Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Department of Mathematics

Purpose: The authors consider parallel four-state tandem open queueing network. The queue capacity is infinite. Passenger arrival rate is Poisson distribution and service rate is exponential distribution. The queue is constructed in the form of tandem queue, and each and every queue of tandem queue is single server (M/M/1) queue. In tandem queue, passengers will leave the system once they receive service from both the states. The purpose of this paper is to provide performance analysis for four-state tandem open queue network, and a governing equation is formulated with the help of transition diagram. Using Burke theorem, the authors formulated equation for average number of passenger in the system, average waiting time of passenger in the system, average number of passenger in the queue and average waiting time of passenger in the queue. Design/methodology/approach: This paper used Burke’s theorem. Findings: In this paper, performance analysis is done for parallel four-state tandem open queueing network and performance measure solved using Burkes theorem formula. K. Sreekanth et al. has done performance analysis for single tandem queue with three states. In this paper, the authors have done performance analysis for two tandem queues parallel with four states. This four-state tandem open queueing network is suitable for real world applications. This paper can extend for more number of service states and multi-server states according to the application, and in such case, the authors have to prove and explain with numerical examples. This analysis is more useful for the applications such as airports, railway stations, bus-stands and banks. Originality/value: In this paper, parallel four-state tandem open queueing network and performance measure has been solved using Burke’s theorem formula. © 2020, Emerald Publishing Limited.

World University root node

School of Advanced Sciences

Vellore Campus

International Journal of Pervasive Computing and Communications

Performance measures of parallel tandem open queueing network

In this paper, we introduce a modified implicit relation and obtain some new fixed point results for σ-implicit type contractive conditions in relational metric-like spaces. We present some nontrivial examples to illustrative facts and compare our results with the related work. We also discuss sufficient conditions for the existence of a unique positive definite solution of the non-linear matrix equation U = D +∑m i=1 A∗iG(U)Ai, where D is an n × n Hermitian positive definite matrix, A1, A2, …, Am are n × n matrices, and G is a non-linear self-mapping of the set of all Hermitian matrices which is continuous in the trace norm. Finally, we discuss a couple of examples, convergence and error analysis, average CPU time analysis and visualization of solution in surface plot. © 2021 the Author(s), licensee AIMS Press.

Fulltext

AIMS Mathematics

Unified relational-theoretic approach in metric-like spaces with an application

Let X be a complex Banach space. We say that X belongs to the class W if for each compact operator T defined on X such that ‖ I+ T‖ > 1 , I+ T attains norm. In this note, we characterize the ϵ- condition spectrum of any compact linear operator defined on X where X is Banach space which belongs to class W. © 2021, Forum D'Analystes, Chennai.

Journal of Analysis

Characterization of the condition spectrum of a compact operator

In this paper, we report on the comprehensive study on Molybdenum disulfide (MoS2) nanolayer coated etched Fiber Bragg Grating (eFBG) strain sensor. MoS2 nanolayer is coated using Physical Vapor Deposition (PVD) of Molybdenum (Mo) on eFBGs followed by sulfurization of the same in an inert atmosphere at 450° C. Such coating technique provides a direct control over the coating thickness of MoS2, thereby enabling a study based on the effect of nanolayer coating thickness on the intrinsic strain sensitivity as well as the power of the back reflected Bragg wavelength of eFBG in the 0.78eV spectral region. High uniformity of MoS2 nanolayer coating ensures consistent, repeatable and highly linear FBG strain sensors with a correlation coefficient of 0.988 in the range of 0 to $2500~\mu \varepsilon $. A maximum intrinsic strain sensitivity of 6.65 pm/ $\mu \varepsilon $ with a resolution of $\sim 150~\text{n}\varepsilon $ have been achieved with optimized MoS2 coated eFBG sensors. This kind of consistent, highly sensitive and linear strain sensors when incorporated with proper packaging schemes can be particularly useful for applications demanding high sensitivity of FBG sensors such detection of seismic vibrations, underwater acoustic signals, low amplitude accelerations, etc. © 2001-2012 IEEE.

IEEE Sensors Journal

A Study on MoS Nanolayer Coated Etched Fiber Bragg Grating Strain Sensor

In this paper, we propose a new conjecture that the complete graph K4m+1 can be decomposed into copies of two arbitrary trees, each of size m, m≥ 1. To support this conjecture we prove that the complete graph K4cm+1 can be decomposed into copies of an arbitrary tree with m edges and copies of the graph H, where H is either a path with m edges or a star with m edges and where c is any positive integer. Further, we discuss related open problems. © 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.

