18907580
A Tutorial on Some New Methods for Performance Evaluation of Queueing Networks
In the 1970's, Baskett, Chandy, Muntz and Palacios, Kelly, and others, generalized the earlier results of Jackson (1957) and obtained explicit solutions for the steady-state distributions of some restricted queueing networks. These queueing networks are called "product-form networks," due to the structure of their explicit solutions. The class of such tractable networks is quite small, however. For example, if customers require different mean service times on different revisits to the same server, or if customers on a later visit are given higher priority, then very little is known concerning whether the network is even stable or what form the steady-state distribution has if it exists. Recently, some new methods have been developed for establishing the stability of a system and for obtaining bounds on key performance measures such as mean delay, mean number in system, or mean throughput. Since they are based on the well-developed computational tool of linear programming, these methods can be widely employed in diverse applications in communication networks, computer systems, and manufacturing systems. We provide a tutorial exposition of some of these recent developments. >
999307
A counterexample in congestion control of wireless networks
One of the triumphs of wireline network research of the last decade has been the casting of the Internet congestion control problem within an optimization framework based on utility functions. Such an approach provides a sound understanding of the underlying stability and fairness issues, as well as a post-facto justification of TCP-like additive-increase multiplicative-decrease (AIMD) algorithms. This paper provides a counter-example showing that the same result cannot be extended to wireless networks, at least not in a straightforward manner.The fundamental difference is that wireless networks are of a broadcast nature. There is no strict notion of a "link," since transmissions from nearby nodes interfere with each other. Using a simple model of interference in wireless networks, a counter-example of a wireless network is presented in which the congestion control mechanism has an unstable equilibrium point at the desired fair solution. Further, ns-2 simulations of this counter-example manifest an oscillatory behavior. Surprisingly, this oscillatory behavior appears to be fairly typical in wireless networks, with most randomly chosen network examples manifesting it. This loss of stability suggests a possible need for the re-design of wireless TCP and wireless queue management to explicitly account for the wireless nature of the effects of interference. wireless interference can make this mechanism unstable. We present counter-example wireless graphs and flow patterns in which the congestion control mechanism fails to remain stable. ns-2 simulations indicate that this loss of stability manifests in practice as oscillatory behavior. Moreover, this oscillatory behavior is fairly typical in wireless networks. This loss of stability suggests a need for the re-design of wireless TCP and wireless queue management to explicitly account for the effects of interference.
63547373
The transport capacity of wireless networks over fading channels
We study the transport capacity of wireless networks with fading, in the high attenuation regime where either the medium is absorptive or the path loss exponent is greater than 3. For a network of n nodes we show that even were the states of all channels to be noncausally known a-priori, the transport capacity is no more than O(n). On the other hand, even when the channels are frequency selective and independent from time to time, G(n) is achievable through a multihop strategy
75138874
An achievable rate for the multiple level relay channel
This paper proposes a new coding scheme and proved a new achievable rate formula for the Gaussian case. The scheme is simpler and avoids some inconvenient techniques (e.g., the Slepian-Wolf partitioning), in giving the same achievable rate for the single relay case. More importantly, this new coding scheme is easier to extend to the multiple level relay case, and generally achieves higher rates. Here we present the results for the discrete memoryless case. The paper also goes on to obtain the capacity of some relay channels under fading, which is the first significant capacity result for such channels, and one, which may possibly constitute a breakthrough in the field.
8476709
On the /spl theta/-coverage and connectivity of large random networks
Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for /spl theta/-coverage is found for wireless networks modeled as n points uniformly distributed in a unit square, with every node connecting to its /spl phi//sub n/ nearest neighbors. A network is called /spl theta/-covered if every node, except those near the boundary, can find one of its /spl phi//sub n/ nearest neighbors in any sector of angle /spl theta/. For all /spl theta//spl isin/(0,2/spl pi/), if /spl phi//sub n/=(1+/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, it is shown that the probability of /spl theta/-coverage goes to one as n goes to infinity, for any /spl delta/>0; on the other hand, if /spl phi//sub n/=(1-/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, the probability of /spl theta/-coverage goes to zero. This sharp characterization of /spl theta/-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if /spl phi//sub n/=(1+/spl delta/)log/sub 2/n. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed.
6349082
The Number of Neighbors Needed for Connectivity of Wireless Networks
Unlike wired networks, wireless networks do not come with links. Rather, links have to be fashioned out of the ether by nodes choosing neighbors to connect to. Moreover the location of the nodes may be random.The question that we resolve is: How many neighbors should each node be connected to in order that the overall network is connected in a multi-hop fashion? We show that in a network with n randomly placed nodes, each node should be connected to Θ(log n) nearest neighbors. If each node is connected to less than 0.074log n nearest neighbors then the network is asymptotically disconnected with probability one as n increases, while if each node is connected to more than 5.1774log n nearest neighbors then the network is asymptotically connected with probability approaching one as n increases. It appears that the critical constant may be close to one, but that remains an open problem.These results should be contrasted with some works in the 1970s and 1980s which suggested that the “magic number” of nearest neighbors should be six or eight.
7166264
Minimal Tail-Biting Trellises for Certain Cyclic Block Codes Are Easy to Construct
We give simple algorithms for the construction of generator matrices for minimal tail-biting trellises for a powerful and practical subclass of the linear cyclic codes, from which the combinatorial representation in the form of a graph can be obtained by standard procedures.
150407
Infrastructure for the quantum internet
A team of researchers from the Massachusetts Institute of Technology (MIT) and Northwestern University (NU) is developing a system for long-distance, high- delity qubit tele-portation. Such a system will be required if future quantum computers are to be linked together into a quantum Internet. This paper presents recent progress that the MIT/NU team has made, beginning with a review of the teleportation architecture and its loss-limited performance analysis.
29567956
Curve reconstruction from noisy samples
359856
Curve reconstruction from noisy samples
We present an algorithm to reconstruct a collection of disjoint smooth closed curves from n noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation of each point in the normal direction with a magnitude smaller than the minimum local feature size. The reconstruction is faithful with a probability that approaches 1 as n increases.We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features.
15090068
A simple provable algorithm for curve reconstruction
We present an algorithm that provably reconstructs a curve in the framework introduced by Amenta, Bern and Eppstein. The highlights of the algorithm are: (i) it is simple, (ii) it requires a sampling density better than previously known, (iii) it can be adapted for curve reconstruction in higher dimensions straightforwardly.