for cost effective transmission of messages to the sink (root). This distributed approach has potential for simple improvements which are of interest when minimisation of storage and communication of network information are a concern. Fast organisation of the network takes place when the number k of connections for each node (degree) is close above its critical value for global network percolation and at the same time there is a threshold for the nodes to decide to advertise network route updates. 1 Transmission within sensor networks This contribution shows simulated examples of simple and rapid organisation of large ad hoc sensor networks [1]. The work may have direct interest for design and application of sensor networks. The present practical examples may also impact theoretical development [2] and have general interest for understanding network organisation outside the scope of sensor and computer networks. The present work is about minimisation of transmission power for sending messages between nodes in a sensor network. This is directly relevant for underwater sensor networks based on acoustic communication. Energy consumption ∗Norwegian Defence Research Establishment (FFI), Postboks 25, NO-2027 Kjeller, Norway 1 ar X iv :0 90 8. 32 31 v3 [ cs .N I] 1 9 M ay 2 01 0 for transmission in this case dominates total energy consumption and hence battery life time [3, ]. Rapid network organisation with a minimum of control traffic and low transmission power is a general protection measure for ad hoc sensor networks. The amount of control traffic and the level of transmission power directly affect the probability to discover and to map a sensor network from outside. Minimisation of storage of network information in nodes (k-local information) and low processing complexity is also a general protection measure reducing opportunities for malicious attacks. 2 The contribution of this work Assume a connected weighted graph (G = (V,E), ω) in the sense of graph theory. It is a well-studied problem to find the shortest path tree spanning such a graph [4, 5, 6, 7, 8]. Vertices (V ) are below called ’nodes’, edges (E) are called ’links’ and weights ω are called ’link cost’. This wording is due to the present focus on sensor networks. The present simulations demonstrate potentials for simple, fast, silent (few messages between nodes) and self-organised buildup of a spanning tree for efficient data relaying from any node (sensor) and to a common sink node (root). A point is also to minimise storage of network information in single nodes. Each node has (or can generate) an estimate of a cost (a real number) for transmitting a message back to a node from which it directly receives a message (for example a function of the ratio between received and transmitted energy assuming the node can measure the received effect and knows the initial output effect). The present simulations are for 4000 nodes with random positions within a flat (2d) square area of 4000×4000 m. The nodes can transmit messages to each other within a restricted range (assuming electromagnetic or acoustic communication). Each node X initially stores (for formal reasons) a cost estimate equal to infinity (C(X,S) =∞) for relaying a message to the sink node S. The sink node at first advertises to its neighbours a cost estimate equal zero for sending a messages to the sink (i.e. to itself). This gives cost estimates for the neighbours and which they further advertise to their neighbours. A node X, which in general receives a cost estimate form a neighbour N (which might be the sink), adds the received cost estimate from the sender plus a cost to transmit directly back to it. This gives a cost estimate to send a message to the sink. If this estimate represents an improved path to the sink (i.e. C(X,S) < C(X,N) + C(N,S)), it updates its cost estimate C(X,S) (setting its value to C(X,N) + C(N,S)). It then also sets a pointer E to point to the neighbour N (or E = (X,N)). In addition it advertises to its neighbours its latest improved cost estimate. This procedure proceeds until convergence, and the set of such pointers gives a shortest path tree spanning all nodes. The above method to find a covering minimum path length tree is wellknown. However, this work tests out the idea to do the following modifications to this approach: • Restrict the set of edges (neighbours) in the original network (subtract) to the nearest neighbours so that the network is close to loose its global connectivity. This means, in other words, that nodes ignore their most distant neighbours.

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عنوان ژورنال:
  • CoRR

دوره abs/0908.3231  شماره 

صفحات  -

تاریخ انتشار 2009