Graphs and Combinatorics

Decomposition of Complete Graphs into Arbitrary Trees

Reducing carbon emissions plays a significant role in developing sustainable inventory systems. In a seller-buyer relationship, an allowable delay in payment is considered for the buyer to manage the stock and simulate the demand. Deteriorating items that usually have specific maximum lifetimes have become a challenge for most firms. Contrary to the importance of these issues, very little research has studied the impact of carbon emissions on deteriorating inventory systems. This paper provides a price-dependent demand for perishable items when carbon cap-and-trade regulation fills the mentioned gap. This model provides a carbon reduction investment scheme and illustrates this investment’s effect on the inventory system. This paper determines the optimal replenishment cycle and selling price, in which: (a) perishable items have specific maximum lifetimes, (b) a specific period of delay in payment is allowed for the buyer to accumulate revenue, (c) carbon is emitted due to ordering and storage operations and carbon cap and trade is regulated along with allowable carbon reduction investment. After developing the model, optimal values are obtained from necessary and sufficient conditions of optimality. Numerical experiments are proposed to validate the model. By developing an algorithm, the optimal values of replenishment cycle, selling price, and carbon reduction technology investment are obtained, and the impact of carbon emissions and efforts to control emissions are outlined. Finally, some managerial applications are mentioned, and future research directions are exposed. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Mathematics

Joint pricing and inventory model for deteriorating items with maximum lifetime and controllable carbon emissions under permissible delay in payments

This paper deals with an economic production quantity (EPQ) inventory model for deteriorating items under preservation technology. The preservation technology is used to protect the items from deterioration. Three different production levels are considered. It is assumed that initially the production rate is at a lower rate and it increases gradually over the period. This is just in order to reduce the holding cost by avoiding the larger stock quantity at the beginning of the production cycle. The shortages are permitted and fully backordered. The objective of the production inventory model is to determine the optimal production policy which minimizes the manufacturer's total cost. Theoretical results are established in order to demonstrate the existence of the optimal solution and a proper solution procedure is presented. A numerical example and sensitivity analysis are presented to validate the theoretical results. Also, some managerial insights are provided. © EDP Sciences, ROADEF, SMAI 2021.

RAIRO - Operations Research

Production inventory model for controllable deterioration rate with shortages

The main aim of this study is to analyze the dynamical properties of hepatitis B-type virus (HBV) infection in terms of mathematical model. The presented mathematical model on HBV involves the various factors such as immune impairment, total carrying capacity, logistic growth term, and antiretroviral therapies. In addition, the effect of time delays is also considered into the model, which are inevitable during the activation of immune response and time taken to infect the healthy cells. Mathematically, the qualitative analyses such as stability, bifurcation, and stabilization analysis are performed to explore the dynamical characteristics of HBV over the period of time. The significance of the model parameters is revealed through Hopf-type bifurcation analysis and the global stability analysis of the proposed model. With the help of data set values that are extracted from the literature, the efficiency of the derived theoretical results is explored. © 2021 John Wiley & Sons, Ltd.

Chennai Campus

Mathematical Methods in the Applied Sciences

Stability and bifurcation analysis of hepatitis B-type virus infection model

This study evaluated the performance of advanced research weather research and forecasting (WRF) modelling system in the forecast of extremely severe cyclonic storm (ESCS) over the Bay of Bengal region that made landfall in Bangladesh on 15 November 2007. Model initial conditions were improved using the three-dimensional variational data assimilation (3D-VAR) system of the WRF model. A set of four numerical experiments were also performed with and without data assimilation techniques at two different grid resolutions (1° × 1° and 0.5° × 0.5°) using NCEP global forecasting system (GFS). Satellite and conventional observations were assimilated using the 3D-VAR modelling system. Results from the assimilation experiment confirms that the analysis using 3D-VAR is better compared to the global datasets in both grid resolutions, attributed due to the availability of quality satellite observations during the analysis period. In addition, the forecasted track, landfall location, maximum wind speed and minimum central pressure of ESCS are better predicted with the data assimilation. The study also presents the forecasted structure in terms of rainfall, wind speed, potential vorticity, and cross-section of horizontal wind speed. Overall, the results clearly revealed that modelling using the 3D-VAR assimilation system is very important in the high-resolution WRF model that enhanced the prediction capability. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.

Modeling Earth Systems and Environment

Numerical simulation of an extremely severe cyclonic storm over the Bay of Bengal using WRF modelling system: influence of model initial condition

This article investigates the peristaltic laminar flow of a two layered model in a channel containing Newtonian fluid in the core region and the region adjacent to the wall is filled with porous medium under the action of an external magnetic field by taking approximations of low Reynolds number and long wavelength. As a part of solution, the shape of interface for the fluid and porous regions were found independently. At the interface of the fluid, shear-stress jump boundary condition was applied. In peristaltic transport, the importance of physical quantities like pumping, axial velocity, and interface are discussed for different considerations of interest governing the flow like effective viscosity, Darcy number, permeability, stress jump constant, and Hartmann number, etc. It is noticed that increasing magnetic parameter results in enhancing the pumping of the fluid. Increasing magnetic field parameter, the axial velocity of the fluid reduces. That is, increasing magnetic parameter strengthens the magnetic field which applies a transverse force on fluid; hence, fluid velocity decreases. The significant observation is that, when stress jump constant β takes the values between 0 to 1 the axial velocity decreases gradually, and for β > 1 we observed no variation in axial velocity. Further, with an increase in shear-stress constant, the pressure rise enhances in pumping region. A sound knowledge on pumping of the fluid and shape of the interface may be useful to understand the gastrointestinal tract mechanism. © 2021 by Begell House, Inc.