Analysis of an M[X]/G(a, b)/1 queueing model with multiple vacation controllable arrival during multiple vacation and two phases of repair with delay

2020 ◽  
Vol 34 (3) ◽  
pp. 409
Author(s):  
G. Ayyappan ◽  
T. Deepa
Keyword(s):  
Queueing Model ◽  
Multiple Vacation ◽  
Two Phases

scholarly journals Sample-Path Analysis of Single-Server Queue with Multiple Vacations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad El-Taha
Keyword(s):  
Stochastic Process ◽  
Conservation Law ◽  
Sample Path ◽  
Single Server ◽  
Queueing Model ◽  
Single Server Queue ◽  
Sample Path Analysis ◽  
Multiple Vacation ◽  
Server Queue ◽  
Background Material

We a give deterministic (sample path) proof of a result that extends the Pollaczek-Khintchine formula for a multiple vacation single-server queueing model. We also give a conservation law for the same system with multiple classes. Our results are completely rigorous and hold under weaker assumptions than those given in the literature. We do not make stochastic assumptions, so the results hold almost surely on every sample path of the stochastic process that describes the system evolution. The article is self contained in that it gives a brief review of necessary background material.

scholarly journals M[x]/G/1 Multistage Queue with Stand-by Server During Main Server’s Interruptions

2018 ◽  
Vol 11 (1) ◽  
pp. 275 ◽  
Author(s):  
Yuvarani Chandrasekaran ◽  
Vijayalakshmi C
Keyword(s):  
Steady State ◽  
Delay Time ◽  
Steady State Solution ◽  
Single Server ◽  
Supplementary Variable ◽  
Transient Solution ◽  
Variable Technique ◽  
Multiple Vacation ◽  
Server Breakdown ◽  
Two Phases

<p>This paper investigates a multistage batch arrival queue with different server interruptions and a second server replaces the main server during the interruptions. The different server interruptions are assumed to be: multiple vacation, extended vacation, breakdown with delay time and server under two phases of repair. Customers are assumed to arrive in batches according to Poisson process and a single server provides service to the customers. When the main server is inactive due to the interruptions, stand-by server provide service to the arrivals. In addition, customers may renege during server breakdown or during server vacation due to impatience. Transient solution and the corresponding steady state solution is derived using supplementary variable technique.</p>

Precipitation of NiHfsi phase in NiAl single crystals containing Hf

1995 ◽  
Vol 53 ◽  
pp. 532-533
Author(s):  
A. Garg ◽  
R. D. Noebe ◽  
R. Darolia
Keyword(s):  
High Temperature ◽  
Single Crystals ◽  
High Temperature Strength ◽  
Bridgman Technique ◽  
Shell Mold ◽  
Third Phase ◽  
Unknown Phase ◽  
Transmission Electron ◽  
Two Phases ◽  
Nial Matrix

Small additions of Hf to NiAl produce a significant increase in the high-temperature strength of single crystals. Hf has a very limited solubility in NiAl and in the presence of Si, results in a high density of G-phase (Ni16Hf6Si7) cuboidal precipitates and some G-platelets in a NiAl matrix. These precipitates have a F.C.C structure and nucleate on {100}NiAl planes with almost perfect coherency and a cube-on-cube orientation-relationship (O.R.). However, G-phase is metastable and after prolonged aging at high temperature dissolves at the expense of a more stable Heusler (β'-Ni2AlHf) phase. In addition to these two phases, a third phase was shown to be present in a NiAl-0.3at. % Hf alloy, but was not previously identified (Fig. 4 of ref. 2 ). In this work, we report the morphology, crystal-structure, O.R., and stability of this unknown phase, which were determined using conventional and analytical transmission electron microscopy (TEM).Single crystals of NiAl containing 0.5at. % Hf were grown by a Bridgman technique. Chemical analysis indicated that these crystals also contained Si, which was not an intentional alloying addition but was picked up from the shell mold during directional solidification.

Imaging of Al-Li-Cu alloys with a Scanning Ion Microprobe

1990 ◽  
Vol 48 (2) ◽  
pp. 314-315
Author(s):  
K.K. Soni ◽  
D.B. Williams ◽  
J.M. Chabala ◽  
R. Levi-Setti ◽  
D.E. Newbury
Keyword(s):  
Mass Spectrometry ◽  
Secondary Ion Mass Spectrometry ◽  
Equilibrium Phase ◽  
Icosahedral Symmetry ◽  
Ion Microprobe ◽  
X Ray ◽  
Cu Alloys ◽  
Two Phases ◽  
The University ◽  
Secondary Ion

In contrast to the inability of x-ray microanalysis to detect Li, secondary ion mass spectrometry (SIMS) generates a very strong Li+ signal. The latter’s potential was recently exploited by Williams et al. in the study of binary Al-Li alloys. The present study of Al-Li-Cu was done using the high resolution scanning ion microprobe (SIM) at the University of Chicago (UC). The UC SIM employs a 40 keV, ∼70 nm diameter Ga+ probe extracted from a liquid Ga source, which is scanned over areas smaller than 160×160 μm2 using a 512×512 raster. During this experiment, the sample was held at 2 × 10-8 torr.In the Al-Li-Cu system, two phases of major importance are T1 and T2, with nominal compositions of Al2LiCu and Al6Li3Cu respectively. In commercial alloys, T1 develops a plate-like structure with a thickness <∼2 nm and is therefore inaccessible to conventional microanalytical techniques. T2 is the equilibrium phase with apparent icosahedral symmetry and its presence is undesirable in industrial alloys.

Defect structures of Nb1+αS2 sulfidation scales

1992 ◽  
Vol 50 (1) ◽  
pp. 38-39
Author(s):  
Chuxin Zhou ◽  
L. W. Hobbs
Keyword(s):  
Stacking Faults ◽  
Rhombohedral Structure ◽  
Stacking Sequence ◽  
Defect Structures ◽  
X Ray Diffraction ◽  
X Ray ◽  
Plane Normal ◽  
Lower Case ◽  
Sulfur Layer ◽  
Two Phases

One of the major purposes in the present work is to study the high temperature sulfidation properties of Nb in severe sulfidizing environments. Kinetically, the sulfidation rate of Nb is satisfactorily slow, but the microstructures and non-stoichiometry of Nb1+αS2 challenge conventional oxidation/sulfidation theory and defect models of non-stoichiometric compounds. This challenge reflects our limited knowledge of the dependence of kinetics and atomic migration processes in solid state materials on their defect structures.Figure 1 shows a high resolution image of a platelet from the middle portion of the Nb1+αS2 scale. A thin lamellar heterogeneity (about 5nm) is observed. From X-ray diffraction results, we have shown that Nb1+αS2 scale is principally rhombohedral structure, but 2H-NbS2 can result locally due to stacking faults, because the only difference between these 2H and 3R phases is variation in the stacking sequence along the c axis. Following an ABC notation, we use capital letters A, B and C to represent the sulfur layer, and lower case letters a, b and c to refer to Nb layers. For example, the stacking sequence of 2H phase is AbACbCA, which is a ∼12Å period along the c axis; the stacking sequence of 3R phase is AbABcBCaCA to form an ∼18Å period along the c axis. Intergrowth of these two phases can take place at stacking faults or by a shear in the basal plane normal to the c axis.

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