Delay analysis for a finite buffer TDMA model

In this paper a two-station, single-server queuing system with random breakdowns is investigated. Two classes of customers arrive at the system with finite buffers where one server is dedicated to only one customer class while the second server can process both types of customers. Interarrival and service times are exponentially distributed while failure and repair times follow the generalized exponential distribution. Motivated by the application of alternative tools in semiconductor manufacturing two different control schemes are considered that trigger processing of customers of the second class on the server that is usually dedicated to customers of the first class. The first two moments of customer flow times for both control schemes are calculated.

The literature on queueing systems with finite buffers addresses mostly asymptotic performance metrics on an aggregate flow, and/or generally relies on a convenient, but provably inaccurate, approximation of the loss probability by the overflow probability in an infinite size buffer. This paper addresses non-asymptotic per-flow metrics in a multi-flow queueing system with finite buffer and FIFO scheduling. The analysis dispenses with the above approximation, and lends itself to several interesting insights on the impact of finite buffers on per-flow metrics. Counterintuitively, the per-flow delay distribution is not monotonous in the buffer size, and such an effect is especially visible in high burstiness regimes. Another observation is that buffer dimensioning becomes insensitive to the type of SLA constraint, e.g., fixed violation probability on either loss or delay, in high multiplexing regimes. In the particular case of aggregate scheduling, the results on the aggregate input flow significantly improve upon existing results by capturing the manifestation of bufferless multiplexing in regimes with many flows.

In this paper, the waiting time analysis for an OFDMA wireless cellular system with finite buffering and Adaptive Modulation and Coding (AMC) is addressed. When AMC is considered, several concentric regions within cells serving users with different data rates are differentiated. Phase type (PHT) distribution functions are used to model the conditional cumulative distribution function of the waiting time for users in the different coverage regions. The representation of the conditional waiting time distribution through PHT distributions allows expressing cumulative distribution function (CDF) as a linear combination of negative exponential distributions. The analytical method proposed here captures the exact behavior of the waiting time and the obtained solution is based on matrix analytic derivation, which allows evaluating system performance for any size of buffer and any number of coverage regions.

We study the performance of a statistical multiplexer whose inputs consist of a superposition of packetized voice sources and data. The performance analysis predicts voice packet delay distributions, which usually have a stringent requirement, as well as data packet delay distributions. The superposition is approximated by a correlated Markov modulated Poisson process (MMPP), which is chosen such that several of its statistical characteristics identically match those of the superposition. Matrix analytic methods are then used to evaluate system performance measures. In particular, we obtain moments of voice and data delay distributions and queue length distributions. We also obtain Laplace-Stieitjes transforms of the voice and data packet delay distributions, which are numerically inverted to evaluate tails of delay distributions. It is shown how the matrix analytic methodology can incorporate practical system considerations such as finite buffers and a class of overload control mechanisms discussed in the literature. Comparisons with simulation show the methods to be accurate. The numerical results for the tails of the voice packet delay distribution show the dramatic effect of traffic variability and correlations on performance.

In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations.

The purpose of this text is to present some new results in the spectral theory of orthogonal polynomials and Schrodinger operators. These results concern perturbations of the free Schrodinger operator and of the free case for orthogonal polynomials on the unit circle (which corresponds to Verblunsky coefficients equal to 0) and the real line (which corresponds to off-diagonal Jacobi coefficients equal to 1 and diagonal Jacobi coefficients equal to 0). The condition central to our results is that of generalized bounded variation. This class consists of finite linear combinations of sequences of rotated bounded variation with an L^1 perturbation. This generalizes both usual bounded variation and expressions of the form lambda(x) cos(phi x + alpha) with lambda(x) of bounded variation (and, in particular, with lambda(x) = x^gamma, Wigner-von Neumann potentials) as well as their finite linear combinations. Assuming generalized bounded variation and an L^p condition (with any finite p) on the perturbation, our results show preservation of absolutely continuous spectrum, absence of singular continuous spectrum, and that embedded pure points in the continuous spectrum can only occur in an explicit finite set.

We study a single server queue with finite buffer that may represent an ATM multiplexer. The input traffic is a superposition of independent heterogeneous batch Markovian arrival processes. Service durations are supposed to be exponential. We derive the loss probability and the delay and jitter distributions for each individual process, as well as for the superposed one. We show that there is a significant difference between performances of individual and global flows, justifying our work. The approach is based on martingale techniques. >

The compatibility of pairs of conditional densities and the uniqueness of the resulting bivariate densities are discussed. Examples ar given involving beta, gamma, and Gaussian conditional densities.

