Asymptotic-Diffusion Analysis for Retrial Queue with Batch Poisson Input and Multiple Types of Outgoing Calls

A multi-server retrial queue with a hyper-exponential service time is considered in this paper. The study is performed by the method of asymptotic diffusion analysis under the condition of long delay in orbit. On the basis of the constructed diffusion process, we obtain approximations of stationary probability distributions of the number of customers in orbit and the number of busy servers. Using simulations and numerical analysis, we estimate the accuracy and applicability area of the obtained approximations.

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Asymptotic Analysis of the Output Process in Retrial Queue with Markov-Modulated Poisson Input Under Low Rate of Retrials Condition

Communications in Computer and Information Science - Distributed Computer and Communication Networks ◽

10.1007/978-3-030-36625-4_25 ◽

2019 ◽

pp. 315-324 ◽

Cited By ~ 1

Author(s):

Ivan Lapatin ◽

Anatoly Nazarov

Keyword(s):

Asymptotic Analysis ◽

Retrial Queue ◽

Output Process ◽

Poisson Input ◽

Markov Modulated ◽

Low Rate

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Faculty Opinions recommendation of In vivo diffusion analysis with quantum dots and dextrans predicts the width of brain extracellular space.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.1019496.371781 ◽

2006 ◽

Author(s):

Silvana Curci

Keyword(s):

Quantum Dots ◽

Extracellular Space ◽

Diffusion Analysis ◽

Brain Extracellular Space

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Faculty Opinions recommendation of Diffusion analysis within single nanometric apertures reveals the ultrafine cell membrane organization.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.723477950.793511406 ◽

2015 ◽

Author(s):

Satyajit Mayor

Keyword(s):

Cell Membrane ◽

Membrane Organization ◽

Diffusion Analysis

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1H NMR characterisation of the diffusional properties of methanogenic granular sludge

Water Science & Technology ◽

10.2166/wst.1999.0358 ◽

1999 ◽

Vol 39 (7) ◽

pp. 187-194 ◽

Cited By ~ 9

Author(s):

P. Lens ◽

F. Vergeldt ◽

G. Lettinga ◽

H. Van As

Keyword(s):

Diffusion Coefficient ◽

Relaxation Time ◽

Bacterial Cell ◽

Granular Sludge ◽

T2 Relaxation ◽

Self Diffusion ◽

Diffusion Analysis ◽

S Matrix ◽

Granular Matrix ◽

Pfg Nmr

The diffusive properties of mesophilic methanogenic granular sludge have been studied using diffusion analysis by relaxation time separated pulsed field gradient nuclear magnetic resonance (DARTS PFG NMR) spectroscopy. NMR measurements were performed at 22°C with 10 ml granular sludge at a magnetic field strength of 0.5 T (20 MHz resonance frequency for protons). Spin-spin relaxation (T2) time measurements indicate that three 1H populations can be distinguished in methanogenic granular sludge beds, corresponding to water in three different environments. The T2 relaxation time measurements clearly differentiate the extragranular water (T2 ≈ 1000 ms) from the water present in the granular matrix (T2 = 40-100 ms) and bacterial cell associated water (T2 = 10-15 ms). Self-diffusion coefficient measurements at 22°C of the different 1H-water populations as the tracer show that methanogenic granular sludge does not contain one unique diffusion coefficient. The observed distribution of self-diffusion coefficients varies between 1.1 × 10−9 m2/s (bacterial cell associated water) and 2.1 × 10−9 m2/s (matrix associated water).

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