Pricing a Shared Access Link for Fair and Efficient Operation with Variable User Data Rates

The literature on pricing implicitly assumes an "infinite data" model, in which sources can sustain any data rate indefinitely. We assume a more realistic "finite data" model, in which sources occasionally run out of data; this leads to variable user data rates. Further, we assume that users have contracts with the service provider, specifying the rates at which they can inject traffic into the network. Our objective is to study how prices can be set such that a single link can be shared efficiently and fairly among users in a dynamically changing scenario where a subset of users occasionally has little data to send. User preferences are modelled by concave increasing utility functions. Further, we introduce two additional elements: a convex increasing disutility function and a convex increasing multiplicative congestion-penally function. The disutility function takes the shortfall (contracted rate minus present rate) as its argument, and essentially encourages users to send traffic at their contracted rates, while the congestion-penalty function discourages heavy users from sending excess data when the link is congested. We obtain simple necessary and sufficient conditions on prices for fair and efficient link sharing; moreover, we show that a single price for all users achieves this. We illustrate the ideas using a simple experiment.

Resource Pricing for Fair and Efficient Link Sharing with a Finite Data Model

The literature on pricing implicitly assumes an "infinite data" model, in which sources can sustain any data rate indefinitely. We assume a more realistic "finite data" model, in which sources occasionally run out of data. Further, we assume that users have contracts with the service provider, specifying the rates at which they can inject traffic into the network. Our objective is to study how prices can be set such that a single link can be shared efficiently and fairly among users in a dynamically changing scenario where a subset of users occasionally has little data to send. We obtain simple necessary and sufficient conditions on prices such that efficient and fair link sharing is possible. We illustrate the ideas using a simple example

Thermal Weight Functions and Stress Intensity Factors for Bonded Dissimilar Media Using Body Analogy

In this study, an analytical method is presented for the computation of thermal weight functions in two dimensional bi-material elastic bodies containing a crack at the interface and subjected to thermal loads using body analogy method. The thermal weight functions are derived for two problems of infinite bonded dissimilar media, one with a semi-infinite crack and the other with a finite crack along the interface. The derived thermal weight functions are shown to reduce to the already known expressions of thermal weight functions available in the literature for the respective homogeneous elastic body. Using these thermal weight functions, the stress intensity factors are computed for the above interface crack problems when subjected to an instantaneous heat source.

Solute solute and solvent solute interactions in solid solutions of Cu+Sn, Au+Sn and Cu+Au+Sn alloys

The chemical potentials of tin in its α-solid solutions with Cu, Au and Cu + Au alloys have been measured using a gas-solid equilibration technique. The variation of the excess chemical potential of tin with its composition in the alloy is related to the solute-solute repulsive interaction, while the excess chemical potential at infinite dilution of the solute is a measure of solvent-solute interaction energies. It is shown that solute-solute interaction is primarily determined by the concentration of (s + p) electrons in the conduction band, although the interaction energies are smaller than those predicted by either the rigid band model or calculation based on Friedel oscillations in the potential function. Finally, the variation of the solvent-solute interaction with solvent composition in the ternary system can be accounted for in terms of a quasi-chemical treatment which takes into account the clustering of the solvent atoms around the solute.

Analysis of a linear one-dimensional active noise control system by means of block diagrams and transfer functions

In arriving at the ideal filter transfer function for an active noise control system in a duct, the effect of the auxiliary sources (generally loudspeakers) on the waves generated by the primary source has invariably been neglected in the existing literature, implying a rigid wall or infinite impedance. The present paper presents a fairly general analysis of a linear one-dimensional noise control system by means of block diagrams and transfer functions. It takes into account the passive as well as active role of a terminal primary source, wall-mounted auxiliary source, open duct radiation impedance, and the effects of mean flow and damping. It is proved that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against an anechoic termination and the other by reflecting the rearward wave (incident on the source) off the passive source impedance. Application of this concept is illustrated for both the types of sources. A concise closed-form expression for the ideal filter transfer function is thus derived and discussed. Finally, the dynamics of an adaptive noise control system is discussed briefly, relating its standing-wave variables and transfer functions with those of the progressive-wave model presented here.

Extending the Supramolecular Synthon Based Fragment Approach (SBFA) for Transferability of Multipole Charge Density Parameters to Monofluorobenzoic Acids and their Cocrystals with Isonicotinamide: Importance of C-H center dot center dot center dot O, C-H center dot center dot center dot F, and F center dot center dot center dot F Intermolecular Regions

An extension of the supramolecular synthon-based fragment approach (SBFA) method for transferability of multipole charge density parameters to include weak supramolecular synthons is proposed. In particular, the SBFA method is applied to C-H center dot center dot center dot O, C-H center dot center dot center dot F, and F center dot center dot center dot F containing synthons. A high resolution charge density study has been performed on 4-fluorobenzoic acid to build a synthon library for C-H center dot center dot center dot F infinite chain interactions. Libraries for C-H center dot center dot center dot O and F center dot center dot center dot F synthons were taken from earlier work. The SBFA methodology was applied successfully to 2- and 3-fluorobenzoic acids, data sets for which were collected in a routine manner at 100 K, and the modularity of the synthons was demonstrated. Cocrystals of isonicotinamide with all three fluorobenzoic acids were also studied with the SBFA method. The topological analysis of inter- and intramolecular interaction regions was performed using Bader's AIM approach. This study shows that the SBFA method is generally applicable to generate charge density maps using information from multiple intermolecular regions.

