1202188
Load-Balancing Performance of Consistent Hashing: Asymptotic Analysis of Random Node Join
Balancing of structured peer-to-peer graphs, including their zone sizes, has recently become an important topic of distributed hash table (DHT) research. To bring analytical understanding into the various peer-join mechanisms based on consistent hashing, we study how zone-balancing decisions made during the initial sampling of the peer space affect the resulting zone sizes and derive several asymptotic bounds for the maximum and minimum zone sizes that hold with high probability. Several of our results contradict those of prior work and shed new light on the theoretical performance limitations of consistent hashing. We use simulations to verify our models and compare the performance of the various methods using the example of recently proposed de Bruijn DHTs.
8744802
On static and dynamic partitioning behavior of large-scale networks
In this paper, we analyze the problem of network disconnection in the context of large-scale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large variety of deterministic and random P2P graphs almost surely (i.e., with probability 1-o(1)) remain connected under random failure if and only if they have no isolated nodes. This simple, yet powerful, result subsequently allows us to derive in closed-form the probability that a P2P network develops isolated nodes, and therefore partitions, under both types of node failure. We finish the paper by demonstrating that our models match simulations very well and that dynamic P2P systems are extremely resilient under node churn as long as the neighbor replacement delay is much smaller than the average user lifetime
47232248
Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience
This paper examines graph-theoretic properties of existing peer-to-peer networks and proposes a new infrastructure based on optimal-diameter de Bruijn graphs. Since generalized de Bruijn graphs exhibit very short average distances and high resilience to node failure, they are well suited for distributed hash tables (DHTs). Using the example of Chord, CAN, and de Bruijn, we study the routing performance, graph expansion, clustering properties, and bisection width of each graph. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peer-to-peer structures, we offer a very simple incremental building process that preserves optimal properties of de Bruijn graphs under uniform user joins/departures. We call the combined peer-to-peer architecture optimal diameter routing infrastructure.
3413304
On Node Isolation Under Churn in Unstructured P2P Networks with Heavy-Tailed Lifetimes
Previous analytical studies [12], [18] of unstructured P2P resilience have assumed exponential user lifetimes and only considered age-independent neighbor replacement. In this paper, we overcome these limitations by introducing a general node-isolation model for heavy-tailed user lifetimes and arbitrary neighbor-selection algorithms. Using this model, we analyze two age-biased neighbor-selection strategies and show that they significantly improve the residual lifetimes of chosen users, which dramatically reduces the probability of user isolation and graph partitioning compared to uniform selection of neighbors. In fact, the second strategy based on random walks on age-weighted graphs demonstrates that for lifetimes with infinite variance, the system monotonically increases its resilience as its age and size grow. Specifically, we show that the probability of isolation converges to zero as these two metrics tend to infinity. We finish the paper with simulations in finite-size graphs that demonstrate the effect of this result in practice.
2819336
Optimal harvesting problems for an age-dependent n-dimensional food chain model with diffusion
We investigate the optimal harvesting problems of an age-dependent n-dimensional food chain model with spartially structured, which is controlled by harvesting. The existence and uniqueness of solution for the system are proven using Banach fixed-point theorem. We establish existence result of optimal control and necessary optimality conditions.
20162487
An efficient and scalable pairwise key pre-distribution scheme for sensor networks using deployment knowledge
Pairwise key establishment is a fundamental security service for sensor networks. However, establishing pairwise key in sensor networks is a challenging problem, particularly due to the resource constraints on sensor nodes and the threat of node compromises. On the other hand, adding new nodes to a sensor network is a fundamental requirement for their continuous operation over time, too. We analyze the weaknesses of security due to node capture when adding sensor nodes using key pre-distribution schemes with ''fixed'' key pools. In this paper, we propose a new approach, which separates the nodes into groups, the nodes in a group communicate with each other using pairwise keys pre-distributed, the communications between any two neighbor groups are accomplished also through pairwise keys, which is computed based on the pre-distributed Hash chain. We show that the performance (e.g. continuous connectivity, continuous network resilience against node capture and memory usage) of sensor networks can be substantially improved by using our scheme. The scheme and its detailed performance evaluation are presented.
41225271
On Internal Cardinal Direction Relations
Internal Cardinal Direction (ICD) relations can be considered as the refinement to the contains/within topological relation. It is widely used to describe the position of an object in a region. In this paper, three ICD models with varying degrees of details are presented – ICD-5, ICD-9 and ICD-13. In each of these, the notion of a “middle part” is defined using Minimum Bounding Rectangles (MBR). Then focusing on ICD-9, three representation methods are discussed. They are major portion, point set of intersections and proportions of intersections respectively. The ICD-9 model is validated by a cognitive experiment, which helped to determine the size of the middle part in ICD-9 and validate the MBR-based partition method. Based on a psychological theory about vague predicates, conceptual neighborhood and intersection of ICD relations are also discussed briefly.
122609601
Attractor dimension estimates for two-dimensional shear flows
Abstract We study the large time behavior of boundary and pressure-gradient driven incompressible fluid flows in elongated two-dimensional channels with emphasis on estimates for their degrees of freedom, i.e., the dimension of the attractor for the solutions of the Navier-Stokes equations. For boundary driven shear flows and flux driven channel flows we present upper bounds for the degrees of freedom of the form cα Re 3 2 where c is a universal constant, α denotes the aspect ratio of the channel (length/width), and Re is the Reynolds number based on the channel width and the imposed “outer” velocity scale. For fixed pressure gradient driven channel flows we obtain an upper bound of form c'α Re2, where c' is another universal positive constant and the Reynolds number is based on a velocity defined by the infimum, over all possible trajectories, of the time averaged mass flux per unit channel width. We discuss these results in terms of physical arguments based on small length scales in turbulent flows.
37286032
A Random Key Management Scheme for Wireless Sensor Networks
The establishment of shared keys between communicating neighbor nodes in wireless sensor networks is a challenge due to resource-constrained sensor networks. Several key pre-distribution schemes have been proposed in literatures to establish pairwise keys between sensor nodes. However, many of them are either too complicated to fit for wireless sensor networks or insecure for some common aggressions. In this paper, we propose a random key management scheme based on random key pre-distribution for wireless sensor networks. To achieve better performance and security, the proposed scheme employs two different phases to establish enhanced pairwise keys between neighboring nodes. Compared with other existing random key pre-distribution schemes, our scheme has better resilience against node capture and also performs better in terms of network connectivity and scalability with appropriate memory, computation and communication overheads.