A RETRIAL QUEUEING MODEL WITH THRESHOLDS AND PHASE TYPE RETRIAL TIMES

CHAKRAVARTHY, SRINIVAS R. The Korean Society for Computational and Applied M 2020 Journal of applied mathematics & informatics Vol.38 No.3

There is an extensive literature on retrial queueing models. While a majority of the literature on retrial queueing models focuses on the retrial times to be exponentially distributed (so as to keep the state space to be of a reasonable size), a few papers deal with nonexponential retrial times but with some additional restrictions such as constant retrial rate, only the customer at the head of the retrial queue will attempt to capture a free server, 2-state phase type distribution, and finite retrial orbit. Generally, the retrial queueing models are analyzed as level-dependent queues and hence one has to use some type of a truncation method in performing the analysis of the model. In this paper we study a retrial queueing model with threshold-type policy for orbiting customers in the context of nonexponential retrial times. Using matrix-analytic methods we analyze the model and compare with the classical retrial queueing model through a few illustrative numerical examples. We also compare numerically our threshold retrial queueing model with a previously published retrial queueing model that uses a truncation method.

A FIFTH ORDER NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS

Chakravarthy, P. Pramod,Phaneendra, K.,Reddy, Y.N. Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.3-4

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

ANALYSIS OF M/M/c RETRIAL QUEUE WITH THRESHOLDS, PH DISTRIBUTION OF RETRIAL TIMES AND UNRELIABLE SERVERS

CHAKRAVARTHY, SRINIVAS R.,OZKAR, SERIFE,SHRUTI, SHRUTI The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.1

This paper treats a retrial queue with phase type retrial times and a threshold type-policy, where each server is subject to breakdowns and repairs. Upon a server failure, the customer whose service gets interrupted will be handed over to another available server, if any; otherwise, the customer may opt to join the retrial orbit or depart from the system according to a Bernoulli trial. We analyze such a multi-server retrial queue using the recently introduced threshold-based retrial times for orbiting customers. Applying the matrix-analytic method, we carry out the steady-state analysis and report a few illustrative numerical examples.

A MULTI-SERVER RETRIAL QUEUEING MODEL WITH POISSON SIGNALS

CHAKRAVARTHY, SRINIVAS R. The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.5

Retrial queueing models have been studied extensively in the literature. These have many practical applications, especially in service sectors. However, retrial queueing models have their own limitations. Typically, analyzing such models involve level-dependent quasi-birth-and-death processes, and hence some form of a truncation or an approximate method or simulation approach is needed to study in steady-state. Secondly, in general, the customers are not served on a first-come-first-served basis. The latter is the case when a new arrival may find a free server while prior arrivals are waiting in the retrial orbit due to the servers being busy during their arrivals. In this paper, we take a different approach to the study of multi-server retrial queues in which the signals are generated in such a way to provide a reasonably fair treatment to all the customers seeking service. Further, this approach makes the study to be level-independent quasi-birth-and-death process. This approach is different from any considered in the literature. Using matrix-analytic methods we analyze MAP/M/c-type retrial queueing models along with Poisson signals in steady-state. Illustrative numerical examples including a comparison with previously published retrial queues are presented and they show marked improvements in providing a quality of service to the customers.

A FIFTH ORDER NUMERICAL METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS WITH NEGATIVE SHIFT

Chakravarthy, P. Pramod,Phaneendra, K.,Reddy, Y.N. The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

Vertical and horizontal facial proportions of Indian American men

Chakravarthy Marx Sadacharan 대한해부학회 2016 Anatomy & Cell Biology Vol.49 No.2

The importance of understanding all gender facial differences is critical in providing a successful cosmetic outcome. Men are a growing segment of the cosmetic industry. Understanding of the male face and its appropriate treatment with minimally invasive cosmetic procedures are essential. The aim was to investigate various facial ratios in Indian American men and to compare them with the Indian and Caucasian norms. Additionally, we wanted to evaluate whether these values satisfy golden and silver ratios. Direct facial anthropometric measurements were made using a digital caliper in 100 Indian American men students (18–30 years) at the American University of Antigua (AUA), Antigua. A set of facial ratios were calculated and compared with coefficients of variation (CV). Most of the facial ratios had small CV thus making them highly reliable due to reduced intra-sample variability. The upper face to face height and mandibulo upper face height indices were close to golden ratios whereas mandibulo lower face height, upper face height biocular width, and nasal indices were close to silver ratios. There was significant difference in most of the values when compared with previous studies. The present facial ratios data can be used as a reference value for Indian American men.

Calibrating Parallel Computers and Interconnects for CFD++ Applications

Sukumar Chakravarthy,Thomas Milford 한국전산유체공학회 2006 한국전산유체공학회 학술대회논문집 Vol.2006 No.5

A fifth order numerical method for singularly Perturbed differential-difference equations with negative shift

P. Pramod Chakravarthy,K. Phaneendra,Y.N. Reddy 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well. In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

Chemical Doping of TiO₂ with Nitrogen and Fluorine and Its Support Effect on Catalytic Activity of CO Oxidation

G Kalyan Chakravarthy,Sunmi Kim,Sang Hoon Kim,Jeong Young Park 한국진공학회 2013 한국진공학회 학술발표회초록집 Vol.2013 No.8

A retrial queueing model with thresholds and phase type retrial times

Srinivas R. Chakravarthy 한국전산응용수학회 2020 Journal of applied mathematics & informatics Vol.38 No.3

There is an extensive literature on retrial queueing models. While a majority of the literature on retrial queueing models focuses on the retrial times to be exponentially distributed (so as to keep the state space to be of a reasonable size), a few papers deal with nonexponential retrial times but with some additional restrictions such as constant retrial rate, only the customer at the head of the retrial queue will attempt to capture a free server, 2-state phase type distribution, and finite retrial orbit. Generally, the retrial queueing models are analyzed as level-dependent queues and hence one has to use some type of a truncation method in performing the analysis of the model. In this paper we study a retrial queueing model with threshold-type policy for orbiting customers in the context of nonexponential retrial times. Using matrix-analytic methods we analyze the model and compare with the classical retrial queueing model through a few illustrative numerical examples. We also compare numerically our threshold retrial queueing model with a previously published retrial queueing model that uses a truncation method.