Researchers use random graph models to analyze complex networks that have no centralized control such as the Internet, peer-to-peer systems, and mobile ad hoc networks. These models explain phenomena like phase changes, clustering, and scaling. It is necessary to understand these phenomena when designing systems where exact node configurations cannot be known in advance. This paper presents a method for analyzing random graph models that combine discrete mathematics and probability theory. A graph connectivity matrix is constructed where each matrix element is the Bernoulli probability that an edge exists between two given nodes. We show how to construct these matrices for many graph classes, and use linear algebra to analyze the connectivity matrix. We present an application that uses this approach to analyze network cluster self-organization for sensor network security. We conclude by discussing the use of these concepts in mobile systems design.
Designing secure sensor networks is difficult. We propose an approach that uses multicast communications and requires fewer encryptions than pairwise communications. The network is partitioned into multicast regions; each region is managed by a sensor node chosen to act as a keyserver. The keyservers solicit nodes in their neighborhood to join the local multicast tree. The keyserver generates a binary tree of keys to maintain communication within the multicast region using a shared key. Our approach supports a distributed key agreement protocol that identifies the compromised keys and supports membership changes with minimum system overhead. We evaluate the overhead of our approach by using the number of messages and encryptions to estimate power consumption. Using data from field tests of a military surveillance application, we show that our multicast approach needs fewer encryptions than pair-wise keying approaches. We also show that this scheme is capable of thwarting many common attacks.
In this paper, we study the efficacy of error control schemes for energy-efficient reliable delivery of large files (hundreds of GBs) over core optical networks. Specifically, we examine two schemes: automatic repeat request (ARQ), and hybrid ARQ (i.e. ARQ combined with forward error correction (FEC) capability). We focus on Reed-Solomon (RS) FEC codes (in hybrid ARQ) and propose a new model, incorporating different block sizes as well as code error-correction capability, to estimate the energy consumption for performing encoding and decoding operations in optical networks. The model considers the impact of varying pre-FEC bit-error rates (BER) of the optical channel, and the signal processing blocks used to implement RS codes. Our results show that when the pre-FEC channel BER is in excess of 10 −5 , hybrid ARQ offers better performance than ARQ in terms of energy efficiency. However, both hybrid ARQ and ARQ have similar performance under lower BER.
Abstract-In this paper, we perform analytical characterization of optical pulses propagating through a polarization-sensitive semiconductor optical amplifier (SOA). We derive analytical expressions for the carrier density, gain and phase evolution along the SOA and show how these expressions prove useful in optical signal processing applications. The propagation of counter-propagating pulses as well as pulse streams across SOAs have been analysed and expressions for energy gain have been derived in all these cases. We also show that our analytical results reduce to corresponding results of polarization insensitive SOAs already published. The analytical results are in excellent agreement with detailed numerical simulations done in MATLAB using the NIMROD portal. The analytical calculations lead to significant savings with regard to simulation time and processing capacity requirements. We further prove that the energy gain difference for counter-propagating pulse streams is directly proportional to the difference delay between in them and hence can be used as a measure of the delay difference. This theoretical result agrees well with experimental results.Index Terms-Analytical results, polarization sensitivity, semiconductor optical amplifier (SOA).
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