Additions to the z transform table

The ztransform method is a widely used tool for the analysis and synthesis of discrete systems. In this note a table of ztransform pairs when F(z) is an irrational function of z is given. The table is also useful for obtaining closed-form sums for some infinite series.

Topological analysis of general linear networks

A new method of network analysis, a generalization in several different senses of existing methods and applicable to all networks for which a branch-admittance (or impedance) matrix can be formed, is presented. The treatment of network determinants is very general and essentially four terminal rather than three terminal, and leads to simple expressions based on trees of a simple graph associated with the network and matrix, and involving products of low-order, usually(2 times 2)determinants of tree-branch admittances, in addition to tree-branch products as in existing methods. By comparison with existing methods, the total number of trees and of tree pairs is usually considerably reduced, and this fact, together with an easy method of tree-pair sign determination which is also presented, makes the new method simpler in general. The method can be very easily adapted, by the use of infinite parameters, to accommodate ideal transformers, operational amplifiers, and other forms of network constraint; in fact, is thought to be applicable to all linear networks.

Matrix Processors Using p-adic Arithmetic for Exact Linear Computations

A unique code (called Hensel's code) is derived for a rational number by truncating its infinite p-adic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure.

Improvement of power-system transient stability by phase-shift insertion

Computational studies of the transient stability of a synchronous machine connected to an infinite busbar by a double-circuit transmission line are used to illustrate the effect of relative phase-shift insertion between the machine and its associated power system. This method of obtaining a change in the effective rotor-excitation angle, and thereby the power transfer, is described, together with an outline of possible methods of implementation by a phase-shifting transformer in a power system.

Monte Carlo simulation of polytypes

Based on the analogy between polytypes and spin-half Ising chains with competing short- and infinite-range interactions, a Monte Carlo simulation of polytypes has been attempted. A general double-layer mechanism connects different states of the polytype chain with about the same probability as the spin-flip mechanism in magnetic Ising chains. It has been possible to simulate various polytypes with periodicities extending up to 12 layers. The Monte Carlo method should be useful in testing different interaction models that may be proposed in the future to describe polytypism.

On porous wave maker problems

The problem of generation of surface water waves at tile interface of two immiscible liquids by a onesided porous wave maker is studied in both the cases of water of infinite as well as finite depth by suitable application of the generalisation of Havelock's expansion theorem. The solution of the the problem of reflection of water waves due to a fixed porous wall is derived as a particular case.

A Revisit to Capture the Entire Behavior of Ultrasonic Wave Dispersion Characteristics of Single Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory and Flugge Shell Model

In this paper, an ultrasonic wave propagation analysis in single-walled carbon nanotube (SWCNT) is re-studied using nonlocal elasticity theory, to capture the whole behaviour. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The revisited nonlocal elasticity calculation shows that the wavenumber tends to infinite at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. This frequency is termed as escape frequency. This behavior is observed only for axial and radial waves in SWCNT. It has been shown that the circumferential waves will propagate dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the explicit expressions of cut-off frequency depend on the nonlocal scaling parameter and the axial wavenumber. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTs is also discussed. The present results are compared with the corresponding results (for first mode) obtained from ab initio and 3-D elastodynamic continuum models. The acoustic phonon dispersion relation predicted by the present model is in good agreement with that obtained from literature. The results are new and can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Thermal Management of Electronics Using PCM-Based Heat Sink Subjected to Cyclic Heat Load

Designing a heat sink based on a phase change material (PCM) under cyclic loading is a critical issue. For cyclic operation, it is required that the fraction of the PCM melting during the heating cycle should completely resolidify during the cooling period, so that that thermal storage unit can be operated for an unlimited number of cycles. Accordingly, studies are carried out to find the parameters influencing the behavior of a PCM under cyclic loading. A number of parameters are identified in the process, the most important ones being the duty cycle and heat transfer coefficient (h) for cooling. The required h or the required cooling period for complete resolidification for infinite cyclic operation of a conventional PCM-based heat sink is found to be very high and unrealistic with air cooling from the surface. To overcome this problem, the conventional design is modified where h and the area exposed to heat transfer can be independently controlled. With this arrangement, the enhanced area provided for cooling keeps h within realistic limits. Analytical investigation is carried out to evaluate the thermal performance of this modified PCM-based heat sink in comparison to those with conventional designs. Experiments are also performed on both the conventional and the modified PCM-based heat sinks to validate the new findings.

Unified Dispersion Characteristics of Structural Acoustic Waveguides

In this article, we show with some formalism that infinite flexible structural acoustic waveguides have a general form for the dispersion equation. The dispersion equation of all such waveguides should conform to a generic form. This allows us to bring out the common features of structural acoustic waveguides. We take three examples to demonstrate this fact, namely, the rectangular, the circular cylindrical and the elliptical geometries. Where necessary, the equations are simplified for applicability to a particular frequency-regime before demonstrating the conformance to the generic form of the dispersion relation. It is then shown that the coupled wavenumber solutions of all these systems can be represented on a single schematic.