On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals

We consider multiplexers in discrete time fed by the superposition of Ternary Markov Sources. Such sources are the natural extension of the Binary Markov Sources (BMS) recently used to model bursty arrivals in a high speed environment. Unlike BMS, we allow sources to have arbitrary (large) variance in the duration of their OFF (silence) or ON (burst) periods.This paper focuses mainly on the impact of large variability either in the ON or OFF period on the performance. Following some asymptotic analysis, simple results on the tail behavior of the number of cells queued in the multiplexer are given.Our results indicate that ignoring the variability in the ON period may grossly underestimate the cell buildup in the multiplexer queue for all levels of the utilization. Furthermore, the impact of large variability of the OFF period depends very much on the utilization of the system. For a lightly-loaded multiplexer (utilization below a given threshold), the impact of large variability of the OFF period is minimal. However, for a heavy-loaded multiplexer (utilization above the threshold) the impact of the large variability in the OFF period is similar to that of the ON period.     

Ranking all units in data envelopment analysis

The motivation of this study is to propose an equitable method for ranking decision making units (DMUs) based on the data envelopment analysis (DEA) concept. For this purpose, first, the minimum and maximum efficiency values of each DMU are computed under the assumption that the sum of efficiency values of all DMUs is equal to unity. Then, the rank of each DMU is determined in proportion to a combination of its minimum and maximum efficiency values.     

A one-model approach based on relaxed combinations of inputs for evaluating input congestion in DEA

This paper provides a one-model approach of input congestion based on input relaxation model developed in data envelopment analysis (e.g. [G.R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion — Considering textile industry of China, Applied Mathematics and Computation (1) (2004) 263–273; G.R. Jahanshahloo, M. Khodabakhshi, Determining assurance interval for non-Archimedean ele improving outputs model in DEA, Applied Mathematics and Computation 151 (2) (2004) 501–506; M. Khodabakhshi, A super-efficiency model based on improved outputs in data envelopment analysis, Applied Mathematics and Computation 184 (2) (2007) 695–703; M. Khodabakhshi, M. Asgharian, An input relaxation measure of efficiency in stochastic data analysis, Applied Mathematical Modelling 33 (2009) 2010–2023]. This approach reduces solving three problems with the two-model approach introduced in the first of the above-mentioned reference to two problems which is certainly important from computational point of view. The model is applied to a set of data extracted from ISI database to estimate input congestion of 12 Canadian business schools.     

Eco-friendly synthesis of 1,4-benzodiazepine-2,5-diones in the ionic liquid [<Emphasis Type="Italic">bmim</Emphasis>]Br

The green reaction of isatoic anhydrides with α-amino acids in presence of the ionic liquid 1-butyl-3-methylimidazolium bromide afforded 1,4-benzodiazepine-2,5-diones in excellent yields in absence of a catalyst. The reaction workup is simple and the ionic liquid was easily recovered from the reaction and reused. The methodology was quite general and a range of cyclic and acyclic α-amino acids were examined to produce 1,4-benzodiazepine-2,5-diones. Correspondence: Khosrow Jadidi, Department of Chemistry, Shahid Beheshti University, PO Box 1983963113, Tehran, Iran.