Departure process in a mixed fork–join synchronization network

This study examines the factors influencing students’ online learning using Microsoft Teams at the PLN Institute of Technology. Using primary data from 301 students, the study found that the use of Microsoft Teams improved student achievement and learning performance during the pandemic. The structural equation model (SEM) method tested the model with low validity, with all variables having an AVE value more than 0.5 and higher than the cross-loading factor valid, the outer model analysis demonstrated good convergent validity. Dependability and trustworthiness were shown by the composite reliability rating, which was over 0.70. Both perceived usefulness (PU) and perceived ease of use (PEOU) were shown to have a strong correlation, and the inner model analysis revealed positive path coefficient values without any weak variables. These results supported by hypothesis testing imply that lecturers can modify their curricula to enhance student performance in the event of a pandemic. There was shown to exist a strong relationship between the perceived ease of use and perceived usefulness.

Now we reach the centerpiece of this volume, which is the theory of bases in Banach spaces. Since every Banach space is a vector space, it has a basis in the ordinary vector space sense, i.e., a set that spans and is linearly independent.However, this definition of basis restricts us to using only finite linear combinations of vectors, while in any normed space it makes sense to deal with infinite series. Restricting to finite linear combinations when working in an infinite-dimensional space is simply too restrictive for most purposes. Moreover, the proof that a vector space basis exists is nonconstructive in general, as it relies on the Axiom of Choice. Hence we need a new notion of basis that is appropriate for infinite-dimensional Banach spaces, and that is the main topic of this chapter.

Through the analysis of X-cor sandwich's microscopic characteristics a finite element model of X-cor sandwich's compressive modulus was proposed. The finite element software ANSYS was used in the computation of compressive modulus. The effects of changing angle, diameter and density on the X-cor sandwich's compressive modulus were analyzed. The numerical analysis results indicate that as the Z-pin's angle increases the X-cor sandwich's compressive modulus decreases, and as the Z-pin's diameter and density increase its compressive modulus increases. Via the analysis of finite model the influencing trends of X-cor sandwich's parameters to its compressive modulus are achieved, the rationality of the proposed finite element model is verified and the finite element model can be used to forecast its compressive modulus.

We have studied the possible association of daily mortality with ambient pollutant concentrations (PM10, CO, O3, SO2, NO2, and fine [PM2 5] and coarse PM) and weather variables (temperature and dew point) in the Pittsburgh, PA, area for two age groups—less than 75, and 75 and over—for the 3-year period of 1989-1991. Correlation functions among pollutant concentrations show important seasonal dependence, and this fact necessitates the use of seasonal models to better identify the link between ambient pollutant concentrations and daily mortality. An analysis of the seasonal model results for the younger-age group reveals significant multicollinearity problems among the highly correlated concentrations of PM10, CO, and NO2 (and O3 in spring and summer), and calls into question the rather consistent results of the single- and multi-pollutant non-seasonal models that show a significant positive association between PM10 and daily mortality. For the older-age group, dew point consistently shows a significant association with daily mortality in all models. Collinearity problems appear in the multi-pollutant seasonal and non-seasonal models such that a significant, positive PM10 coefficient is accompanied by a significant, negative coefficient of another ambient pollutant, and the identity of this other pollutant changes with season. The PM25 data set is half that of PM10. Identical-model runs for both data sets reveal instability in the pollutant coefficients, especially for the younger age group. The concern for the instability of the pollutant coefficients due to a small signal-to-noise ratio makes it impossible to ascertain credibly the relative associations of the fine- and coarse-particle modes with daily mortality. In this connection, we call for caution in the interpretation of model results for causal inference when the models use fully or partially estimated PM values to fill large data gaps.

Design, analysis and verification of a knee joint oncological prosthesis finite element model

The far field (FF) of a radiating or scattering object immersed in an acoustic fluid can be represented in the frequency domain as a finite dimension linear combination of basis functions, which are determined by the shape and the size of the object in acoustic wavelengths. The coefficients of the linear combination are obtained as the outputs of a bank of spatial filters whose inputs are either the boundary normal velocity—for the radiation problem—or the boundary pressure and the normal velocity—for the scattering problem—measured by a dense set of sensors. The filter outputs provide the information sufficient to reconstruct the radiated or scattered far field, amplitude and phase. The structure of the filters is identified from the singular valve decomposition of the appropriate radiation or scattering operator, mapping the boundary normal velocity, or the combination of normal velocity and pressure, into the FF. Also, from the filter outputs, the efficiently radiating component of the boundary field can be extracted. For example the boundary total normal velocity may have a localized high peak, which however may be completely or almost completely absent in the radiating component. Selected results of an extensive simulation are presented illustrating the accuracy of the reconstruction of the FF from the spatial filtering of the boundary field.