Accurate computation of the smallest eigenvalue of a diagonally dominant -matrix

If each off-diagonal entry and the sum of each row of a diagonally dominant -matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms.

     

Qualitative and quantitative analysis of gallic acid in Alchemilla vulgaris, Allium ursinum, Acorus calamus and Solidago virga-aurea by chip-electrospray ionization mass spectrometry and high performance liquid chromatography

This study presents the results obtained from qualitative and quantitative analysis of gallic acid from hydro-alcoholic extracts (methanol, ethanol) of plants from Plantae regnum. Plant qualitative analysis was performed using a novel mass spectrometric (MS) method based on fully automated chip-nanoelectrospray ionization (nanoESI) high capacity ion trap (HCT) while quantitative analysis was carried out by high performance liquid chromatography (HPLC). These methods were applied to Alchemilla vulgaris — common lady’s-mantle (aerial part), Allium ursinum — bear’s garlic (leaves), Acorus calamus — common sweet flag (roots), Solidago virga-aurea — goldenrod (aerial part). Obtained results indicated that methanol extracts (96%, 80%) have a gallic acid content ranging between 0.0011–0.0576 mg mL⁻¹ extract while the ethanol extracts (96%, 60%) exhibit a gallic acid concentration that varies between 0.0010–0.0182 mg mL⁻¹ extract.      

Combined Elapsed Time and Matrix-Analytic Method for the Discrete Time GI/G/1 and GI X /G/1 Systems

In this paper, we show that the discrete GI/G/1 system can be easily analysed as a QBD process with infinite blocks by using the elapsed time approach in conjunction with the Matrix-geometric approach. The positive recurrence of the resulting Markov chain is more easily established when compared with the remaining time approach. The G-measure associated with this Markov chain has a special structure which is usefully exploited. Most importantly, we show that this approach can be extended to the analysis of the GI ^X /G/1 system. We also obtain the distributions of the queue length, busy period and waiting times under the FIFO rule. Exact results, based on computational approach, are obtained for the cases of input parameters with finite support – these situations are more commonly encountered in practical problems.     

Discrete NT-policy single server queue with Markovian arrival process and phase type service

We consider a discrete time single server queueing system in which arrivals are governed by the Markovian arrival process. During a service period, all customers are served exhaustively. The server goes on vacation as soon as he/she completes service and the system is empty. Termination of the vacation period is controlled by two threshold parameters N and T, i.e. the server terminates his/her vacation as soon as the number waiting reaches N or the waiting time of the leading customer reaches T units. The steady state probability vector is shown to be of matrix-geometric type. The average queue length and the probability that the server is on vacation (or idle) are obtained. We also derive the steady state distribution of the waiting time at arrivals and show that the vacation period distribution is of phase type.     

A Numerical Method for Evaluating Delay to a Customer in a Time-Inhomogeneous,Single Server Queue with Batch Arrivals

Using the method of discrete time analysis, a numerical method is developed for evaluating the distribution of the delay encountered by a customer in a time-inhomogeneous, single server queue with batch arrivals.     

Sommerfeld effect in a gyroscopic overhung rotor-disk system

Deflection of a rotor-disk at the free end of a flexible overhung rotor-shaft causes rotation about diametral axis and consequently leads to a strong gyroscopic coupling in a spinning overhung rotor system. When the rotor is spun up about its axis, the unbalance in the rotor-disk causes transverse and rotational vibrations to increase as the spin speed approaches the critical speed of the rotor. These transverse and rotational vibrations dissipate a lot of energy, and if the rotor is driven through a non-ideal drive, i.e., a motor which can supply a limited amount of power, then the entire motor power may be spent to account for the energy dissipation. As a result, the rotor speed may get stuck in resonance at the critical speed or jump through the critical speed to a much higher speed with lower transverse and rotational vibration levels. These symptoms, normally referred to as the Sommerfeld effect, occur due to the intrinsic energetic coupling between the drive and the driven systems and are important design considerations for development of various rotating machinery with flexible rotor-shafts or supports (bearings). Sommerfeld effect in a strongly gyroscopic rotor dynamic system is studied in this article. The dynamics of an overhung rotor system near the regimes of Sommerfeld effect is studied by using a discrete and a continuous shaft-rotor model coupled with the model of the non-ideal motor drive. The models are developed using multi-energy domain modeling approach in bond graph model form. A steady-state analysis of power transfer mechanism is used to postulate the ideal characteristics of Sommerfeld effect in the neighborhood of the critical speed, and thereafter, full transient analysis is performed with aid of the bond graph model-generated coupled equations of motion to validate the postulated characteristics of the Sommerfeld effect.     

A queueing model of delayed product differentiation

We consider a production system in which a supplier produces semi-finished items on a make-to-stock basis for a manufacturer that will customize the items on a make-to-order basis. The proportion of total processing time undertaken by the supplier determines how suitable the semi-finished items will be to meet customer demand. The manufacturer wishes to determine the optimal point of differentiation (the proportion of processing completed by the supplier) and its optimal semi-finished goods buffer size. We use matrix geometric methods to evaluate various performance measures for this system, and then, with enumeration techniques, obtain optimal solutions. We find that delayed product differentiation is attractive when the manufacturer can balance the costs of customer order fulfillment delay with the costs associated with unsuitable items.     

Phase-type models for cellular networks supporting voice, video and data traffic

This paper presents an analytical model for cellular networks supporting voice, video and data traffic. Self-similar and bursty nature of the incoming traffic causes correlation in inter-arrival times of the incoming traffic. Therefore, arrival of calls is modeled with Markovian arrival process as it allows for the correlation. Call holding times, cell residence times and retrial times are modeled as phase-type distributions. We consider that the cells in a cellular network are statistically homogeneous, so it is enough to investigate a single cell for the performance analysis of the entire networks. With appropriate assumptions, the stochastic process that describes the state of a cell is a Quasi-birth–death (QBD) process. We derive explicit expressions for the infinitesimal generator matrix of this QBD process. Also, expressions for performance measures are obtained. Further, complexity involved in computing the steady-state probabilities is discussed. Finally, queueing examples are provided that can be obtained as particular cases of the proposed analytical model.