On the Fluid Limits of Some Loss Networks

We study the fluid limits of loss networks under Kelly's scaling. In the case of heavy traffic for a single node and J classes of calls, we prove a degenerate diffusion approximation theorem around the corresponding fluid limit. After a careful analysis of some reflected random walks in N, we prove that Hunt and Kurtz's conjecture (1994) for the trunk reservation policy is wrong. We conclude with some remarks on the conjecture in the case of an uncontrolled network

Using natural means to reduce surface transport noise during propagation outdoors

This paper reviews ways of reducing surface transport noise by natural means. The noise abatement solutions of interest can be easily (visually) incorporated in the landscape or help with greening the (sub)urban environment. They include vegetated surfaces (applied to faces or tops of noise walls and on building façades and roofs ), caged piles of stones (gabions), vegetation belts (tree belts, shrub zones and hedges), earth berms and various ways of exploiting ground-surface-related effects. The ideas presented in this overview have been tested in the laboratory and/or numerically evaluated in order to assess or enhance the noise abatement they could provide. Some in-situ experiments are discussed as well. When well-designed, such natural devices have the potential to abate surface transport noise, possibly by complementing and sometimes improving common (non-green) noise reducing devices or measures. Their applicability strongly depends on the available space reserved for the noise abatement and the receiver position

Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

Development and application of a clothed thermoregulatory model

Mathematical models of human thermoregulation can be used to assess the habitability of thermal environments prior to human exposure. Work continues to improve the performance of these models to reduce concerns surrounding the accuracy of their predictions. The aims of this thesis were to develop an existing thermoregulatory model (LUT25-node model). The developments made to the LUT25-node model, now enable it to predict the thermal responses of heat acclimated subjects of differing size, while its clothing model was improved to consider the addition and distribution of clothing properties. Validations of these modifications, confirmed that predictions from the model were improved. The thesis also looks at practical applications of the LUT25-node model. This included a modification to the model enabling backward modelling; predicting how the thermal stress should be altered to achieve a desired limit of thermal strain. Several hypothetical scenarios illustrated the practical applications of this modification. In addition, the LUT25-node model was used to explain the initial drop in deep body temperature at the onset of exercise. This investigation concluded that the temperature drop is due to the return of cool blood to the body core from initially cool working muscles. Finally, the poor predictions of the LUT25-node model for cold exposures was investigated. Previous investigators suspected that this was due to the limited number of thermal layers in the body segments of the model. However, predictions from a multi-layered LUT25-node model, developed with the finite volume software package PHOENICS, suggest that increasing the number of thermal layers reduces the accuracy of the model's predictions for cold exposures. In conclusion, this thesis has contributed to the continued development of a human thermoregulatory model and illustrated its practical benefits. It is recommended that future work centres on addressing additional limitations of the LUT25-node model identified in this study

University of Michigan Undergraduate Research Journal, Issue 7, Winter 2010

Articlehttp://deepblue.lib.umich.edu/bitstream/2027.42/97002/1/UMURJ-Issue07_2010.pd

Impact of Mobility and Wireless Channel on the Performance of Wireless Networks

This thesis studies the impact of mobility and wireless channel characteristics, i. e. , variability and high bit-error-rate, on the performance of integrated voice and data wireless systems from network, transport protocol and application perspectives. From the network perspective, we study the impact of user mobility on radio resource allocation. The goal is to design resource allocation mechanisms that provide seamless mobility for voice calls while being fair to data calls. In particular, we develop a distributed admission control for a general integrated voice and data wireless system. We model the number of active calls in a cell of the network as a Gaussian process with time-dependent mean and variance. The Gaussian model is updated periodically using the information obtained from neighboring cells about their load conditions. We show that the proposed scheme guarantees a prespecified dropping probability for voice calls while being fair to data calls. Furthermore, the scheme is stable, insensitive to user mobility process and robust to load variations. From the transport protocol perspective, we study the impact of wireless channel variations and rate scheduling on the performance of elastic data traffic carried by TCP. We explore cross-layer optimization of the rate adaptation feature of cellular networks to optimize TCP throughput. We propose a TCP-aware scheduler that switches between two rates as a function of TCP sending rate. We develop a fluid model of the steady-state TCP behavior for such a system and derive analytical expressions for TCP throughput that explicitly account for rate variability as well as the dependency between the scheduler and TCP. The model is used to choose RF layer parameters that, in conjunction with the TCP-aware scheduler, improve long-term TCP throughput in wireless networks. A distinctive feature of our model is its ability to capture variability of round-trip-time, channel rate and packet error probability inherent to wireless communications. From the application perspective, we study the performance of wireless messaging systems. Two popular wireless applications, the short messaging service and multimedia messaging service are considered. We develop a mathematical model to evaluate the performance of these systems taking into consideration the fact that each message tolerates only a limited amount of waiting time in the system. Using the model, closed-form expressions for critical performance parameters such as message loss, message delay and expiry probability are derived. Furthermore, a simple algorithm is presented to find the optimal temporary storage size that minimizes message delay for a given set of system parameters

Acoustical Exploitation of Rough, Mixed Impedance and Porous Surfaces Outdoors

This thesis is a contribution towards developing cost-effective ways for reducing outdoor traffic noise in outdoor environments by exploiting the interaction between sound travelling directly to a listener from the source and sound reflected by the intervening ground. Sound propagation over different kinds of porous, rough and mixed impedance ground surfaces have been studied experimentally and numerically. Measurements of short-range acoustic level difference spectra over outdoor ground surfaces and artificially-created surfaces outdoors and in the laboratory have been compared with predictions to establish suitable impedance models. Sound propagation over mixed impedance ground having single or multiple impedance discontinuities has also been studied. Acoustic transmission loss through vegetation, crops and hedges has been investigated. The phenomenon of sound diffraction and periodicity due to rough periodic ground surfaces has been explored through artificially created rough surfaces in the laboratory and outdoors. The phenomenon of surface wave propagation over rough hard surfaces and porous surfaces has been explored through laboratory experiments. Measured data indoors and outdoors have been used to validate numerical (BEM and FEM), empirical and analytical (MST) prediction techniques. The validated numerical methods have been used to make predictions at scales suitable for attenuating traffic noise by means of carefully designed ground treatments. The work has also been extended to railway and tramway noise. It has been found that replacing hard ground with porous ground, introducing single or multiple impedance discontinuities, growing vegetation and introducing low height roughness can all contribute between 3 and 15 dB additional attenuation of traffic noise. In respect of replacing hard ground by porous ground, it is concluded that the ground with lowest flow resistivity i.e. grassland left untouched and allowed to grow wild gives the best attenuation performance. However, dividing a single width of soft ground into alternating strips of hard and soft surfaces does not improve the insertion loss. The overall width of the soft surface is the main factor. Cultivating crops over porous ground can enhance the attenuation but the effect is not very significant for A-weighted levels as most of additional attenuation occurs at higher frequencies above 3 kHz. A 0.3 m high and at least 3 m wide lattice structure design is found to be very useful for traffic noise attenuation since it offers greater insertion loss than the same width and height of parallel low walls and the resulting attenuation is azimuthal angle independent. It has been shown also that the potentially negative effect on insertion loss due to propagation of roughness-induced surface waves over rough surfaces can be reduced by introducing sound absorbing material in between the walls