Performance Evaluation of Distance-Hop Proportionality on Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approach- ing unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c q ln n n . We show that, for a given hop distance h of a node from a fixed anchor on the unit square,the Euclidean distance lies within [(1−ǫ)(h−1)r(n), hr(n)],for ǫ > 0, with probability approaching unity as n → ∞.This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this an- nulus centred at the anchor location, and of width roughly r(n), rather than close to a circle whose radius is exactly proportional to h. We show that if the radius r of the ge- ometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that il- lustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.

Voltage and Temperature Scalable Standard Cell Leakage Models Based on Stacks for Statistical Leakage Characterization

With extensive use of dynamic voltage scaling (DVS) there is increasing need for voltage scalable models. Similarly, leakage being very sensitive to temperature motivates the need for a temperature scalable model as well. We characterize standard cell libraries for statistical leakage analysis based on models for transistor stacks. Modeling stacks has the advantage of using a single model across many gates there by reducing the number of models that need to be characterized. Our experiments on 15 different gates show that we needed only 23 models to predict the leakage across 126 input vector combinations. We investigate the use of neural networks for the combined PVT model, for the stacks, which can capture the effect of inter die, intra gate variations, supply voltage(0.6-1.2 V) and temperature (0 - 100degC) on leakage. Results show that neural network based stack models can predict the PDF of leakage current across supply voltage and temperature accurately with the average error in mean being less than 2% and that in standard deviation being less than 5% across a range of voltage, temperature.

Voltage and Temperature Scalable Gate Delay and Slew Models Including Intra-Gate Variations

We investigate the feasibility of developing a comprehensive gate delay and slew models which incorporates output load, input edge slew, supply voltage, temperature, global process variations and local process variations all in the same model. We find that the standard polynomial models cannot handle such a large heterogeneous set of input variables. We instead use neural networks, which are well known for their ability to approximate any arbitrary continuous function. Our initial experiments with a small subset of standard cell gates of an industrial 65 nm library show promising results with error in mean less than 1%, error in standard deviation less than 3% and maximum error less than 11% as compared to SPICE for models covering 0.9- 1.1 V of supply, -40degC to 125degC of temperature, load, slew and global and local process parameters. Enhancing the conventional libraries to be voltage and temperature scalable with similar accuracy requires on an average 4x more SPICE characterization runs.

Voltage and Temperature Scalable Gate Delay and Slew Models Including Intra-Gate Variations

We investigate the feasibility of developing a comprehensive gate delay and slew models which incorporates output load, input edge slew, supply voltage, temperature, global process variations and local process variations all in the same model. We find that the standard polynomial models cannot handle such a large heterogeneous set of input variables. We instead use neural networks, which are well known for their ability to approximate any arbitrary continuous function. Our initial experiments with a small subset of standard cell gates of an industrial 65 nm library show promising results with error in mean less than 1%, error in standard deviation less than 3% and maximum error less than 11% as compared to SPICE for models covering 0.9- 1.1 V of supply, -40degC to 125degC of temperature, load, slew and global and local process parameters. Enhancing the conventional libraries to be voltage and temperature scalable with similar accuracy requires on an average 4x more SPICE characterization runs.

A comparative study of ordinary kriging and support vector machine models for the spatial variability of rock depth in Bangalore

In this paper, reduced level of rock at Bangalore, India is arrived from the 652 boreholes data in the area covering 220 sq.km. In the context of prediction of reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth, ordinary kriging and Support Vector Machine (SVM) models have been developed. In ordinary kriging, the knowledge of the semivariogram of the reduced level of rock from 652 points in Bangalore is used to predict the reduced level of rock at any point in the subsurface of Bangalore, where field measurements are not available. A cross validation (Q1 and Q2) analysis is also done for the developed ordinary kriging model. The SVM is a novel type of learning machine based on statistical learning theory, uses regression technique by introducing e-insensitive loss function has been used to predict the reduced level of rock from a large set of data. A comparison between ordinary kriging and SVM model demonstrates that the SVM is superior to ordinary kriging in predicting rock depth.

Modeling Architecture-OS interactions using Layered Queuing Network Models

The prevalent virtualization technologies provide QoS support within the software layers of the virtual machine monitor(VMM) or the operating system of the virtual machine(VM). The QoS features are mostly provided as extensions to the existing software used for accessing the I/O device because of which the applications sharing the I/O device experience loss of performance due to crosstalk effects or usable bandwidth. In this paper we examine the NIC sharing effects across VMs on a Xen virtualized server and present an alternate paradigm that improves the shared bandwidth and reduces the crosstalk effect on the VMs. We implement the proposed hardwaresoftware changes in a layered queuing network (LQN) model and use simulation techniques to evaluate the architecture. We find that simple changes in the device architecture and associated system software lead to application throughput improvement of up to 60%. The architecture also enables finer QoS controls at device level and increases the scalability of device sharing across multiple virtual machines. We find that the performance improvement derived using LQN model is comparable to that reported by similar but real implementations.

An optimal weighted-average congestion based pricing scheme for enhanced QoS, , LNCS 4882, 2007

Pricing is an effective tool to control congestion and achieve quality of service (QoS) provisioning for multiple differentiated levels of service. In this paper, we consider the problem of pricing for congestion control in the case of a network of nodes under a single service class and multiple queues, and present a multi-layered pricing scheme. We propose an algorithm for finding the optimal state dependent price levels for individual queues, at each node. The pricing policy used depends on a weighted average queue length at each node. This helps in reducing frequent price variations and is in the spirit of the random early detection (RED) mechanism used in TCP/IP networks. We observe in our numerical results a considerable improvement in performance using our scheme over that of a recently proposed related scheme in terms of both throughput and delay performance. In particular, our approach exhibits a throughput improvement in the range of 34 to 69 percent in all cases studied (over all routes) over the above scheme.

Faster algorithms for all-pairs small stretch distances in weighted graphs

Abstract. Let G = (V,E) be a weighted undirected graph, with non-negative edge weights. We consider the problem of efficiently computing approximate distances between all pairs of vertices in G. While many efficient algorithms are known for this problem in unweighted graphs, not many results are known for this problem in weighted graphs. Zwick [14] showed that for any fixed ε> 0, stretch 1 1 + ε distances between all pairs of vertices in a weighted directed graph on n vertices can be computed in Õ(n ω) time, where ω < 2.376 is the exponent of matrix multiplication and n is the number of vertices. It is known that finding distances of stretch less than 2 between all pairs of vertices in G is at least as hard as Boolean matrix multiplication of two n×n matrices. It is also known that all-pairs stretch 3 distances can be computed in Õ(n 2) time and all-pairs stretch 7/3 distances can be computed in Õ(n 7/3) time. Here we consider efficient algorithms for the problem of computing all-pairs stretch (2+ε) distances in G, for any 0 < ε < 1. We show that all pairs stretch (2 + ε) distances for any fixed ε> 0 in G can be computed in expected time O(n 9/4 logn). This algorithm uses a fast rectangular matrix multiplication subroutine. We also present a combinatorial algorithm (that is, it does not use fast matrix multiplication) with expected running time O(n 9/4) for computing all-pairs stretch 5/2 distances in G. 1