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Analysis of Shortest Path Routing for Large Multi-Hop Wireless Networks
Analysis of Shortest Path Routing for Large Multi-Hop Wireless Networks

Abstract—In this paper, we analyze the impact of straight line routing in large homogeneous multi-hop wireless networks.We estimate the nodal load, which is defined as the number of packets
served at a node, induced by straight line routing. For a given total
offered load on the network, our analysis shows that the nodal load
at each node is a function of the node’s Voronoi cell, the node’s location in the network, and the traffic pattern specified by the source and destination randomness and straight line routing. In the
asymptotic regime, we show that each node’s probability that the node serves a packet arriving to the network approaches the products of half the length of the Voronoi cell perimeter and the load density function that a packet goes through the node’s location.
The density function depends on the traffic pattern generated by straight line routing, and determines where the hot spot is created in the network. Hence, contrary to conventional wisdom, straight line routing can balance the load over the network, depending on the traffic patterns.



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02-04-2010, 12:12 PM
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RE: Analysis of Shortest Path Routing for Large Multi-Hop Wireless Networks
Paradox of Shortest Path Routing for Large Multi-Hop Wireless Networks
In this article, the impact of straight
line routing in large homogeneous multi-hop wireless networks is analysed. the nodal load, is defined as the number of
packets served at a node. The nodal load induced by straight line routing is calculated first. Nodal load at each node is a function of:
a) the node’s Voronoi cell,
b)the node’s location in the network, and
c)the traffic pattern specified by the source and destination randomness and
d)straight line routing for a given total offered load on the network.

INTRODUCTION
a significant amount of interest in the study of ad-hoc and sensor networks has been witnessed in the recent years. The ad-hoc networks can use other nodes as relays to deliver data from different sources to destinations.
The relaying functionality makes these “multi-hop” wireless networks scalable and applicable in a variety of different areas. The analysis of network performance of multi-hop networks is made complex by the relaying functionality. Congestion in the hot-spot
areas could also reduce the overall capacity of the wireless
network. In random
networks with power control the load induced by relaying
traffic can be reduced.

SYSTEM MODELS:
a multi-hop wireless network is modeled as a directed graph G. It is a function of the the set of nodes and the set of edges in the network. radius of the disk be assumed as one for simplicity. Each node can control its transmission range. It s assumed that the number of nodes is large enough and that
their maximum coverage areas are overlapped in a way in
which the unit disk is entirely covered by the nodes’ maximum
transmission coverage.the nodes are
totally connected. a logical Voronoi tessellation is defined over the unit disk For a given deployment of nodes on a disk.

refer this pdf for more on this topic:


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