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.     

Coupled-states statistical investigation of vibrational and rotational relaxation of OH(2pi) by collisions with atomic hydrogen

We report state-to-state cross sections and thermal rate constants for vibrational and rotational relaxation of OH(2pi) by collision with H atoms. The cross sections are calculated by the coupled-states (CS) statistical method including the full open-shell character of the OH + H system. Four potential energy surfaces (PESs) ((1,3)A' and (1,3)A') describe the interaction of OH(X2pi) with H atoms. Of these, three are repulsive, and one (1A') correlates with the deep H2O well. Consequently, rotationally and ro-vibrationally inelastic scattering of OH in collisions with H can occur by scattering on the repulsive PESs, in a manner similar to the inelastic scattering of OH by noble gas atoms, or by collisions which enter the H2O well and then reemerge. At 300 K, we predict large (approximately 1 x 10(-10) cm3 molecule(-1) s(-1)) vibrational relaxation rates out of both v = 2 and v = 1, comparable to earlier experimental observations. This anomalously fast relaxation results from capture into the H2O complex. There exists a significant propensity toward formation of OH in the pi(A') lambda-doublet level. We also report state-resolved cross sections and rate constants for rotational excitation within the OH v = 0 manifold. Collisional excitation from the F1 to the F2 spin-orbit manifold leads to an inverted lambda-doublet population.     

Crystal structure and nonlinear optical properties of the K2UO2(SO4)2 · 2H2O compound at 293 K

Single crystals of potassium uranyl sulfate are grown, and their atomic structure is determined using X-ray diffraction analysis. The compound crystallizes in the orthorhombic crystal system with space group Pna2₁ [a = 13.773(4) Å, b = 7.288(2) Å, c = 11.556(4) Å, R ₁ = 0.033, wR ₂ = 0.0892 for 2630 reflections with I > 2σ(I)]. The crystal structure of the K₂UO₂(SO₄)₂ · 2H₂O compound is built up of two-dimensional infinite, negatively charged layers of the composition [UO₂(SO₄)₂·H₂O] _2∞ ^δ? ], which are linked together through the K⁺ ions. The specific features of the atomic arrangement in the structure of this compound are analyzed, and the second harmonic generation of laser radiation is investigated.     

Comparison of high-performance liquid chromatography of cyclotriphosphazene derivatives with one or two equivalent stereogenic centres

High-performance liquid chromatographic (HPLC) methods have been developed for investigating the stereogenic properties of two analogous series of dibenzylamino derivatives of cyclotriphosphazene containing either one or two equivalent stereogenic centres. Separation of the enantiomers of all the racemic compounds has been investigated by chiral HPLC using Whelk-01 and Chiralcel OD columns. In all cases, conditions for separation of enantiomers have been found using a Whelk-01 column with different ratios of tetrahydrofuran in n-hexane as the mobile phase. It is found that both the separation factor (alpha) and resolution factor (R(S)) of molecules with two equivalent stereogenic centres are greater than those for analogues with only one centre.     

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.     

Matrix analytic methods for a multi-server retrial queue with buffer

We present numerical methods for obtaining the stationary distribution of states for multi-server retrial queues with Markovian arrival process, phase type service time distribution with two states and finite buffer; and moments of the waiting time. The methods are direct extensions of the ones for the single server retrial queues earlier developed by the authors. The queue is modelled as a level dependent Markov process and the generator for the process is approximated with one which is spacially homogeneous above some levelN. The levelN is chosen such that the probability associated with the homogeneous part of the approximated system is bounded by a small tolerance and the generator is eventually truncated above that level. Solutions are obtained by efficient application of block Gaussian elimination.     

The $$MMAP\left[ K \right]/PH\left[ K \right]/1$$ queues with a last-come-first-served preemptive service discipline

This paper studies two queueing systems with a Markov arrival process with marked arrivals and PH-distribution service times for each type of customer. Customers (regardless of their types) are served on a last-come-first-served preemptive resume and repeat basis, respectively. The focus is on the stationary distribution of queue strings in the system and busy periods. Efficient algorithms are developed for computing the stationary distribution of queue strings, the mean numbers of customers served in a busy period, and the mean length of a busy period. Comparison is conducted numerically between performance measures of queueing systems with preemptive resume and preemptive repeat service disciplines. A counter-intuitive observation is that for a class of service time distributions, the repeat discipline performs better than the resume one. This revised version was published online in June 2006 with corrections to the Cover Date.     

Synthesis and non-aqueous medium titrations of some new 4-benzylidenamino-4,5-dihydro-1H-1,2,4-triazol-5-one derivatives

The synthesis of 3-alkyl(aryl)-4-(3-ethoxy-4-hydroxybenzylidenamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones 3 from the reactions of 3-alkyl(aryl)-4-amino-4,5-dihydro-1H-1,2,4-triazol-5-ones 2 with 3-ethoxy-4-hydroxybenzaldehyde is described.The acetylation and methylation reactions of the compounds 3 giving compounds of type 4 and 5, respectively, were investigated. The newly synthesized compounds were characterized using elemental analyses and IR, (1)H-NMR, (13)C-NMR and UV spectral data.In addition, to investigate the effects of solvents and molecular structure upon acidity,compounds 3 were titrated potentiometrically with tetrabutylammonium hydroxide in four non-aqueous solvents (isopropyl alcohol, tert-butyl alcohol, acetonitrile and N,N-dimethylformamide). The half-neutralization potential values and the corresponding pKa values were determined for all cases.     

On approximating higher order MAPs with MAPs of order two

We show that the autocorrelation sequence of interarrival times for a Markovian arrival process (MAP) of order two is geometric. We determine the set of feasible values for the autocorrelation decay parameter and the first two or three moments of the interarrival time distribution. A method is derived for matching these parameters to a MAP of order two and some numerical examples are included to illustrate approximating higher dimensional MAPs by two dimensional ones. The numerical examples have helped us pose important questions regarding the significance of correlation in a MAP of order two when it is used as input to a queueing model.