Importance sampling for the estimation of buffer overflow probabilities via trace-driven simulations

We develop an importance sampling technique that can be used to speed up the simulation of a model of a buffered communication multiplexer fed by a large number of independent sources. The sources generate traffic according to a periodic function with a random phase. This traffic model accommodates a wide range of situations of practical interest, including ON-OFF periodic traffic models and sequences of bit rates generated by actual variable bit rate sources, such as MPEG video compressors. The simulation seeks to obtain estimates for the buffer overflow probability that in most cases of interest is very small. We use a large deviations result to devise the change of measure used in the importance sampling technique and demonstrate through numerical results that this change of measure leads to a dramatic reduction in the required simulation time over direct Monte Carlo simulation. Possible practical applications include short-term network resource planning and even real-time call admission control.     

Parametric linear programming techniques for the indefnite quadratic programming problem

In this paper, we discuss a multiparametric technique for findinga global minimum for an indefinite quadratic programming problembased on the spectral decomposition of the matrix of the quadraticform. Special attention is given to the case where this matrixhas only rank 1, where the multiparametric linear program turnsout to be a single-parameter linear program. An extension ofthe traditional linear parametric procedure is introduced whichin general solves this problem efficiently. However, an exampleis presented showing that this technique may take an exponentialnumber of steps.     

Optimal repair-cost limit for a consumer following expiry of a warranty

This paper develops a methodology for obtaining the optimalrepair-cost limit for the repair-replace decision that a consumerfaces on the expiry of a product warranty, where the producthas been minimally repaired on failure during the warranty.Three cases are considered; (i) an exponentially distributedtime to failure with an arbitrary repair-cost distribution,(ii) an exponentially distributed time to failure with a uniformrepair-cost distribution, and (iii) a Weibull-distributed timeto failure with a beta-distributed repair cost. Numerical optimizationsare performed for the third case, and conclusions drawn as tothe sensitivity of the optimal repair-cost limit on the parametervalues of the distributions involved.     

Data-adaptive evolutionary spectral estimation

We present a novel data-adaptive estimator for the evolutionary spectrum of nonstationary signals. We model the signal at a frequency of interest as a sinusoid with a time-varying amplitude, which is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and use it to estimate the time-varying spectrum at that frequency, all while minimizing the interference from the signal components at other frequencies. Repeating the process over all frequencies, we obtain a power distribution that is consistent with the Wold-Cramer evolutionary spectrum and reduces to Capon's (1969) method for the stationary case. Our estimator possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrelation of nonstationary signals. This autocorrelation estimate is needed in the data-adaptive spectral estimation. We illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-frequency distribution with exponential kernels     

The automatic conversion of spinor equations to dyad form in MAPLE

A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated spinor equations to their expansions with respect to a normalized spinor dyad. By following a simple index convention, we obtain a powerful computational tool with a straightforward and easy to use syntax. A number of examples, including nontrivial applications of the package to recent research, are provided.     

Periodic solutions of second-order quasilinear hyperbolic equations

We study a periodic boundary-value problem for a quasilinear equation with the d'Alembert operator on the left-hand side and a nonlinear operator on the right-hand side and establish conditions under which the solution of the indicated problem is unique.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1370–1375, October, 1995.     

Conditions for the onset of sliding in a plane system with friction

The problem of the plane motion of a rigid body along a fixed surface in the presence of dry (Coulomb) friction is considered. The constraint is assumed to be non-restraining. It is shown that the validity of a certain system of two inequalities of the same type guarantees that the surfaces maintain contact and that the body will continue to roll without sliding. These conditions are analysed in a few specific cases of mechanical systems.     

Rheology of a mixture of liquid-crystal polymers in solution

The rheological behavior of a mixture of two liquid-crystal polymers, hydroxypropyl cellulose and ethyl cellulose, in acetone solution is studied. The total polymer concentration in the solvent is held constant (40%) as the ratio of the two polymers is varied. The mixtures are anisotropic, isotropic, or biphasic (isotropic/anisotropic), depending on the concentration. Curves of viscosity vs shear rate for all the mixtures studied show three regions of viscosity, as described by Onogi and Asada for liquid-crystal polymers. The viscosity as a function of the weight ratio of the two polymers at constant shear rate exhibits deviations from additivity of viscosities of the two components at all concentrations. In mixtures of two polymers in the melt, deviations are also observed; the negative ones are attributed to phase separation and the positive ones to homogenous mixing (comparison with the phase diagram). All the mixtures studied (anisotropic, isotropic, or biphasic), show ranges of shear rates where the first normal-stress difference is negative, as is generally observed for anisotropic liquid-crystal polymers. It is concluded that the isotropic solutions become anisotropic under shear, as they are not far from the critical concentration. © 1994 John Wiley & Sons, Inc.     

Properties of polystyrene-poly(methylmethacrylate) random and diblock copolymers in dilute and semidilute solutions

Solution properties for random and diblock copolymers of polystyrene (PS) and poly(methyl methacrylate) (PMMA) have been measured by dynamic and total intensity light scattering in solvents of differing quality. The results are compared with the corresponding properties for PS and PMMA homopolymers of similar molecular weight, in order to determine if interactions between unlike monomers are significant. The hydrodynamic radius (R_h) and diffusion second virial coefficient (k_d) for the random copolymer are found to be larger than the corresponding values for the homopolymers in a solvent which is near-theta for the two homopolymers, whereas no such effect is observed for the block copolymer. This suggests that most intrachain interactions occur a relatively short distance along the chain backbone. In a mutual good solvent R_h and k_d of the random copolymer are comparable to the average of the values for the homopolymers, indicating that in a good solvent monomer/solvent interactions dominate over monomer/monomer interactions. For an isolated diblock copolymer in a mutual good solvent, there is no evidence that interactions between unlike monomers lead to additional expansion of the entire molecule, as measured by R_h, nor expansion of the individual blocks as probed by light scattering with one block optically masked. However, at low but finite concentration there is evidence (the coefficients of the binary interaction terms in the viscosity and the mutual diffusion coefficient, and the second and third virial coefficients) that a weak ordering effect may exist in block copolymer solutions, far from the conditions where microphase separation occurs. Finally, measurements of ternary polymer-polymer-solvent solutions show no dependence on monomer composition or monomer distribution for the tracer diffusion of probe PS-PMMA copolymers in a PMMA/toluene matrix. This indicate that the frictional interaction is largely unaffected by interactions between unlike monomers. However, there is evidence that the thermodynamic interaction is more unfavorable between a random copolymer and the homopolymer matrix than between a diblock and the matrix. © 1994 John Wiley & Sons, Inc.     

High-frequency asymptotic behavior of the electromagnetic field on the surface of a stratified medium

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 174–180, Izd. Moskovskogo Universiteta, Moscow, 1990.